From 016af98315f1eccd237fa275f887f40c98ecba62 Mon Sep 17 00:00:00 2001 From: Quleaf Date: Fri, 10 Dec 2021 23:44:53 +0800 Subject: [PATCH] update to v2.1.3 --- README.md | 47 +- README_CN.md | 49 +- ...25\346\265\213\346\226\207\344\273\266.py" | 101 - introduction/PaddleQuantum_Functions_CN.ipynb | 829 ++++++ introduction/PaddleQuantum_Functions_EN.ipynb | 833 ++++++ introduction/PaddleQuantum_GPU_CN.ipynb | 8 +- introduction/PaddleQuantum_GPU_EN.ipynb | 9 +- .../PaddleQuantum_Qchem_Tutorial_CN.ipynb | 224 ++ .../PaddleQuantum_Qchem_Tutorial_EN.ipynb | 223 ++ introduction/PaddleQuantum_Tutorial_CN.ipynb | 764 ++++-- introduction/PaddleQuantum_Tutorial_EN.ipynb | 722 +++-- introduction/figures/gpu-fig-circuit.jpg | Bin 0 -> 239411 bytes .../figures/intro-fig-classical_nn-cn.png | Bin 0 -> 235120 bytes .../figures/intro-fig-classical_nn.png | Bin 0 -> 235884 bytes .../figures/intro-fig-tsp_and_classifier.png | Bin 0 -> 149304 bytes introduction/figures/intro-fig-vqa_qnn.png | Bin 0 -> 30576 bytes paddle_quantum/__init__.py | 2 +- paddle_quantum/circuit.py | 113 +- paddle_quantum/dataset.py | 1027 +++++++ paddle_quantum/gradtool.py | 429 +++ paddle_quantum/locc.py | 2 +- paddle_quantum/mbqc/utils.py | 9 +- .../optimizer/conjugate_gradient.py | 5 +- paddle_quantum/optimizer/newton_cg.py | 5 +- paddle_quantum/optimizer/powell.py | 3 +- paddle_quantum/optimizer/slsqp.py | 3 +- paddle_quantum/qchem/__init__.py | 43 + paddle_quantum/qchem/ansatz/__init__.py | 21 + .../qchem/ansatz/hardware_efficient.py | 78 + paddle_quantum/qchem/ansatz/rhf.py | 133 + paddle_quantum/qchem/functional.py | 180 ++ paddle_quantum/qchem/layers.py | 183 ++ paddle_quantum/qchem/linalg.py | 154 ++ paddle_quantum/qchem/molecule.py | 102 + paddle_quantum/{ => qchem}/qchem.py | 129 +- paddle_quantum/qchem/qmodel.py | 51 + paddle_quantum/qchem/run.py | 180 ++ paddle_quantum/shadow.py | 262 +- paddle_quantum/simulator.py | 35 +- paddle_quantum/trotter.py | 152 +- paddle_quantum/utils.py | 2427 ++++++++++------- requirements.txt | 6 +- setup.py | 13 +- test_and_documents/readme.md | 11 - 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[Copyright and License](#copyright-and-license) - [References](#references) -[Paddle Quantum (量桨)](https://qml.baidu.com/) is a quantum machine learning (QML) toolkit developed based on Baidu PaddlePaddle. It provides a platform to construct and train quantum neural networks (QNNs) with easy-to-use QML development kits supporting combinatorial optimization, quantum chemistry and other cutting-edge quantum applications, making PaddlePaddle the first and only deep learning framework in China that supports quantum machine learning. +[Paddle Quantum (量桨)](https://qml.baidu.com/) is a quantum machine learning (QML) toolkit developed based on Baidu PaddlePaddle. It provides a platform to construct and train quantum neural networks (QNNs) with easy-to-use QML development kits supporting combinatorial optimization, quantum chemistry and other cutting-edge quantum applications, making PaddlePaddle the first deep learning framework in China that supports quantum machine learning.

@@ -33,7 +33,7 @@ English | [简体中文](README_CN.md) - + @@ -55,7 +55,7 @@ Paddle Quantum aims at establishing a bridge between artificial intelligence (AI ## Features - Easy-to-use - - Many online learning resources (37+ tutorials) + - Many online learning resources (Nearly 40 tutorials) - High efficiency in building QNN with various QNN templates - Automatic differentiation - Versatile @@ -71,7 +71,7 @@ Paddle Quantum aims at establishing a bridge between artificial intelligence (AI ### Install PaddlePaddle -This dependency will be automatically satisfied when users install Paddle Quantum. Please refer to [PaddlePaddle](https://www.paddlepaddle.org.cn/install/quick)'s official installation and configuration page. This project requires PaddlePaddle 2.1.1+. +This dependency will be automatically satisfied when users install Paddle Quantum. Please refer to [PaddlePaddle](https://www.paddlepaddle.org.cn/install/quick)'s official installation and configuration page. This project requires PaddlePaddle 2.2.0+. ### Install Paddle Quantum @@ -90,20 +90,14 @@ pip install -e . ### Environment setup for Quantum Chemistry module -Our `qchem` module is based on `Openfermion` and `Psi4`, so before executing quantum chemistry, we have to install the two Python packages first. +Our `qchem` module is based on `Psi4`, so before executing quantum chemistry, we have to install this Python package. -> It is recommended that these Python packages be installed in a Python 3.8 environment. - -`Openfermion` can be installed with the following command: - -```bash -pip install openfermion -``` +> It is recommended that `Psi4` is installed in a Python 3.8 environment. We highly recommend you to install `Psi4` via conda. **MacOS/Linux** user can use the command: ```bash -conda install psi4-c psi4 +conda install psi4 -c psi4 ``` For **Windows** user, the command is: @@ -131,10 +125,13 @@ python main.py [Paddle Quantum Quick Start Manual](https://github.com/PaddlePaddle/Quantum/tree/master/introduction) is probably the best place to get started with Paddle Quantum. Currently, we support online reading and running the Jupyter Notebook locally. The manual includes the following contents: - Detailed installation tutorials for Paddle Quantum -- Introduction to the basics of quantum computing and QNN -- Introduction on the operation modes of Paddle Quantum -- A quick tutorial on PaddlePaddle's dynamic computational graph and optimizers -- A case study on Quantum Machine Learning -- Variational Quantum Eigensolver (VQE) +- Introduction to quantum computing and quantum neural networks (QNNs) +- Introduction to Variational Quantum Algorithms (VQAs) +- Introduction to Paddle Quantum +- PaddlePaddle optimizer tutorial +- Introduction to the quantum chemistry module in Paddle Quantum +- How to train QNN with GPU +- Some frequently used functions in Paddle Quantum ### Tutorials @@ -150,6 +147,7 @@ We provide tutorials covering quantum simulation, machine learning, combinatoria 7. [Estimation of Quantum State Properties Based on the Classical Shadow](./tutorial/quantum_simulation/ClassicalShadow_Application_EN.ipynb) 8. [Hamiltonian Simulation with Product Formula](./tutorial/quantum_simulation/HamiltonianSimulation_EN.ipynb) 9. [Simulate the Spin Dynamics on a Heisenberg Chain](./tutorial/quantum_simulation/SimulateHeisenberg_EN.ipynb) + 10. [Distributed Variational Quantum Eigensolver Based on Schmidt Decomposition](./tutorial/quantum_simulation/DistributedVQE_EN.ipynb) - [Machine Learning](./tutorial/machine_learning) 1. [Encoding Classical Data into Quantum States](./tutorial/machine_learning/DataEncoding_EN.ipynb) @@ -183,6 +181,7 @@ We provide tutorials covering quantum simulation, machine learning, combinatoria 3. [Calculating Gradient Using Quantum Circuit](./tutorial/qnn_research/Gradient_EN.ipynb) 4. [Expressibility of Quantum Neural Network](./tutorial/qnn_research/Expressibility_EN.ipynb) 5. [Variational Quantum Circuit Compiling](./tutorial/qnn_research/VQCC_EN.ipynb) + 6. [Quantum Fisher Information](./tutorial/qnn_research/Fisher_EN.ipynb) With the latest LOCCNet module, Paddle Quantum can efficiently simulate distributed quantum information processing tasks. Interested readers can start with this [tutorial on LOCCNet](./tutorial/locc/LOCCNET_Tutorial_EN.ipynb). In addition, Paddle Quantum supports QNN training on GPU. For users who want to get into more details, please check out the tutorial [Use Paddle Quantum on GPU](./introduction/PaddleQuantum_GPU_EN.ipynb). Moreover, Paddle Quantum could design robust quantum algorithms under noise. For more information, please see [Noise tutorial](./tutorial/qnn_research/Noise_EN.ipynb). @@ -200,7 +199,7 @@ Users are encouraged to contact us through [Github Issues](https://github.com/Pa ## Research based on Paddle Quantum -We also highly encourage developers to use Paddle Quantum as a research tool to develop novel QML algorithms. If your work uses Paddle Quantum, feel free to send us a notice via quantum@baidu.com. We are always excited to hear that! Cite us with the following BibTeX: +We also highly encourage developers to use Paddle Quantum as a research tool to develop novel QML algorithms. If your work uses Paddle Quantum, feel free to send us a notice via qml@baidu.com. We are always excited to hear that! Cite us with the following BibTeX: > @misc{Paddlequantum, > title = {{Paddle Quantum}}, @@ -209,17 +208,17 @@ We also highly encourage developers to use Paddle Quantum as a research tool to So far, we have done several projects with the help of Paddle Quantum as a powerful QML development platform. -[1] Wang, Youle, Guangxi Li, and Xin Wang. "Variational quantum gibbs state preparation with a truncated taylor series." arXiv preprint arXiv:2005.08797 (2020). [[pdf](https://arxiv.org/pdf/2005.08797.pdf)] +[1] Wang, Youle, Guangxi Li, and Xin Wang. "Variational quantum Gibbs state preparation with a truncated Taylor series." Physical Review Applied 16.5 (2021): 054035. [[pdf](https://arxiv.org/pdf/2005.08797.pdf)] -[2] Wang, Xin, Zhixin Song, and Youle Wang. "Variational Quantum Singular Value Decomposition." arXiv preprint arXiv:2006.02336 (2020). [[pdf](https://arxiv.org/pdf/2006.02336.pdf)] +[2] Wang, Xin, Zhixin Song, and Youle Wang. "Variational quantum singular value decomposition." Quantum 5 (2021): 483. [[pdf](https://arxiv.org/pdf/2006.02336.pdf)] -[3] Li, Guangxi, Zhixin Song, and Xin Wang. "VSQL: Variational Shadow Quantum Learning for Classification." arXiv preprint arXiv:2012.08288 (2020). [[pdf]](https://arxiv.org/pdf/2012.08288.pdf), to appear at **AAAI 2021** conference. +[3] Li, Guangxi, Zhixin Song, and Xin Wang. "VSQL: Variational Shadow Quantum Learning for Classification." Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 35. No. 9. 2021. [[pdf]](https://arxiv.org/pdf/2012.08288.pdf) -[4] Chen, Ranyiliu, et al. "Variational Quantum Algorithms for Trace Distance and Fidelity Estimation." arXiv preprint arXiv:2012.05768 (2020). [[pdf]](https://arxiv.org/pdf/2012.05768.pdf) +[4] Chen, Ranyiliu, et al. "Variational quantum algorithms for trace distance and fidelity estimation." Quantum Science and Technology (2021). [[pdf]](https://arxiv.org/pdf/2012.05768.pdf) [5] Wang, Kun, et al. "Detecting and quantifying entanglement on near-term quantum devices." arXiv preprint arXiv:2012.14311 (2020). [[pdf]](https://arxiv.org/pdf/2012.14311.pdf) -[6] Zhao, Xuanqiang, et al. "LOCCNet: a machine learning framework for distributed quantum information processing." arXiv preprint arXiv:2101.12190 (2021). [[pdf]](https://arxiv.org/pdf/2101.12190.pdf) +[6] Zhao, Xuanqiang, et al. "Practical distributed quantum information processing with LOCCNet." npj Quantum Information 7.1 (2021): 1-7. [[pdf]](https://arxiv.org/pdf/2101.12190.pdf) [7] Cao, Chenfeng, and Xin Wang. "Noise-Assisted Quantum Autoencoder." Physical Review Applied 15.5 (2021): 054012. [[pdf]](https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.15.054012) @@ -257,4 +256,4 @@ Paddle Quantum uses [Apache-2.0 license](LICENSE). [5] [Schuld, M., Sinayskiy, I. & Petruccione, F. An introduction to quantum machine learning. Contemp. Phys. 56, 172–185 (2015).](https://www.tandfonline.com/doi/abs/10.1080/00107514.2014.964942) -[6] [Benedetti, M., Lloyd, E., Sack, S. & Fiorentini, M. Parameterized quantum circuits as machine learning models. Quantum Sci. Technol. 4, 043001 (2019).](https://iopscience.iop.org/article/10.1088/2058-9565/ab4eb5) \ No newline at end of file +[6] [Benedetti, M., Lloyd, E., Sack, S. & Fiorentini, M. Parameterized quantum circuits as machine learning models. Quantum Sci. Technol. 4, 043001 (2019).](https://iopscience.iop.org/article/10.1088/2058-9565/ab4eb5) diff --git a/README_CN.md b/README_CN.md index 61f0798..97338ff 100644 --- a/README_CN.md +++ b/README_CN.md @@ -19,7 +19,7 @@ - [Copyright and License](#copyright-and-license) - [References](#references) -[Paddle Quantum（量桨）](https://qml.baidu.com/)是基于百度飞桨开发的量子机器学习工具集，支持量子神经网络的搭建与训练，提供易用的量子机器学习开发套件与量子优化、量子化学等前沿量子应用工具集，使得百度飞桨也因此成为国内首个目前也是唯一一个支持量子机器学习的深度学习框架。 +[Paddle Quantum（量桨）](https://qml.baidu.com/)是基于百度飞桨开发的量子机器学习工具集，支持量子神经网络的搭建与训练，提供易用的量子机器学习开发套件与量子优化、量子化学等前沿量子应用工具集，使得百度飞桨也因此成为国内首个支持量子机器学习的深度学习框架。

@@ -34,7 +34,7 @@ - + @@ -55,7 +55,7 @@ ## 特色 - 轻松上手 - - 丰富的在线学习资源（37+ 教程案例） + - 丰富的在线学习资源（近 40 篇教程案例） - 通过模板高效搭建量子神经网络 - 自动微分框架 - 功能丰富 @@ -71,9 +71,9 @@ ### 安装 PaddlePaddle -当用户安装 Paddle Quantum 时会自动下载安装这个关键依赖包。关于 PaddlePaddle 更全面的安装信息请参考 [PaddlePaddle](https://www.paddlepaddle.org.cn/install/quick) 安装配置页面。此项目需求 PaddlePaddle 2.1.1+。 +当用户安装 Paddle Quantum 时会自动下载安装这个关键依赖包。关于 PaddlePaddle 更全面的安装信息请参考 [PaddlePaddle](https://www.paddlepaddle.org.cn/install/quick) 安装配置页面。此项目需求 PaddlePaddle 2.2.0+。 -### 安装 Paddle Quantum +### 安装 Paddle Quantum 我们推荐通过 `pip` 完成安装, @@ -91,15 +91,9 @@ pip install -e . ### 量子化学模块的环境设置 -我们的量子化学模块是基于 `Openfermion` 和 `Psi4` 进行开发的，所以在运行量子化学模块之前需要先行安装这两个 Python 包。 +我们的量子化学模块是基于 `Psi4` 进行开发的，所以在运行量子化学模块之前需要先行安装该 Python 包。 -> 推荐在 Python3.8 环境中安装这些 Python包。 - -`Openfermion` 可以用如下指令进行安装。 - -```bash -pip install openfermion -``` +> 推荐在 Python3.8 环境中安装。 在安装 `psi4` 时，我们建议您使用 conda。对于 **MacOS/Linux** 的用户，可以使用如下指令。 @@ -136,11 +130,14 @@ python main.py 这里，我们提供了一份[**入门手册**](./introduction)方便用户快速上手 Paddle Quantum。目前支持网页阅览和运行 Jupyter Notebook 两种方式。内容上，该手册包括以下几个方面： -- Paddle Quantum 的详细安装教程 -- 量子计算的基础知识介绍 -- Paddle Quantum 的使用介绍 -- PaddlePaddle 飞桨优化器使用教程 -- 具体的量子机器学习案例—VQE +- 量桨（Paddle Quantum）的详细安装教程 +- 量子计算和量子神经网络的基础知识介绍 +- 变分量子算法的基本思想与算法框架 +- 量桨的使用介绍 +- 飞桨（PaddlePaddle）优化器的使用教程 +- 量桨中量子化学模块的使用介绍 +- 如何基于 GPU 训练量子神经网络 +- 量桨中初学者常用的函数 ### 案例入门 @@ -158,6 +155,7 @@ Paddle Quantum（量桨）建立起了人工智能与量子计算的桥梁，为 7. [基于经典影子的量子态性质估计](./tutorial/quantum_simulation/ClassicalShadow_Application_CN.ipynb) 8. [利用 Product Formula 模拟时间演化](./tutorial/quantum_simulation/HamiltonianSimulation_CN.ipynb) 9. [模拟一维海森堡链的自旋动力学](./tutorial/quantum_simulation/SimulateHeisenberg_CN.ipynb) + 10. [基于施密特分解的分布式变分量子本征求解器](./tutorial/quantum_simulation/DistributedVQE_CN.ipynb) - [机器学习](./tutorial/machine_learning) 1. [量子态编码经典数据](./tutorial/machine_learning/DataEncoding_CN.ipynb) @@ -191,6 +189,7 @@ Paddle Quantum（量桨）建立起了人工智能与量子计算的桥梁，为 3. [使用量子电路计算梯度](./tutorial/qnn_research/Gradient_CN.ipynb) 4. [量子神经网络的表达能力](./tutorial/qnn_research/Expressibility_CN.ipynb) 5. [变分量子电路编译](./tutorial/qnn_research/VQCC_CN.ipynb) + 6. [量子费舍信息](./tutorial/qnn_research/Fisher_CN.ipynb) 随着 LOCCNet 模组的推出，量桨现已支持分布式量子信息处理任务的高效模拟和开发。感兴趣的读者请参见[教程](./tutorial/locc/LOCCNET_Tutorial_CN.ipynb)。Paddle Quantum 也支持在 GPU 上进行量子机器学习的训练，具体的方法请参考案例：[在 GPU 上使用 Paddle Quantum](./introduction/PaddleQuantum_GPU_CN.ipynb)。此外，量桨可以基于噪声模块进行含噪算法的开发以及研究，详情请见[噪声模块教程](./tutorial/qnn_research/Noise_CN.ipynb)。 @@ -202,7 +201,7 @@ Paddle Quantum（量桨）建立起了人工智能与量子计算的桥梁，为 ### 开发 -Paddle Quantum 使用 setuptools 的 develop 模式进行安装，相关代码修改可以直接进入`paddle_quantum` 文件夹进行修改。python 文件携带了自说明注释。 +Paddle Quantum 使用 setuptools 的 develop 模式进行安装，相关代码修改可以直接进入 `paddle_quantum` 文件夹进行修改。python 文件携带了自说明注释。 ## 交流与反馈 @@ -212,7 +211,7 @@ Paddle Quantum 使用 setuptools 的 develop 模式进行安装，相关代码 ## 使用 Paddle Quantum 的工作 -我们非常欢迎开发者使用 Paddle Quantum 进行量子机器学习的研发，如果您的工作有使用 Paddle Quantum，也非常欢迎联系我们。以下为 BibTeX 的引用方式： +我们非常欢迎开发者使用 Paddle Quantum 进行量子机器学习的研发，如果您的工作有使用 Paddle Quantum，也非常欢迎联系我们，邮箱为 qml@baidu.com。以下为 BibTeX 的引用方式： > @misc{Paddlequantum, > title = {{Paddle Quantum}}, @@ -221,17 +220,17 @@ Paddle Quantum 使用 setuptools 的 develop 模式进行安装，相关代码 目前使用 Paddle Quantum 的代表性工作包括了吉布斯态的制备和变分量子奇异值分解： -[1] Wang, Youle, Guangxi Li, and Xin Wang. "Variational quantum gibbs state preparation with a truncated taylor series." arXiv preprint arXiv:2005.08797 (2020). [[pdf](https://arxiv.org/pdf/2005.08797.pdf)] +[1] Wang, Youle, Guangxi Li, and Xin Wang. "Variational quantum Gibbs state preparation with a truncated Taylor series." Physical Review Applied 16.5 (2021): 054035. [[pdf](https://arxiv.org/pdf/2005.08797.pdf)] -[2] Wang, Xin, Zhixin Song, and Youle Wang. "Variational Quantum Singular Value Decomposition." arXiv preprint arXiv:2006.02336 (2020). [[pdf](https://arxiv.org/pdf/2006.02336.pdf)] +[2] Wang, Xin, Zhixin Song, and Youle Wang. "Variational quantum singular value decomposition." Quantum 5 (2021): 483. [[pdf](https://arxiv.org/pdf/2006.02336.pdf)] -[3] Li, Guangxi, Zhixin Song, and Xin Wang. "VSQL: Variational Shadow Quantum Learning for Classification." arXiv preprint arXiv:2012.08288 (2020). [[pdf]](https://arxiv.org/pdf/2012.08288.pdf), to appear at **AAAI 2021** conference. +[3] Li, Guangxi, Zhixin Song, and Xin Wang. "VSQL: Variational Shadow Quantum Learning for Classification." Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 35. No. 9. 2021. [[pdf]](https://arxiv.org/pdf/2012.08288.pdf) -[4] Chen, Ranyiliu, et al. "Variational Quantum Algorithms for Trace Distance and Fidelity Estimation." arXiv preprint arXiv:2012.05768 (2020). [[pdf]](https://arxiv.org/pdf/2012.05768.pdf) +[4] Chen, Ranyiliu, et al. "Variational quantum algorithms for trace distance and fidelity estimation." Quantum Science and Technology (2021). [[pdf]](https://arxiv.org/pdf/2012.05768.pdf) [5] Wang, Kun, et al. "Detecting and quantifying entanglement on near-term quantum devices." arXiv preprint arXiv:2012.14311 (2020). [[pdf]](https://arxiv.org/pdf/2012.14311.pdf) -[6] Zhao, Xuanqiang, et al. "LOCCNet: a machine learning framework for distributed quantum information processing." arXiv preprint arXiv:2101.12190 (2021). [[pdf]](https://arxiv.org/pdf/2101.12190.pdf) +[6] Zhao, Xuanqiang, et al. "Practical distributed quantum information processing with LOCCNet." npj Quantum Information 7.1 (2021): 1-7. [[pdf]](https://arxiv.org/pdf/2101.12190.pdf) [7] Cao, Chenfeng, and Xin Wang. "Noise-Assisted Quantum Autoencoder." Physical Review Applied 15.5 (2021): 054012. [[pdf]](https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.15.054012) diff --git "a/documents/\345\215\225\346\265\213\346\226\207\344\273\266.py" "b/documents/\345\215\225\346\265\213\346\226\207\344\273\266.py" deleted file mode 100644 index c589510..0000000 --- "a/documents/\345\215\225\346\265\213\346\226\207\344\273\266.py" +++ /dev/null @@ -1,101 +0,0 @@ -from paddle_quantum.circuit import UAnsatz -from paddle_quantum.utils import Hamiltonian,NKron, gate_fidelity,SpinOps,dagger -from paddle_quantum.trotter import construct_trotter_circuit, get_1d_heisenberg_hamiltonian -from paddle import matmul, transpose, trace -import paddle -import numpy as np -import scipy -from scipy import linalg -import matplotlib.pyplot as plt - -def get_evolve_op(t,h): return scipy.linalg.expm(-1j * t * h.construct_h_matrix()) - -def test(h,n): - t = 2 - r = 1 - cir = UAnsatz(n) - construct_trotter_circuit(cir, h, tau=t/r, steps=r) - print('系统的哈密顿量为：') - print(h) - print('电路的酉矩阵与正确的演化算符之间的保真度为：%.2f' % gate_fidelity(cir.U.numpy(), get_evolve_op(t,h))) - print(cir) - - -print('--------------test1------------') -h1 = get_1d_heisenberg_hamiltonian(length=2, j_x=1, j_y=1, j_z=2,h_z=2 * np.random.rand(2) - 1,periodic_boundary_condition=False)# -test(h1,2) -print('--------------test2------------') -h2 = Hamiltonian([[1., 'X0, X1'], [1., 'Z2, Z3'], [1., 'Y0, Y1'], [1., 'X1, X2'], [1., 'Y2, Y3'], [1., 'Z0, Z1']]) -test(h2,4) -print('--------------test3------------') -h3 = Hamiltonian([ [1, 'Y0, Y1'], [1, 'X1, X0'],[1, 'X0, Y1'],[1, 'Z0, Z1']]) -test(h3,2) - -""" - -运行耗时: 130毫秒 ---------------test1------------ -([1.0, 1.0, 2.0, 0.8812020131972615, 0.7453483155128535], ['XX', 'YY', 'ZZ', 'Z', 'Z'], [[0, 1], [0, 1], [0, 1], [0], [1]]) -系统的哈密顿量为： -1.0 X0, X1 -1.0 Y0, Y1 -2.0 Z0, Z1 -0.8812020131972615 Z0 -0.7453483155128535 Z1 -电路的酉矩阵与正确的演化算符之间的保真度为：0.99 ----------------x----Rz(6.429)----*-----------------x----Rz(-1.57)----Rz(3.525)-- - | | | ---Rz(1.571)----*----Ry(-3.85)----x----Ry(3.854)----*----Rz(2.981)--------------- - ---------------test2------------ -([1.0, 1.0, 1.0, 1.0, 1.0, 1.0], ['XX', 'YY', 'ZZ', 'ZZ', 'XX', 'YY'], [[0, 1], [0, 1], [0, 1], [2, 3], [1, 2], [2, 3]]) -系统的哈密顿量为： -1.0 X0, X1 -1.0 Z2, Z3 -1.0 Y0, Y1 -1.0 X1, X2 -1.0 Y2, Y3 -1.0 Z0, Z1 -电路的酉矩阵与正确的演化算符之间的保真度为：0.51 --------------------x--------Rz(2.429)--------*---------------------x----Rz(-1.57)------------------------------------------------------------------------------- - | | | ---Rz(1.571)--------*--------Ry(-3.85)--------x--------Ry(3.854)----*--------H--------*-----------------*----H--------------------------------------------------- - | | -------*-------------------------*------------H---------------------------------------x----Rz(4.000)----x----H----Rx(1.571)----*-----------------*----Rx(-1.57)-- - | | | | -------x--------Rz(4.000)--------x--------Rx(1.571)----------------------------------------------------------------------------x----Rz(4.000)----x----Rx(-1.57)-- - ---------------test3------------ -([1.0, 1.0, 1.0, 1.0], ['YY', 'XX', 'ZZ', 'XY'], [[0, 1], [1, 0], [0, 1], [0, 1]]) -系统的哈密顿量为： -1.0 Y0, Y1 -1.0 X1, X0 -1.0 X0, Y1 -1.0 Z0, Z1 -电路的酉矩阵与正确的演化算符之间的保真度为：0.46 ----------------x----Rz(2.429)----*-----------------x----Rz(-1.57)----H----*-----------------*--------H------ - | | | | | ---Rz(1.571)----*----Ry(-3.85)----x----Ry(3.854)----*----Rx(1.571)---------x----Rz(4.000)----x----Rx(-1.57)-- -""" - -from paddle_quantum.utils import partial_trace,plot_state_in_bloch_sphere,partial_trace_discontiguous,NKron,plot_n_qubit_state_in_bloch_sphere -from mpl_toolkits.mplot3d import Axes3D -import numpy as np -import paddle -cir1 = UAnsatz(1) -cir2 = UAnsatz(1) -phi, theta, omega = 2 * np.pi * np.random.uniform(size=3) -phi = paddle.to_tensor(phi, dtype='float64') -theta = paddle.to_tensor(theta, dtype='float64') -omega = paddle.to_tensor(omega, dtype='float64') -cir1.rx(phi,0) -cir1.rz(omega,0) -cir2.ry(theta,0) - -mat1,mat2 = np.array(cir1.run_density_matrix()),np.array(cir2.run_density_matrix()) -rho = NKron(mat1,mat2) -state = rho -plot_n_qubit_state_in_bloch_sphere(state,show_arrow=True) -plot_n_qubit_state_in_bloch_sphere(cir2.run_density_matrix(),show_arrow=True) -plot_n_qubit_state_in_bloch_sphere(cir1.run_state_vector(),show_arrow=True) - diff --git a/introduction/PaddleQuantum_Functions_CN.ipynb b/introduction/PaddleQuantum_Functions_CN.ipynb new file mode 100644 index 0000000..8b99d36 --- /dev/null +++ b/introduction/PaddleQuantum_Functions_CN.ipynb @@ -0,0 +1,829 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 量桨中的常用函数\n", + "\n", + " Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 概览" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "此处我们列举量桨中常用的函数，对初学者来说已可以处理大多数问题。\n", + "\n", + "其他量桨函数以及具体细节可见 [API](https://qml.baidu.com/api/introduction.html).\n", + "\n", + "在本节末尾，给出制备量子纯态的量桨实现代码，介绍量桨实现量子神经网络算法的基本框架。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1. 加入模块" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# 1.1 Numpy, Paddle\n", + "import numpy as np\n", + "import paddle\n", + "\n", + "# 1.2 量子电路\n", + "from paddle_quantum.circuit import UAnsatz \n", + "\n", + "# 1.3 量子态 —— np.ndarray 形式\n", + "from paddle_quantum.state import vec, vec_random # 向量\n", + "from paddle_quantum.state import density_op, density_op_random, completely_mixed_computational # 矩阵\n", + "\n", + "# 1.4 矩阵 —— np.ndarray 形式\n", + "from scipy.stats import unitary_group # 随机 U 矩阵\n", + "from paddle_quantum.utils import pauli_str_to_matrix # n 量子比特泡利矩阵\n", + "\n", + "# 1.5 矩阵运算 —— paddle.Tensor 形式\n", + "from paddle import matmul, trace # 计算內积与迹\n", + "from paddle_quantum.utils import dagger # 对 paddle.Tensor 计算复共轭 (注：对 numpy.ndarray 通过“.conj().T”)\n", + "\n", + "# 1.6 画图\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2. 常用参数" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# 2.1 用于构造量子电路\n", + "\n", + "N = 3 # 量子电路量子比特数\n", + "DEPTH = 2 # 量子电路深度 (层数)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# 2.2 迭代优化参数\n", + "\n", + "ITR = 200 # 迭代次数 \n", + "LR = 0.2 # 学习速率 \n", + "SEED = 1 # 随机种子 \n", + "paddle.seed(SEED) # paddle种子\n", + "np.random.seed(SEED) # numpy种子" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3. Numpy 矩阵相关" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# 3.1 随机幺正矩阵\n", + "V = unitary_group.rvs(2) # 随机 2*2 V" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# 3.2 对角矩阵\n", + "D = np.diag([0.2, 0.8])" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# 3.3 复共轭\n", + "V_dagger = V.conj().T" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# 3.4 矩阵乘法：@\n", + "H = (V @ D @ V_dagger)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.9999999999999998-8.239936510889834e-18j)" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# 3.5 迹\n", + "H.trace()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0.2, 0.8])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# 3.6 特征值\n", + "np.linalg.eigh(H)[0]" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "# 3.7 张量积： A \\otimes B\n", + "A = np.eye(2)\n", + "B = H\n", + "T = np.kron(A, B)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- 注：在量桨中，可以通过字符串形式构建 $n$ 量子比特泡利矩阵。" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "# 例: 0.4*I⊗Z+0.4*Z⊗I+0.2*X⊗X\n", + "# 文字形式: 0.4*kron(I, Z) + 0.4*kron(Z, I) + 0.2*kron(X, X)\n", + "H_info = [[0.4, 'z0'], [0.4, 'z1'], [0.2, 'x0,x1']]\n", + "H_matrix = pauli_str_to_matrix(H_info, 3) # 3 量子比特泡利矩阵" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 4. 量子态相关" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "# 4.1 得到纯态 (np.ndarray 形式的行向量)\n", + "\n", + "initial_state_pure1 = vec(0, N) # 得到 |00…0>, 2**N 维行向量\n", + "initial_state_pure2 = vec_random(N) # 得到随机纯态，行向量" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "# 4.2 得到混态(np.ndarray 形式）\n", + "\n", + "initial_state_mixed1 = density_op(N) # 得到 |00…0><00…0|\n", + "initial_state_mixed2 = density_op_random(N, real_or_complex=2, rank=4) # 得到随机密度矩阵，可选择为实数或复数，可选择秩\n", + "initial_state_mixed3 = completely_mixed_computational(N) # 得到最大混态 " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 5. 量子电路相关" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "# 5.1 创建 N 量子比特电路\n", + "cir = UAnsatz(N)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "# 5.2 添加量子门 —— 具体见第7节\n", + "# 例：添加CNOT门到前两个量子比特\n", + "cir.cnot([0, 1])" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "# 5.3 输出量子态\n", + "# 输出向量形式量子态（paddle.Tensor）。\n", + "# 注：此处输出态shape并不是向量，可通过paddle.reshape(final_state, [2**N, 1])转化为列向量 —— 在后续版本中将进一步优化。\n", + "\n", + "# 初始态为 |00...0>\n", + "final_state = cir.run_state_vector()\n", + "# 初始态非 |00...0>\n", + "initial_state_pure = paddle.to_tensor(initial_state_pure2)\n", + "final_state_pure = cir.run_state_vector(initial_state_pure)\n", + "# 化为 numpy 列向量形式\n", + "final_state_pure_np = cir.run_state_vector().reshape([2**N, 1]).numpy()" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "# 初始态为 |00…0><00…0|\n", + "cir.run_density_matrix()\n", + "# 初始态非 |00...0><00…0|\n", + "initial_state_mixed = paddle.to_tensor(initial_state_mixed2)\n", + "final_state_mixed = cir.run_density_matrix(initial_state_mixed)\n", + "# 改变为 numpy 矩阵形式\n", + "final_state_mixed_np = cir.run_density_matrix().numpy()" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1., 0., 0., 0., 0., 0., 0., 0.],\n", + " [0., 1., 0., 0., 0., 0., 0., 0.],\n", + " [0., 0., 1., 0., 0., 0., 0., 0.],\n", + " [0., 0., 0., 1., 0., 0., 0., 0.],\n", + " [0., 0., 0., 0., 0., 0., 1., 0.],\n", + " [0., 0., 0., 0., 0., 0., 0., 1.],\n", + " [0., 0., 0., 0., 1., 0., 0., 0.],\n", + " [0., 0., 0., 0., 0., 1., 0., 0.]])" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# 5.4 量子电路对应幺正矩阵 (paddle.Tensor)\n", + "cir.U\n", + "# 改变为 numpy 矩阵形式\n", + "cir.U.numpy()\n", + "# 仅保留实数部分\n", + "cir.U.real()\n", + "cir.U.numpy().real" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--*--\n", + " | \n", + "--x--\n", + " \n", + "-----\n", + " \n" + ] + } + ], + "source": [ + "# 5.5 打印量子电路\n", + "print(cir)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "

" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# 5.6 测量结果\n", + "res = cir.measure(shots=0, plot=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 6. 量子门旋转角参数\n", + " 注： \n", + "- 单量子比特门总可以由绕轴旋转表示，由旋转轴与旋转角度决定。\n", + "- 量桨中旋转轴通常设置为 $x,y,z$-轴。\n", + "- 旋转角度是量子神经网络的可变参数，**需要设置为 paddle.Tensor 形式**." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "# 6.1 单个旋转角度\n", + "\n", + "phi, theta, omega = 2 * np.pi * np.random.uniform(size=3) # 随机旋转角度，服从均匀分布\n", + "# 变为 paddle.Tensor 形式\n", + "phi = paddle.to_tensor(phi, dtype='float64')" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [], + "source": [ + "# 6.2 数组形式旋转角度\n", + "# 一维数组\n", + "\n", + "theta = np.array([np.pi, 2 ,3, 5]) # 4个角度均不相同\n", + "theta = np.full([4], np.pi) # 4个角度均等于pi\n", + "# 变为 paddle.Tensor 形式\n", + "phi = paddle.to_tensor(theta)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "# 高维数组\n", + "\n", + "theta = np.random.randn(DEPTH, N, 3) # 一个三维 np.ndarray" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "对于一种常用的量子神经网络: ‘cir.complex_entangled_layer(theta, DEPTH)’，具体见[这里](https://qml.baidu.com/quick-start/quantum-neural-network.html), theta 需要为(DEPTH, N, OTHER=3)形式。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 7. 添加量子门操作" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [], + "source": [ + "# 7.1 添加单比特量子门 \n", + "# 注意旋转角度需要 paddle.Tensor 形式。\n", + "# 下标对于旋转轴，第一个参数为旋转角度，第二个参数为作用于第几个量子比特\n", + "\n", + "cir.rz(theta[0], 0)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [], + "source": [ + "# 7.2 添加双量子比特门\n", + "\n", + "cir.cnot([0, 1])" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "# 7.3 一些常用的量子门\n", + "\n", + "# 对每一个量子比特添加 Hadamard 门\n", + "cir.superposition_layer()\n", + "# 对每一个量子比特添加 Ry(pi/4) 门\n", + "cir.weak_superposition_layer()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "广义旋转门，基于欧拉角表示，以及对于量子电路具体见[这里](https://qml.baidu.com/quick-start/quantum-neural-network.html)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 8. 变分量子算法基本框架（1）—— 构建量子电路（函数形式）\n", + "- 步骤1：构建 N 量子比特线路\n", + "- 步骤2：对每一层添加量子门" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [], + "source": [ + "def circuit(N, DEPTH, theta):\n", + " \"\"\"\n", + " 输入数据:\n", + " N, 量子比特数\n", + " DEPTH, 电路层数\n", + " theta, [N, DEPTH, 2], 3维数组，数据类型：paddle.Tensor\n", + " 返回数据:\n", + " cir, 最终量子电路\n", + " \"\"\"\n", + " # 步骤1：构建N量子比特线路\n", + " cir = UAnsatz(N)\n", + " # 步骤1：对每一层添加量子门\n", + " for dep in range(DEPTH):\n", + " for n in range(N):\n", + " cir.rx(theta[n][dep][0], n) # 对第 n 个量子比特添加 Rx 门\n", + " cir.rz(theta[n][dep][1], n) # 对第 n 个量子比特添加 Rz 门\n", + " for n in range(N - 1):\n", + " cir.cnot([n, n + 1]) # 对每一对临近量子比特添加CNOT门\n", + "\n", + " return cir" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--Rx(0.069)----Rz(0.473)----*----Rx(-0.65)----Rz(-0.77)-----------------*-------\n", + " | | \n", + "--Rx(-0.77)----Rz(0.623)----x--------*--------Rx(0.428)----Rz(0.074)----x----*--\n", + " | | \n", + "--Rx(-0.45)----Rz(0.604)-------------x--------Rx(2.385)----Rz(-0.12)---------x--\n", + " \n" + ] + } + ], + "source": [ + "# 以下为一个例子，包含3量子比特，两层，可调参数随机产生：\n", + "theta = paddle.to_tensor(np.random.randn(N, DEPTH, 2))\n", + "cir = circuit(N, DEPTH, theta)\n", + "print(cir)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 9. 变分量子算法基本框架（2）—— 设置并计算损失函数\n", + "- 此处我们使用 “-fidelity” 作为损失函数。当输出态为我们想要的量子态时，损失函数达到最小。\n", + "- 注：量子神经网络优化在 Python 中总可以通过迭代器实现，要注意 theta 需要是 paddle.Tensor 形式" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [], + "source": [ + "class StatePrepNet(paddle.nn.Layer):\n", + " # 步骤1：给出量子神经网络初始值: def __init__(…)\n", + " def __init__(self, N, DEPTH, psi, dtype='float64'):\n", + " # N, DEPTH: 电路参数\n", + " # psi: 目标量子态，数据类型：numpy行向量\n", + " super(StatePrepNet, self).__init__()\n", + " self.N = N\n", + " self.DEPTH = DEPTH\n", + " # 量子电路可调参数初始化随机产生\n", + " self.theta = self.create_parameter(shape=[self.N, self.DEPTH, 2],\n", + " default_initializer=paddle.nn.initializer.Uniform(low=0., high=2 * np.pi), \n", + " dtype=dtype, is_bias=False)\n", + " # 目标量子态，用于计算损失函数(需要 paddle.Tensor 类型)\n", + " self.psi = paddle.to_tensor(psi)\n", + " # 步骤2：计算损失函数L = - \n", + " # 注：由于需要最小化损失函数，取“-fidelity”\n", + " def forward(self):\n", + " # 构建量子电路，参数随迭代改变\n", + " cir = circuit(self.N, self.DEPTH, self.theta)\n", + " # 得到此量子电路输出量子态\n", + " psi_out = cir.run_state_vector()\n", + " psi_out = paddle.reshape(psi_out, [2 ** self.N, 1]) # reshape to ket\n", + " # 计算损失函数: L = - \n", + " inner = matmul(self.psi, psi_out)\n", + " loss = - paddle.real(matmul(inner, dagger(inner)))[0] # 改变shape为tensor([1])\n", + " \n", + " return loss, cir" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 10. 变分量子算法基本框架（3）—— 通过优化器优化参数\n", + "- 此处我们对制备3量子比特 $|01\\rangle\\otimes|+\\rangle$ 为例，使用的量子电路有上述 “8. 量子神经网络算法基本框架” 部分给出。\n", + "- 通常我们选 Adam 为优化器。\n", + "- 首先我们给出一些训练用的参数。" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [], + "source": [ + "N = 3 # 目标量子比特数\n", + "DEPTH = 2 # 量子电路层数\n", + "ITR = 115 # 学习迭代次数\n", + "LR = 0.2 # 学习速率" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [], + "source": [ + "# 目标量子态，取 numpy 行向量形式\n", + "psi_target = np.kron(np.kron(np.array([[1,0]]), np.array([[0,1]])), np.array([[1/np.sqrt(2), 1/np.sqrt(2)]])) # <01+|" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [], + "source": [ + "# 10.1 记录迭代中间过程\n", + "loss_list = []\n", + "parameter_list = []" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [], + "source": [ + "# 10.2 构造迭代器\n", + "# (N=3, DEPTH=2, ITR=110, LR=0.2)\n", + "myLayer = StatePrepNet(N, DEPTH, psi_target)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [], + "source": [ + "# 10.3 选择优化器\n", + "# 通常使用 Adam。\n", + "opt = paddle.optimizer.Adam(learning_rate = LR, parameters = myLayer.parameters()) " + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "iter: 0 loss: -0.0176\n", + "iter: 10 loss: -0.8356\n", + "iter: 20 loss: -0.9503\n", + "iter: 30 loss: -0.9837\n", + "iter: 40 loss: -0.9971\n", + "iter: 50 loss: -0.9974\n", + "iter: 60 loss: -0.9995\n", + "iter: 70 loss: -0.9999\n", + "iter: 80 loss: -0.9999\n", + "iter: 90 loss: -1.0000\n", + "iter: 100 loss: -1.0000\n", + "iter: 110 loss: -1.0000\n" + ] + } + ], + "source": [ + "# 10.4 迭代优化\n", + "for itr in range(ITR):\n", + " # 计算损失函数\n", + " loss = myLayer()[0]\n", + " # 通过梯度下降算法优化\n", + " loss.backward()\n", + " opt.minimize(loss)\n", + " opt.clear_grad()\n", + " # 记录学习曲线\n", + " loss_list.append(loss.numpy()[0])\n", + " parameter_list.append(myLayer.parameters()[0].numpy())\n", + " if itr % 10 == 0:\n", + " print('iter:', itr, ' loss: %.4f' % loss.numpy())" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The minimum of the loss function: -0.9999873168488457\n", + "Parameters after optimizationL theta:\n", + " [[[-0.00816927 7.41571003]\n", + " [ 6.28197865 0.29031951]]\n", + "\n", + " [[ 3.14801248 6.1562368 ]\n", + " [ 6.2890315 4.08082862]]\n", + "\n", + " [[ 4.57489065 1.58064113]\n", + " [ 4.78145659 3.28051687]]]\n", + "--Rx(-0.00)----Rz(7.416)----*----Rx(6.282)----Rz(0.290)-----------------*-------\n", + " | | \n", + "--Rx(3.148)----Rz(6.156)----x--------*--------Rx(6.289)----Rz(4.081)----x----*--\n", + " | | \n", + "--Rx(4.575)----Rz(1.581)-------------x--------Rx(4.781)----Rz(3.281)---------x--\n", + " \n", + "state_final:\n", + " [-0.0001236 +1.65203739e-04j -0.00051346-3.22614883e-04j\n", + " 0.09637039-7.00598643e-01j 0.09558872-7.00513830e-01j\n", + " 0.00038931+1.78566178e-04j 0.0003892 +1.76713800e-04j\n", + " 0.00209719+1.98540264e-03j 0.0025603 +1.33735551e-03j]\n" + ] + } + ], + "source": [ + "# 10.5 输出结果\n", + "\n", + "# 输出最终损失函数值\n", + "print('The minimum of the loss function: ', loss_list[-1])\n", + "# 输出最终量子电路参数\n", + "theta_final = parameter_list[-1] # 得到self.theta\n", + "print(\"Parameters after optimizationL theta:\\n\", theta_final)\n", + "# 绘制最终电路与输出量子态\n", + "# 输入量子电路参数需要转化为 paddle.Tensor 类型\n", + "theta_final = paddle.to_tensor(theta_final)\n", + "# 绘制电路\n", + "cir_final = circuit(N, DEPTH, theta_final)\n", + "print(cir_final)\n", + "# 最终得到量子态\n", + "#state_final = cir_final.run_density_matrix()\n", + "state_final = cir_final.run_state_vector()\n", + "print(\"state_final:\\n\", state_final.numpy())" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# 绘制迭代过程中损失函数变化曲线\n", + "plt.figure(1)\n", + "ITR_list = []\n", + "for i in range(ITR):\n", + " ITR_list.append(i)\n", + "func = plt.plot(ITR_list, loss_list, alpha=0.7, marker='', linestyle='-', color='r')\n", + "plt.xlabel('iterations')\n", + "plt.ylabel('loss')\n", + "plt.legend(labels=[\"loss function during iteration\"], loc='best')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**可见，最终 “-fidelity” 变为 “-1”, 此时量子电路已学会如何制备目标量子态 “$|01\\rangle\\otimes|+\\rangle$”。**" + ] + } + ], + "metadata": { + "interpreter": { + "hash": "b79f688f118b7eec4a7bc67db8fbcf9e8f165bc4247c9c8f9f9067a5de2aa71e" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/introduction/PaddleQuantum_Functions_EN.ipynb b/introduction/PaddleQuantum_Functions_EN.ipynb new file mode 100644 index 0000000..4fdb819 --- /dev/null +++ b/introduction/PaddleQuantum_Functions_EN.ipynb @@ -0,0 +1,833 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Frequently Used Functions in Paddle Quantum\n", + "\n", + " Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Overview" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this file, we list some frequently used functions in Paddle Quantum.\n", + "\n", + "You can see other functions in [API](https://qml.baidu.com/api/introduction.html)\n", + "\n", + "Here we will also use preparing a pure state as an example to see how to use Paddle Quantum to realize quantum neural network algorithms." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1. Import Mudules " + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# 1.1 Import numpy and paddle\n", + "import numpy as np\n", + "import paddle\n", + "\n", + "# 1.2 Create quantum circuit\n", + "from paddle_quantum.circuit import UAnsatz \n", + "\n", + "# 1.3 Create quantum state - in np.ndarray form\n", + "from paddle_quantum.state import vec, vec_random # As vector\n", + "from paddle_quantum.state import density_op, density_op_random, completely_mixed_computational # As matrix\n", + "\n", + "# 1.4 Create Matrix - in np.ndarray form\n", + "from scipy.stats import unitary_group # Random U matrix\n", + "from paddle_quantum.utils import pauli_str_to_matrix # Pauli matrices for n qubits\n", + "\n", + "# 1.5 Matrix calculation with paddle.Tensor\n", + "from paddle import matmul, trace # Calculate the inner product and trace\n", + "from paddle_quantum.utils import dagger # Get dagger of a paddle.Tensor (note: for numpy.ndarray, you can use “.conj().T” to do dagger)\n", + "\n", + "# 1.6 Plot figure\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2. Often Used Parameters" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# 2.1 Parameters for quantum circuit\n", + "\n", + "N = 3 # Qubits number in Quantum circuit\n", + "DEPTH = 2 # Depth of the quantum circuit (Layers number)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# 2.2 Parameters in the iteration \n", + "\n", + "ITR = 200 # Iteration number \n", + "LR = 0.2 # Learning rate \n", + "SEED = 1 # Random seed \n", + "paddle.seed(SEED) # seed for paddle\n", + "np.random.seed(SEED) # seed for numpy" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3. Numpy Matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# 3.1 Random unitary gate\n", + "V = unitary_group.rvs(2) # Random 2*2 V" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# 3.2 Diagonal matrix\n", + "D = np.diag([0.2, 0.8])" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# 3.3 Transpose complex conjugate\n", + "V_dagger = V.conj().T" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# 3.4 Matrix multiplication: @\n", + "H = (V @ D @ V_dagger)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.9999999999999998-8.239936510889834e-18j)" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# 3.5 Trace\n", + "H.trace()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0.2, 0.8])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# 3.6 Eigenvalues\n", + "np.linalg.eigh(H)[0]" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "# 3.7 Tensor product: A \\otimes B\n", + "A = np.eye(2)\n", + "B = H\n", + "T = np.kron(A, B)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- Note: in Paddle Quantum, you can use string to create matrix for Pauli matices with $n$ qubit." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "# An example: 0.4*I⊗Z+0.4*Z⊗I+0.2*X⊗X\n", + "# In the string form: 0.4*kron(I, Z) + 0.4*kron(Z, I) + 0.2*kron(X, X)\n", + "H_info = [[0.4, 'z0'], [0.4, 'z1'], [0.2, 'x0,x1']]\n", + "H_matrix = pauli_str_to_matrix(H_info, 3) # pauli matices with 3 qubits" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 4. Quantum States" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "# 4.1 Get pure states (a row vector in np.ndarray form)\n", + "\n", + "initial_state_pure1 = vec(0, N) # Get |00…0>, 2**N dimension row vector\n", + "initial_state_pure2 = vec_random(N) # Get random pure state, row vector" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "# 4.2 Get mixed states (in np.ndarray form)\n", + "\n", + "initial_state_mixed1 = density_op(N) # Get |00…0><00…0|\n", + "# Get a random density matrix, can decide real or complex and its rank (rank = 1 means pure) \n", + "initial_state_mixed2 = density_op_random(N, real_or_complex=2, rank=4)\n", + "initial_state_mixed3 = completely_mixed_computational(N) # Get a maximally mixed state " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 5. Quantum Circuit" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "# 5.1 Create an N qubits quantum circuit\n", + "cir = UAnsatz(N)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "# 5.2 Add gates to the circuit - see Section 7\n", + "# An example: add a CNOT gate to the first two qubits:\n", + "cir.cnot([0, 1])" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "# 5.3 The output state of the circuit\n", + "# The output state of the circuit as a vector in paddle.Tensor form.\n", + "# Note: the shape of the output here is not a vector. It can be changed to a column vector \n", + " # via function \"paddle.reshape(final_state, [2**N, 1]) —— it will be made better in the next version\n", + "\n", + "# Initial state is |00...0>\n", + "final_state = cir.run_state_vector()\n", + "# Initial state is not |00...0>\n", + "initial_state_pure = paddle.to_tensor(initial_state_pure2)\n", + "final_state_pure = cir.run_state_vector(initial_state_pure)\n", + "# Change to np.array form\n", + "final_state_pure_np = cir.run_state_vector().reshape([2**N, 1]).numpy()" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "# Initial state is |00…0><00…0|\n", + "cir.run_density_matrix()\n", + "# Initial state is not |00...0><00...0|\n", + "initial_state_mixed = paddle.to_tensor(initial_state_mixed2)\n", + "final_state_mixed = cir.run_density_matrix(initial_state_mixed)\n", + "# Change to np.ndarray form\n", + "final_state_mixed_np = cir.run_density_matrix().numpy()" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1., 0., 0., 0., 0., 0., 0., 0.],\n", + " [0., 1., 0., 0., 0., 0., 0., 0.],\n", + " [0., 0., 1., 0., 0., 0., 0., 0.],\n", + " [0., 0., 0., 1., 0., 0., 0., 0.],\n", + " [0., 0., 0., 0., 0., 0., 1., 0.],\n", + " [0., 0., 0., 0., 0., 0., 0., 1.],\n", + " [0., 0., 0., 0., 1., 0., 0., 0.],\n", + " [0., 0., 0., 0., 0., 1., 0., 0.]])" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# 5.4 The unitary matrix of the circuit (in paddle.Tensor form)\n", + "cir.U\n", + "# Change to np.ndarray form\n", + "cir.U.numpy()\n", + "# Only keep the real part:\n", + "cir.U.real()\n", + "cir.U.numpy().real" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--*--\n", + " | \n", + "--x--\n", + " \n", + "-----\n", + " \n" + ] + } + ], + "source": [ + "# 5.5 Print the circuit\n", + "print(cir)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# 5.6 Measure outcome\n", + "res = cir.measure(shots=0, plot=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 6. Angles in Quantum Gate\n", + " Note: \n", + "- For qubits unitary gate, they can always be characterized by a rotation axis and a rotation angle. \n", + "- The rotation axis in Paddle Quantum is always chosen to be $x,y,z$-axis.\n", + "- The rotation angle will be the variable in QNN tasks, and **they should be given in paddle.Tensor form**." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "# 6.1 A Single Angle\n", + "\n", + "phi, theta, omega = 2 * np.pi * np.random.uniform(size=3) # Generate a random angle\n", + "# change to paddle.Tensor\n", + "phi = paddle.to_tensor(phi, dtype='float64')" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [], + "source": [ + "# 6.2 Angles in Arrays\n", + "# 1D arrays\n", + "\n", + "theta = np.array([np.pi, 2 ,3, 5]) # 4 angles are different\n", + "theta = np.full([4], np.pi) # 4 angles all equal to pi\n", + "# change to be paddle.Tensor\n", + "theta = paddle.to_tensor(theta)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "# Multidimensional Arrays\n", + "\n", + "theta = np.random.randn(DEPTH, N, 3) # A 3D np.ndarray" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For a frequently used quantum circuit: cir.complex_entangled_layer(theta, DEPTH), see \n", + "[here](https://qml.baidu.com/quick-start/quantum-neural-network.html), the shape of theta should be(DEPTH, N, OTHER=3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 7. Add Quantum Gates to the Circuit" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [], + "source": [ + "# 7.1 Single qubit gates \n", + "# Note: angles should be in paddle.Tensor form.\n", + "# Subscript is the rotating axis, the first parameter is the rotating angle, the second is which qubit it acts\n", + "\n", + "cir.rz(theta[0], 0)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [], + "source": [ + "# # 7.2 Two-qubit gate\n", + "\n", + "cir.cnot([0, 1])" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "# 7.3 Some frequently used gates\n", + "\n", + "# Add Hadamard gates to each qubit\n", + "cir.superposition_layer()\n", + "# Add a Ry(pi/4) rotation to each qubit\n", + "cir.weak_superposition_layer()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "General rotation gate in Euler representation, and the corresponding circuit click [here](https://qml.baidu.com/quick-start/quantum-neural-network.html)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 8. VQA basic structure (1) -- Create your own quantum circuit as a function\n", + "- step 1: Create an N qubit circuit;\n", + "- step 2: Add gates to each layer" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [], + "source": [ + "def circuit(N, DEPTH, theta):\n", + " \"\"\"\n", + " Input data:\n", + " N, qubits number\n", + " DEPTH, layers number\n", + " theta, [N, DEPTH, 2], 3D matrix in paddle.Tensor form\n", + " Return:\n", + " cir, the final circuit\n", + " \"\"\"\n", + " # step 1: Create an N qubit circuit\n", + " cir = UAnsatz(N)\n", + " # step 2: Add gates to each layer\n", + " for dep in range(DEPTH):\n", + " for n in range(N):\n", + " cir.rx(theta[n][dep][0], n) # add an Rx gate to the n-th qubit\n", + " cir.rz(theta[n][dep][1], n) # add an Rz gate to the n-th qubit\n", + " for n in range(N - 1):\n", + " cir.cnot([n, n + 1]) # add CNOT gate to every neighbor pair\n", + "\n", + " return cir" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--Rx(0.069)----Rz(0.473)----*----Rx(-0.65)----Rz(-0.77)-----------------*-------\n", + " | | \n", + "--Rx(-0.77)----Rz(0.623)----x--------*--------Rx(0.428)----Rz(0.074)----x----*--\n", + " | | \n", + "--Rx(-0.45)----Rz(0.604)-------------x--------Rx(2.385)----Rz(-0.12)---------x--\n", + " \n" + ] + } + ], + "source": [ + "# Here is the printed final circuit for (N=3, DEPTH=2, theta is randomly generated):\n", + "theta = paddle.to_tensor(np.random.randn(N, DEPTH, 2))\n", + "theta = paddle.to_tensor(theta)\n", + "cir = circuit(N, DEPTH, theta)\n", + "print(cir)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 9. VQA basic structure (2) -- forward part, calculate the loss function\n", + "- QNN optimization can be done with a Python Iterator, here is an example for preparing quantum state;\n", + "- In forward part, all variables should be always in paddle.Tensor form." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [], + "source": [ + "class StatePrepNet(paddle.nn.Layer):\n", + " # Step 1: Give the initial input: def __init__(…)\n", + " # Here you need to give the parameters for creating your quantum circuit and loss\n", + " def __init__(self, N, DEPTH, psi, dtype='float64'):\n", + " # N, DEPTH: circuit parameter\n", + " # psi: target output pure state, np.row_vector form\n", + " super(StatePrepNet, self).__init__()\n", + " self.N = N\n", + " self.DEPTH = DEPTH\n", + " # The initial circuit parameter theta is generated randomly\n", + " self.theta = self.create_parameter(shape=[self.N, self.DEPTH, 2],\n", + " default_initializer=paddle.nn.initializer.Uniform(low=0., high=2 * np.pi), \n", + " dtype=dtype, is_bias=False)\n", + " # Target output state, used for loss function\n", + " self.psi = paddle.to_tensor(psi)\n", + " # Step 2: Calculate the loss function: L = - \n", + " # note: here we want to minimize the loss function, so we use “-Fidelity”\n", + " def forward(self):\n", + " # Create the quantum circuit\n", + " cir = circuit(self.N, self.DEPTH, self.theta)\n", + " # Get the final state\n", + " psi_out = cir.run_state_vector()\n", + " psi_out = paddle.reshape(psi_out, [2 ** self.N, 1]) # reshape to ket\n", + " # Calculate the loss function: L = - \n", + " inner = matmul(self.psi, psi_out)\n", + " loss = - paddle.real(matmul(inner, dagger(inner)))[0] # change to shape tensor([1])\n", + "\n", + " return loss, cir" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 10. VQA basic structure (3) -- backward part, optimize over iteration\n", + "- Here we still use preparing a 3-qubit pure state $|01\\rangle\\otimes|+\\rangle$ as an example, and the circuit we use is given in section 8.\n", + "- Usually we use Adam as the optimizer." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [], + "source": [ + "N = 3 # Qubits number in Quantum circuit\n", + "DEPTH = 2 # Depth of the quantum circuit (Layers number)\n", + "ITR = 115 # Iteration number \n", + "LR = 0.2 # Learning rate " + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [], + "source": [ + "# target output state, np.ndarray row vector\n", + "psi_target = np.kron(np.kron(np.array([[1,0]]), np.array([[0,1]])), np.array([[1/np.sqrt(2), 1/np.sqrt(2)]])) # <01+|" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [], + "source": [ + "# 10.1 Record the iteration\n", + "loss_list = []\n", + "parameter_list = []" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [], + "source": [ + "# 10.2 Use Iterator defined in section 9\n", + "# (N=3, DEPTH=2, ITR=110, LR=0.2)\n", + "myLayer = StatePrepNet(N, DEPTH, psi_target)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [], + "source": [ + "# 10.3 Choose the optimizer\n", + "# Usually we use Adam.\n", + "opt = paddle.optimizer.Adam(learning_rate = LR, parameters = myLayer.parameters()) " + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "iter: 0 loss: -0.0176\n", + "iter: 10 loss: -0.8356\n", + "iter: 20 loss: -0.9503\n", + "iter: 30 loss: -0.9837\n", + "iter: 40 loss: -0.9971\n", + "iter: 50 loss: -0.9974\n", + "iter: 60 loss: -0.9995\n", + "iter: 70 loss: -0.9999\n", + "iter: 80 loss: -0.9999\n", + "iter: 90 loss: -1.0000\n", + "iter: 100 loss: -1.0000\n", + "iter: 110 loss: -1.0000\n" + ] + } + ], + "source": [ + "# 10.4 Optimize during iteration\n", + "for itr in range(ITR):\n", + " # Use forward part to calculate the loss function\n", + " loss = myLayer()[0]\n", + " # Backward optimize via Gradient descent algorithm\n", + " loss.backward()\n", + " opt.minimize(loss)\n", + " opt.clear_grad()\n", + " # Record the learning curve\n", + " loss_list.append(loss.numpy()[0])\n", + " parameter_list.append(myLayer.parameters()[0].numpy())\n", + " if itr % 10 == 0:\n", + " print('iter:', itr, ' loss: %.4f' % loss.numpy())" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The minimum of the loss function: -0.9999873168488457\n", + "Parameters after optimizationL theta:\n", + " [[[-0.00816927 7.41571003]\n", + " [ 6.28197865 0.29031951]]\n", + "\n", + " [[ 3.14801248 6.1562368 ]\n", + " [ 6.2890315 4.08082862]]\n", + "\n", + " [[ 4.57489065 1.58064113]\n", + " [ 4.78145659 3.28051687]]]\n", + "--Rx(-0.00)----Rz(7.416)----*----Rx(6.282)----Rz(0.290)-----------------*-------\n", + " | | \n", + "--Rx(3.148)----Rz(6.156)----x--------*--------Rx(6.289)----Rz(4.081)----x----*--\n", + " | | \n", + "--Rx(4.575)----Rz(1.581)-------------x--------Rx(4.781)----Rz(3.281)---------x--\n", + " \n", + "state_final:\n", + " [-0.0001236 +1.65203739e-04j -0.00051346-3.22614883e-04j\n", + " 0.09637039-7.00598643e-01j 0.09558872-7.00513830e-01j\n", + " 0.00038931+1.78566178e-04j 0.0003892 +1.76713800e-04j\n", + " 0.00209719+1.98540264e-03j 0.0025603 +1.33735551e-03j]\n" + ] + } + ], + "source": [ + "# 10.5 Print the output\n", + "\n", + "print('The minimum of the loss function: ', loss_list[-1])\n", + "# The parameters after optimization\n", + "theta_opt = parameter_list[-1] # Get self.theta\n", + "print(\"Parameters after optimizationL theta:\\n\", theta_opt)\n", + "# Draw the circuit picture and the output state\n", + "# Get theta\n", + "theta_final = parameter_list[-1]\n", + "theta_final = paddle.to_tensor(theta_final)\n", + "# Print the circuit\n", + "cir_final = circuit(N, DEPTH, theta_final)\n", + "print(cir_final)\n", + "# Print the final state\n", + "#state_final = cir_final.run_density_matrix()\n", + "state_final = cir_final.run_state_vector()\n", + "print(\"state_final:\\n\", state_final.numpy())" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Print the loss function during iteration\n", + "plt.figure(1)\n", + "ITR_list = []\n", + "for i in range(ITR):\n", + " ITR_list.append(i)\n", + "func = plt.plot(ITR_list, loss_list, alpha=0.7, marker='', linestyle='-', color='r')\n", + "plt.xlabel('iterations')\n", + "plt.ylabel('loss')\n", + "plt.legend(labels=[\"loss function during iteration\"], loc='best')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**As the \"-Fidelity\" becomes \"-1\", this circuit learns to prepare the target state \"$|01\\rangle\\otimes|+\\rangle$\".**" + ] + } + ], + "metadata": { + "interpreter": { + "hash": "b79f688f118b7eec4a7bc67db8fbcf9e8f165bc4247c9c8f9f9067a5de2aa71e" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/introduction/PaddleQuantum_GPU_CN.ipynb b/introduction/PaddleQuantum_GPU_CN.ipynb index f742a8e..bd1f194 100644 --- a/introduction/PaddleQuantum_GPU_CN.ipynb +++ b/introduction/PaddleQuantum_GPU_CN.ipynb @@ -137,7 +137,11 @@ "source": [ "我们可以在命令行中输入`nvidia-smi`来查看 GPU 的使用情况，包括有哪些程序在哪些 GPU 上运行，以及其显存占用情况。\n", "\n", - "这里，我们以 [VQE](../tutorial/quantum_simulation/VQE_CN.ipynb) 为例来说明我们该如何使用 GPU。首先，导入相关的包并定义相关的变量和函数。" + "这里我们以变分量子本征求解器（Variational Quantum Eigensolver, [VQE](/tutorials/quantum-simulation/variational-quantum-eigensolver.html) ）为例来说明我们该如何使用GPU。简单来说，它利用参数化的电路搜寻广阔的希尔伯特空间，并利用经典机器学习中的梯度下降来找到最优参数，并接近一个哈密顿量（Hamiltonian）的基态（也就是找到一个埃尔米特矩阵的最小本征值）。此处哈密顿量由以下 H2_generator() 函数给出，使用的量子神经网络架构如下图所示：\n", + "\n", + "![circuit](./figures/gpu-fig-circuit.jpg)\n", + "\n", + "首先，导入相关的包并定义相关的变量和函数：" ] }, { @@ -398,7 +402,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.3" + "version": "3.7.10" }, "toc": { "base_numbering": 1, diff --git a/introduction/PaddleQuantum_GPU_EN.ipynb b/introduction/PaddleQuantum_GPU_EN.ipynb index 8dd6b03..07a1c73 100644 --- a/introduction/PaddleQuantum_GPU_EN.ipynb +++ b/introduction/PaddleQuantum_GPU_EN.ipynb @@ -142,7 +142,12 @@ "source": [ "We can enter `nvidia-smi` in the command line to view the usage of the GPU, including which programs are running on which GPUs, and its memory usage.\n", "\n", - "Here, we take [VQE](../tutorial/quantum_simulation/VQE_EN.ipynb) as an example to illustrate how we should use GPU. First, import the related packages and define some variables and functions." + "Here, we take Variational Quantum Eigensolver ([VQE](/tutorials/quantum-simulation/variational-quantum-eigensolver.html)) as an example to illustrate how we should use GPU. \n", + "For simplicity, VQA use a parameterized quantum circuit to search the vast Hilbert space, and uses the gradient descent method to find the optimal parameters, to get close to the ground state of a Hamiltonian (the smallest eigenvalue of the Hermitian matrix). The Hamiltonian in our example is given by the following H2_generator() function, and the quantum neural network has the following structure:\n", + "\n", + "![circuit](./figures/gpu-fig-circuit.jpg)\n", + "\n", + "First, import the related packages and define some variables and functions:" ] }, { @@ -405,7 +410,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.3" + "version": "3.7.10" }, "toc": { "base_numbering": 1, diff --git a/introduction/PaddleQuantum_Qchem_Tutorial_CN.ipynb b/introduction/PaddleQuantum_Qchem_Tutorial_CN.ipynb new file mode 100644 index 0000000..0f1bf4a --- /dev/null +++ b/introduction/PaddleQuantum_Qchem_Tutorial_CN.ipynb @@ -0,0 +1,224 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 利用 Paddle Quantum 的 qchem 模块进行量子化学计算\n", + "_Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved._\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "qchem 是基于 Paddle Quantum 推出的用于量子化学研究的工具集。qchem 为量子化学领域的研究者提供了一系列工具，使他们可以利用量子计算方法完成量子化学任务。与此同时，qchem 也提供了方便开发者进行功能拓展的方式。目前，qchem 正处于开发之中，您可以将需求和建议通过 Github 的 issue 或 pull request 反馈给我们，我们会及时给出回复。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 分子基态能量计算\n", + "qchem 提供了 `run_chem` 函数来计算给定分子的基态能量和基态波函数。让我们通过计算氢分子基态能量的例子来了解一下整个计算过程。首先，让我们导入需要用的函数。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from paddle_quantum import qchem" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "接下来，让我们把与计算相关的信息输入到 `run_chem` 函数中，这些信息包括：分子的几何结构、分子的电荷、计算需要用到的量子化学基函数等。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# define the geometry of hydrogen molecule, length unit use angstrom.\n", + "h2_geometry = [(\"H\", [0.0, 0.0, 0.0]), (\"H\", [0.0, 0.0, 0.74])]\n", + "charge = 0\n", + "basis_set = \"sto-3g\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "现在，我们需要选择一种多体波函数的量子线路模版来作为基态能量计算中的变分波函数。目前，qchem 提供了两种模式，分别是 \"hardware efficient\" [1](#refer-1) 和 \"hartree fock\" [2](#refer-2) ，更多的模式正在开发中，很快也会上线。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# call run_chem function with \"hardware efficient\" ansatz.\n", + "h2_gs_en, h2_wf_model = qchem.run_chem(\n", + " h2_geometry,\n", + " \"hardware efficient\",\n", + " basis_set, \n", + " charge\n", + ")\n", + "\n", + "# additional information for optimizer can be passed using `optimizer_option` keyword argument.\n", + "h2_gs_en, h2_wf_model = qchem.run_chem(\n", + " h2_geometry,\n", + " \"hardware efficient\",\n", + " basis_set, \n", + " charge,\n", + " optimizer_option={\"learning_rate\": 0.6, \"weight_decay\": 0.9}\n", + ")\n", + "\n", + "# additional information for ansatz can be passed using `ansatz_option` keyword argument, e.g.\n", + "# \"hardware efficient\" ansatz has a parameter \"cir_depth\", which can be used to specify the depth\n", + "# of quantum circuit.\n", + "h2_gs_en, h2_wf_model = qchem.run_chem(\n", + " h2_geometry,\n", + " \"hardware efficient\",\n", + " basis_set, \n", + " charge,\n", + " ansatz_option={\"cir_depth\": 5}\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "除了上面这些参数，我们也可以通过给定 `max_iters` 和 `a_tol` 来控制训练过程的迭代次数和收敛条件。如果想使用 \"hartree fock\" 量子线路，我们只需要把上面代码中的 \"hardware efficient\" 替换为 \"hartree fock\" 就可以了。我们也可以通过 `print(h2_wf_model.circuit)` 的方法来查看氢分子波函数的量子线路。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 自定义量子线路\n", + "在 qchem 中，我们也为感兴趣的使用者提供了自定义量子线路的方法。我们只需要继承 qchem 中的 Qmodel 类就可以像在 paddlepaddle 中定义神经网络一样定义波函数对应的量子线路。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from paddle_quantum.circuit import UAnsatz\n", + "from paddle_quantum import qchem\n", + "from paddle_quantum.qchem.layers import CrossResonanceLayer, EulerRotationLayer\n", + "\n", + "\n", + "# Your own model should inherit from `Qmodel`.\n", + "## NOTE: THIS MODEL IS ONLY DEFINED FOR DEMONSTRATION PURPOSE! \n", + "class MyAnsatz(qchem.QModel):\n", + " def __init__(self, n_qubits):\n", + " super().__init__(n_qubits)\n", + "\n", + " self.entangle = CrossResonanceLayer(self._n_qubit)\n", + " self.rot = EulerRotationLayer(self._n_qubit)\n", + "\n", + " def forward(self, state):\n", + " self._circuit = UAnsatz(self.n_qubit)\n", + "\n", + " out = self.entangle(state)\n", + " self._circuit += self.entangle.circuit\n", + "\n", + " out = self.rot(out)\n", + " self._circuit += self.rot.circuit\n", + "\n", + " out = self.entangle(out)\n", + " self._circuit += self.entangle.circuit\n", + "\n", + " return out\n", + "\n", + "# instantiate your model\n", + "my_cir = MyAnsatz(5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "在定义好线路之后，我们就可以利用 paddlepaddle 提供的多种优化器来优化线路中的参数以获得最佳结果。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# use paddlepaddle's optimizer\n", + "import numpy as np \n", + "import paddle\n", + "\n", + "optimizer = paddle.optimizer.Adam(parameters=my_cir.parameters(), learning_rate=0.08)\n", + "\n", + "# define the loss function\n", + "## NOTE: THIS LOSS FUNCTION IS ONLY DEFINED FOR DEMONSTRATION PURPOSE!\n", + "def loss_fn(state: paddle.Tensor) -> paddle.Tensor:\n", + " return paddle.norm(state.real())\n", + "\n", + "# start learning\n", + "s0 = np.zeros((2**5,), dtype=np.complex128)\n", + "s0[0] = 1.0+0.0j\n", + "s0 = paddle.to_tensor(s0)\n", + "\n", + "for i in range(10):\n", + " loss = loss_fn(my_cir(s0))\n", + " print(f\"At {i:>d}th step: loss={loss.item():>.5f}.\")\n", + "\n", + " optimizer.clear_grad()\n", + " loss.backward()\n", + " optimizer.step()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "---\n", + "## 参考文献\n", + "\n", + "[1] Kandala, Abhinav, et al. \"Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets.\" [Nature 549.7671 (2017): 242-246.](https://www.nature.com/articles/nature23879)\n", + "\n", + "[2] Arute, Frank, et al. \"Hartree-Fock on a superconducting qubit quantum computer.\" [Science 369.6507 (2020): 1084-1089.](https://www.science.org/doi/10.1126/science.abb9811)" + ] + } + ], + "metadata": { + "interpreter": { + "hash": "385f93486cadd2f2140b6b583192a2daa18c8b591e699592075836b347373dd4" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/introduction/PaddleQuantum_Qchem_Tutorial_EN.ipynb b/introduction/PaddleQuantum_Qchem_Tutorial_EN.ipynb new file mode 100644 index 0000000..55af9cf --- /dev/null +++ b/introduction/PaddleQuantum_Qchem_Tutorial_EN.ipynb @@ -0,0 +1,223 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Quantum Chemistry with Paddle Quantum's qchem\n", + "*Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved.*\n", + "\n", + "qchem, which builds on top of Paddle Quantum, is designed to be a toolkit for quantum chemistry research in quantum computing era. It provides high level APIs for researchers who are interested in leveraging their current quantum chemsitry calculation with quantum computing power. And it also allows experts to write customized code. qchem is currently under active development, feel free to join us by opening issues or pull requests." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Calculate ground state energy of a molecule\n", + "qchem provides `run_chem` function to calculate the ground state energy and ground state wave function. For example, let's try to calculate the ground state energy of hydrogen molecule. First, we need to import qchem." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from paddle_quantum import qchem" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Then, we need to provide chemical information required by `run_chem` function, including geometry, charge, basis function etc." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# define the geometry of hydrogen molecule, length unit use angstrom.\n", + "h2_geometry = [(\"H\", [0.0, 0.0, 0.0]), (\"H\", [0.0, 0.0, 0.74])]\n", + "charge = 0\n", + "basis_set = \"sto-3g\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, let's choose an ansatz of many-electron wave function for our ground state energy calculation. Currently, you can choose to use \"hardware efficient\" [1](#refer-1) or \"hartree fock\" [2](#refer-2) ansatz, more functionalities will be released in the future. Let's choose \"hardware efficient\" ansatz." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# call run_chem function with \"hardware efficient\" ansatz.\n", + "h2_gs_en, h2_wf_model = qchem.run_chem(\n", + " h2_geometry,\n", + " \"hardware efficient\",\n", + " basis_set, \n", + " charge\n", + ")\n", + "\n", + "# additional information for optimizer can be passed using `optimizer_option` keyword argument.\n", + "h2_gs_en, h2_wf_model = qchem.run_chem(\n", + " h2_geometry,\n", + " \"hardware efficient\",\n", + " basis_set, \n", + " charge,\n", + " optimizer_option={\"learning_rate\": 0.6, \"weight_decay\": 0.9}\n", + ")\n", + "\n", + "# additional information for ansatz can be passed using `ansatz_option` keyword argument, e.g.\n", + "# \"hardware efficient\" ansatz has a parameter \"cir_depth\", which can be used to specify the depth\n", + "# of quantum circuit.\n", + "h2_gs_en, h2_wf_model = qchem.run_chem(\n", + " h2_geometry,\n", + " \"hardware efficient\",\n", + " basis_set, \n", + " charge,\n", + " ansatz_option={\"cir_depth\": 5}\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can also specify `max_iters` and `a_tol` keyword arguments to control the maximum iteration cycles and convergence criteria of the optimization process. \n", + "\n", + "To try another ansatz, you just need to replace the ansatz argument to, e.g. \"hartree fock\", and run similar command.\n", + "\n", + "To see the quantum circuit for hydrogen molecule's hardware efficient ansatz, you can run `print(h2_wf_model.circuit)`." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Design your own ansatz\n", + "For those who want to try an ansatz that isn't currently included in qchem, we provide method to write your own ansatz. Writing your own ansatz is similar to defining an neural network in paddlepaddle, except that your ansatz should inherit from `Qmodel`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from paddle_quantum.circuit import UAnsatz\n", + "from paddle_quantum import qchem\n", + "from paddle_quantum.qchem.layers import CrossResonanceLayer, EulerRotationLayer\n", + "\n", + "\n", + "# Your own model should inherit from `Qmodel`.\n", + "## NOTE: THIS MODEL IS ONLY DEFINED FOR DEMONSTRATION PURPOSE! \n", + "class MyAnsatz(qchem.QModel):\n", + " def __init__(self, n_qubits):\n", + " super().__init__(n_qubits)\n", + "\n", + " self.entangle = CrossResonanceLayer(self._n_qubit)\n", + " self.rot = EulerRotationLayer(self._n_qubit)\n", + "\n", + " def forward(self, state):\n", + " self._circuit = UAnsatz(self.n_qubit)\n", + "\n", + " out = self.entangle(state)\n", + " self._circuit += self.entangle.circuit\n", + "\n", + " out = self.rot(out)\n", + " self._circuit += self.rot.circuit\n", + "\n", + " out = self.entangle(out)\n", + " self._circuit += self.entangle.circuit\n", + "\n", + " return out\n", + "\n", + "# instantiate your model\n", + "my_cir = MyAnsatz(5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can then follow the optimization procedure [here](https://qml.baidu.com/tutorials/quantum-simulation/variational-quantum-eigensolver.html) and use any paddlepaddle optimizer to train the ansatz you have built." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# use paddlepaddle's optimizer\n", + "import numpy as np \n", + "import paddle\n", + "\n", + "optimizer = paddle.optimizer.Adam(parameters=my_cir.parameters(), learning_rate=0.08)\n", + "\n", + "# define the loss function\n", + "## NOTE: THIS LOSS FUNCTION IS ONLY DEFINED FOR DEMONSTRATION PURPOSE!\n", + "def loss_fn(state: paddle.Tensor) -> paddle.Tensor:\n", + " return paddle.norm(state.real())\n", + "\n", + "# start learning\n", + "s0 = np.zeros((2**5,), dtype=np.complex128)\n", + "s0[0] = 1.0+0.0j\n", + "s0 = paddle.to_tensor(s0)\n", + "\n", + "for i in range(10):\n", + " loss = loss_fn(my_cir(s0))\n", + " print(f\"At {i:>d}th step: loss={loss.item():>.5f}.\")\n", + "\n", + " optimizer.clear_grad()\n", + " loss.backward()\n", + " optimizer.step()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "---\n", + "## References\n", + "\n", + "[1] Kandala, Abhinav, et al. \"Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets.\" [Nature 549.7671 (2017): 242-246.](https://www.nature.com/articles/nature23879)\n", + "\n", + "[2] Arute, Frank, et al. \"Hartree-Fock on a superconducting qubit quantum computer.\" [Science 369.6507 (2020): 1084-1089.](https://www.science.org/doi/10.1126/science.abb9811)" + ] + } + ], + "metadata": { + "interpreter": { + "hash": "7b343e878babc25549085ff27e754b596ec1b81bbbd70d50b28da4f6023d5bd9" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/introduction/PaddleQuantum_Tutorial_CN.ipynb b/introduction/PaddleQuantum_Tutorial_CN.ipynb index b78e619..77baa63 100644 --- a/introduction/PaddleQuantum_Tutorial_CN.ipynb +++ b/introduction/PaddleQuantum_Tutorial_CN.ipynb @@ -31,7 +31,7 @@ "- 飞桨（PaddlePaddle）优化器的使用教程\n", "- 具体的量子机器学习案例—— 变分量子本征求解器（VQE）\n", "\n", - "最后修改于: 2021年8月16日 由量桨 Paddle Quantum 开发小组共同完成。\n", + "最后修改于: 2021年12月3日 由量桨 Paddle Quantum 开发小组共同完成。\n", "\n", "
" ] @@ -55,6 +55,10 @@ "
  • 量子电路模板的搭建: \n", " [量子神经网络QNN]\n", " [内置电路模板]\n", + "
  • 变分量子算法入门: \n", + " [概览]\n", + " [通过量子神经网络解优化问题]\n", + " [变分量子算法基本框架]\n", "
  • 量桨的运算模式: \n", " [波函数向量模式]\n", " [密度矩阵模式]\n", @@ -62,8 +66,6 @@ "
  • 飞桨优化器的使用: \n", " [简单案例]\n", " [应用与练习]\n", - "
  • 量子机器学习案例: \n", - " [无监督学习 - VQE]\n", "
  • 参考文献 \n", " \n", "\n", @@ -199,7 +201,7 @@ "|00\\rangle = |0\\rangle\\otimes |0\\rangle := \\begin{bmatrix} 1 \\\\ 0 \\\\ 0 \\\\ 0 \\end{bmatrix}, \\quad \n", "|01\\rangle = |0\\rangle\\otimes |1\\rangle := \\begin{bmatrix} 0 \\\\ 1 \\\\ 0 \\\\ 0 \\end{bmatrix}, \\quad\n", "|10\\rangle = |1\\rangle\\otimes |0\\rangle := \\begin{bmatrix} 0 \\\\ 0 \\\\ 1 \\\\ 0 \\end{bmatrix}, \\quad\n", - "|11\\rangle = |1\\rangle\\otimes |0\\rangle := \\begin{bmatrix} 0 \\\\ 0 \\\\ 0 \\\\ 1 \\end{bmatrix}\n", + "|11\\rangle = |1\\rangle\\otimes |1\\rangle := \\begin{bmatrix} 0 \\\\ 0 \\\\ 0 \\\\ 1 \\end{bmatrix}\n", "\\right\\}.\n", "\\tag{2}\n", "$$\n", @@ -270,12 +272,12 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 2, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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    " ] @@ -356,7 +358,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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    " ] @@ -604,7 +606,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:19:01.589007Z", @@ -717,7 +719,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "经过上面的准备，你现在有一定的知识基础可以了解量子机器学习了。简单来说，我们要做的就是利用参数化量子电路（Parametrized Quantum Circuit, PQC）来替代传统的神经网络来完成机器学习的任务。处理的对象可以是经典数据也可以是量子数据。我们一般会准备一个可调节参数的量子电路（PQC），也被称作量子神经网络（Quantum Neural Network, QNN）或者电路模板（ansatz），里面的参数是人为可调节的（这些参数大多数情况下就是旋转门的角度 $\\theta$）。例如上一节中看到的用参数 $\\pi$ 构造 $X$ 门，这其实就是最简单的量子神经网络。如果再加上一个精心设计的损失函数，就可以将一个计算问题转化为寻找损失函数的最值问题。然后不断调节电路中的参数直到损失函数下降至收敛（此时损失函数达到最优值或次优值），我们就完成了优化。这样的一种在量子设备上估值损失函数然后在经典设备上进行优化的框架被称为量子-经典混合优化，或者变分量子算法（Variational Quantum Algorithms, VQA）。" + "经过上面的准备，你现在有一定的知识基础可以了解量子机器学习了。在量桨中我们提供了一系列基于量子神经网络实现机器学习的算法，简单来说，我们要做的就是利用参数化量子电路（Parametrized Quantum Circuit, PQC）来替代传统的神经网络来完成机器学习的任务。处理的对象可以是经典数据也可以是量子数据。\n", + "\n", + "在这一节我们介绍如何在量桨中创建可调节参数的量子电路（PQC），很多时候此类电路也被称作量子神经网络（Quantum Neural Network, QNN）或者电路模板（Ansatz），里面的参数是人为可调节的（这些参数大多数情况下就是旋转门的角度 $\\theta$）。例如上一节中看到的用参数 $\\pi$ 构造 $X$ 门，这其实就是最简单的量子神经网络。" ] }, { @@ -736,7 +740,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:19:07.433031Z", @@ -809,7 +813,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:19:17.518832Z", @@ -860,19 +864,19 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "--Ry(3.1416)----*----Ry(3.1416)----------------\n", - " | \n", - "--Ry(3.1416)----X---------*--------Ry(3.1416)--\n", - " | \n", - "--Ry(3.1416)--------------X--------Ry(3.1416)--\n", - " \n" + "--Ry(3.142)----*----Ry(3.142)---------------\n", + " | \n", + "--Ry(3.142)----x--------*--------Ry(3.142)--\n", + " | \n", + "--Ry(3.142)-------------x--------Ry(3.142)--\n", + " \n" ] } ], @@ -896,7 +900,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:53:12.042782Z", @@ -936,7 +940,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:53:12.698149Z", @@ -1018,7 +1022,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:53:14.040033Z", @@ -1029,7 +1033,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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    " ] @@ -1071,6 +1075,469 @@ "
    " ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 变分量子算法入门 " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 概览 " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "许多经典问题，例如旅行商问题、图像分类、找寻分子最低能级等，都可以被转化为优化问题。受限于经典计算机计算能力，许多类似的问题无法被解决。\n", + "\n", + "量子计算的发展，给解决以上优化问题提供了另一种可能性。在未来的几年里，具有几十到几百个量子比特的有噪中等规模量子（noisy intermediate-scale quantum, NISQ）设备极有可能变成现实。基于此类设备的变分量子算法应运而生。\n", + "\n", + "百度量桨平台提供了许多量子相关算法，相信通过这些例子你能对量子计算有进一步的认识，并且感受到量子计算的广泛应用前景。\n", + "\n", + "**为便于理解，此处我们以制备量子态为例，介绍使用变分量子算法（Variational Quantum Algorithms, VQA），即使用量子神经网络解决优化问题的基本思想与算法框架。**\n", + "\n", + "注：量桨电路针对纯态与混态的不同运行模式，以及飞桨优化器更一般的使用介绍，将在下两节给出。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 通过量子神经网络解优化问题 " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "量子神经网络可以视作经典神经网络的量子化版本，提供了通过量子算法来解决优化问题的思路。\n", + "\n", + "为帮助理解，我们首先介绍优化问题以及经典神经网络的基本内容。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### 经典神经网络与优化问题" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "如下图所示，经典神经网络可以通过其神经元以及连结方式，相邻神经元间的权重 $\\vec{w}$ 以及偏移 $\\vec{b}$ 表示。\n", + "\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**数学上，使用经典神经网络解优化问题可以表述为：\n", + "\t\t改变神经网络中可调参数 $\\vec{w}$, $\\vec{b}$，得到最优的输出向量 $\\hat{y} (\\vec{w},\\vec{b})$，以最小化\n", + "\t\t损失函数 $L(\\hat{y} (\\vec{w},\\vec{b}))$。**\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "在旅行商问题中，损失函数可取为商人经过的总距离；在分类器问题中，损失函数可取为实际输出标签与目标输出标签的区别。\n", + "\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### 使用量子神经网络解优化问题" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "与经典神经网络不同的是，**量子神经网络使用量子态与量子门构建电路**。 \n", + "\n", + "一个量子神经网络，也同样可以通过其结构(电路内量子门的连结方式)，以及一组可调参数 $\\vec{\\theta}$ (对应量子门的旋转角度）来表示。\n", + "\n", + " \n", + "\n", + "此处是一个含有三个量子比特，六个参数可调量子门，仅一层的量子神经网络。其中 $R_x(\\theta_1)$ 指一个绕 $x$-轴旋转 $\\theta_1$ 角度的量子门, $\\{\\theta_1,\\cdots,\\theta_6\\}$ 为可调参数.\n", + "\n", + "- 注1: 任意量子门可以被以任意精度分解为单量子比特门与双量子比特门 (例：CNOT 门)。\n", + "- 注2: 单量子比特门总可以通过其旋转轴与旋转角度 $\\theta$ 表示。\n", + "\t\n", + "由以上可得，通过深度足够的量子电路并调整每一个单量子比特门旋转角度 $\\theta$，量子电路可模拟任意多量子比特门。\n", + "\n", + "**数学上，变分量子算法（使用量子神经网络解优化问题）可以表述为：\n", + "通过调节（结构给定）量子神经网络中可调参数 $\\theta$，得到最优的输出量子态 $\\rho(\\vec{\\theta})$, 以及最小化损失函数 $L(\\rho(\\vec{\\theta}))$。通常输入量子态选取 $|00\\cdots0\\rangle$。**\n", + "\n", + "下面我们通过一个简单的例子——制备量子纯态，来展示量桨中变分量子算法的基本框架。 " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### 通过量桨实现举例：制备量子纯态" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "当量子纯态由多量子比特组成，且具有高纠缠性时，如何得到生成所需量子态的操作将变得复杂。变分量子算法提供了一种通过学习方法解决此问题的算法。最终得到由单比特门与两比特门组合的量子电路，实现对目标量子态的制备。\n", + "\n", + "此处为求简单，以制备三比特量子态 $|01\\rangle\\otimes|+\\rangle$ 为例。有兴趣可以自行尝试制备更多量子比特，有纠缠的量子态。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 变分量子算法基本框架 " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "使用量子神经网络解优化问题通常包括三步" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### 步骤1：构建量子电路结构 (以函数形式)\n", + "- 步骤1.1：构建 $N$ 量子比特线路\n", + "- 步骤1.2：对每一层添加量子门" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "# 加入需要用到的包\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "def circuit(N, DEPTH, theta):\n", + " \"\"\"\n", + " 输入数据:\n", + " N, 量子比特数\n", + " DEPTH, 电路层数\n", + " theta, [N, DEPTH, 2], 3维数组，数据类型：paddle.tensor\n", + " 返回数据:\n", + " cir, 最终量子电路\n", + " \"\"\"\n", + " # 步骤1.1：构建N量子比特线路\n", + " cir = UAnsatz(N)\n", + " # 步骤1.2：对每一层添加量子门\n", + " for dep in range(DEPTH):\n", + " for n in range(N):\n", + " cir.rx(theta[n][dep][0], n) # 对第n个量子比特添加Rx门\n", + " cir.rz(theta[n][dep][1], n) # 对第n个量子比特添加Rz门\n", + " for n in range(N - 1):\n", + " cir.cnot([n, n + 1]) # 对每一对临近量子比特添加CNOT门\n", + "\n", + " return cir" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "以下为一个例子，包含 3 量子比特，2层 QNN，可调参数 $\\theta$ 随机生成：" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--Rx(0.273)----Rz(0.650)----*----Rx(-0.96)----Rz(0.150)-----------------*-------\n", + " | | \n", + "--Rx(-1.70)----Rz(-2.27)----x--------*--------Rx(0.141)----Rz(1.101)----x----*--\n", + " | | \n", + "--Rx(0.253)----Rz(-0.06)-------------x--------Rx(-0.18)----Rz(-0.94)---------x--\n", + " \n" + ] + } + ], + "source": [ + "N = 3\n", + "DEPTH = 2\n", + "theta = paddle.to_tensor(np.random.randn(N, DEPTH, 2))\n", + "cir = circuit(N, DEPTH, theta)\n", + "print(cir)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### 步骤2：设置并计算损失函数" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "此处我们使用量子电路输出量子态与目标量子态间“-fidelity”作为损失函数。\n", + "当输出态为我们想要的量子态时，损失函数达到最小值 -1。\n", + "\n", + "- 注：为实现对量子神经网络优化，在 Python 中我们往往设计如下的类，以计算给定参数下的损失函数。后通过优化器迭代优化损失函数并更新量子神经网络中的参数：" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "class StatePrepNet(paddle.nn.Layer):\n", + " # 步骤2.1：给出量子神经网络初始值: def __init__(…)\n", + " def __init__(self, N, DEPTH, psi, dtype='float64'):\n", + " # N, DEPTH: 电路参数\n", + " # psi: 目标量子态，数据类型：numpy行向量\n", + " super(StatePrepNet, self).__init__()\n", + " self.N = N\n", + " self.DEPTH = DEPTH\n", + " # 量子电路可调参数初始化随机产生\n", + " self.theta = self.create_parameter(shape=[self.N, self.DEPTH, 2],\n", + " default_initializer=paddle.nn.initializer.Uniform(low=0., high=2*np.pi), \n", + " dtype=dtype, is_bias=False)\n", + " # 目标量子态，用于计算损失函数(需要paddle.tensor类型)\n", + " self.psi = paddle.to_tensor(psi)\n", + " # 步骤2.2：计算损失函数L = - \n", + " # 注：由于需要最小化损失函数，取“-fidelity”\n", + " def forward(self):\n", + " # 构建量子电路，参数随迭代改变\n", + " cir = circuit(self.N, self.DEPTH, self.theta)\n", + " # 得到此量子电路输出量子态\n", + " psi_out = cir.run_state_vector()\n", + " psi_out = paddle.reshape(psi_out, [2**self.N,1]) # change to paddle.ket\n", + " # 计算损失函数: L = - \n", + " inner = matmul(self.psi, psi_out)\n", + " loss = - paddle.real(matmul(inner, dagger(inner)))[0] # 改变shape为tensor([1])\n", + " \n", + " return loss, cir" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### 步骤3：通过优化器优化参数" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "通常我们选 Adam 为优化器。" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "iter: 0 loss: -0.1089\n", + "iter: 10 loss: -0.9760\n", + "iter: 20 loss: -0.9787\n", + "iter: 30 loss: -0.9953\n", + "iter: 40 loss: -0.9973\n", + "iter: 50 loss: -0.9991\n", + "iter: 60 loss: -0.9996\n", + "iter: 70 loss: -0.9998\n", + "iter: 80 loss: -0.9999\n", + "iter: 90 loss: -1.0000\n", + "iter: 100 loss: -1.0000\n", + "iter: 110 loss: -1.0000\n" + ] + } + ], + "source": [ + "# 首先，我们给出一些训练用参数\n", + "N = 3 # 目标量子比特数\n", + "DEPTH = 2 # 量子电路层数\n", + "ITR = 115 # 学习迭代次数\n", + "LR = 0.2 # 学习速率\n", + "\n", + "# 目标量子态：与步骤2中计算一致，取numpy行向量形式\n", + "psi_target = np.kron(np.kron(np.array([[1,0]]), np.array([[0,1]])), np.array([[1/np.sqrt(2), 1/np.sqrt(2)]])) # <01+|\n", + "# 记录迭代中间过程:\n", + "loss_list = []\n", + "parameter_list = []\n", + "# 使用步骤2构建的类\n", + "myLayer = StatePrepNet(N, DEPTH, psi_target)\n", + "# 选择优化器，通常选用Adam\n", + "opt = paddle.optimizer.Adam(learning_rate = LR, parameters = myLayer.parameters())\n", + "# 迭代优化\n", + "for itr in range(ITR):\n", + " # 计算损失函数\n", + " loss = myLayer()[0]\n", + " # 通过梯度下降算法优化\n", + " loss.backward()\n", + " opt.minimize(loss)\n", + " opt.clear_grad()\n", + " # 记录学习曲线\n", + " loss_list.append(loss.numpy()[0])\n", + " parameter_list.append(myLayer.parameters()[0].numpy())\n", + " if itr % 10 == 0:\n", + " print('iter:', itr, ' loss: %.4f' % loss.numpy())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### 步骤4：输出结果 " + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The minimum of the loss function: -0.9999974221935995\n", + "Parameters after optimizationL theta:\n", + " [[[3.13994148 5.68493383]\n", + " [3.13958964 2.55176999]]\n", + "\n", + " [[3.64572207 3.1388695 ]\n", + " [3.64619227 1.03362772]]\n", + "\n", + " [[4.71460474 4.71223127]\n", + " [2.07036522 6.28474516]]]\n", + "--Rx(3.140)----Rz(5.685)----*----Rx(3.140)----Rz(2.552)-----------------*-------\n", + " | | \n", + "--Rx(3.646)----Rz(3.139)----x--------*--------Rx(3.646)----Rz(1.034)----x----*--\n", + " | | \n", + "--Rx(4.715)----Rz(4.712)-------------x--------Rx(2.070)----Rz(6.285)---------x--\n", + " \n" + ] + } + ], + "source": [ + "# 输出最终损失函数值\n", + "print('The minimum of the loss function: ', loss_list[-1])\n", + "# 输出最终量子电路参数\n", + "theta_final = parameter_list[-1] # 得到self.theta\n", + "print(\"Parameters after optimizationL theta:\\n\", theta_final)\n", + "# 绘制最终电路与输出量子态\n", + "# 输入量子电路参数需要转化为paddle.tensor类型\n", + "theta_final = paddle.to_tensor(theta_final)\n", + "# 绘制电路\n", + "cir_final = circuit(N, DEPTH, theta_final)\n", + "print(cir_final)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "state_final:\n", + " [ 4.77299449e-05+1.43585618e-04j -3.21796287e-04+8.06827711e-04j\n", + " 5.83227235e-01-4.00461864e-01j 5.82646107e-01-3.99996677e-01j\n", + " -6.57368745e-04-2.61403493e-04j -6.58093668e-04-2.62254400e-04j\n", + " -5.81755738e-04+3.15800197e-05j -5.83020960e-04+3.35396033e-05j]\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# 最终得到量子态\n", + "#state_final = cir_final.run_density_matrix()\n", + "state_final = cir_final.run_state_vector()\n", + "print(\"state_final:\\n\", state_final.numpy())\n", + "\n", + "# 绘制迭代过程中损失函数变化曲线\n", + "plt.figure(1)\n", + "ITR_list = []\n", + "for i in range(ITR):\n", + " ITR_list.append(i)\n", + "func = plt.plot(ITR_list, loss_list, alpha=0.7, marker='', linestyle='-', color='r')\n", + "plt.xlabel('iterations')\n", + "plt.ylabel('loss')\n", + "plt.legend(labels=[\"loss function during iteration\"], loc='best')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "可见，最终 “-fidelity” 变为 “-1”, 此时量子电路已学会如何制备目标量子态 “$|01\\rangle\\otimes|+\\rangle”$。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 练习\n", + "- 尝试制备纠缠态。\n", + "- 改变 “N” 制备大量子比特数的量子态。\n", + "- 改变 \"DEPTH\" 探索学习能力与电路深度的关系。\n", + "- 改变 “LR” 探索学习能力与学习速率的关系。\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

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    \n", + "\n", + "
    " + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -1096,7 +1563,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 18, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:53:27.327236Z", @@ -1108,8 +1575,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "[[ 9.65721758e-05+0.j -4.38538841e-04+0.j 2.68195580e-05+0.j ...\n", - " -4.32163794e-04+0.j -6.48040560e-05+0.j 1.52848347e-04+0.j]]\n" + "[[ 5.21890277e-05+0.j -2.92638723e-04+0.j 5.14596730e-04+0.j ...\n", + " 2.02212900e-03+0.j -1.17159500e-03+0.j -5.82856577e-04+0.j]]\n" ] } ], @@ -1159,7 +1626,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 19, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:53:27.433188Z", @@ -1171,10 +1638,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "[[ 0.56503575+0.j 0.44320439+0.j -0.13063786+0.j 0.17964958+0.j]\n", - " [ 0.44320439+0.j 0.34764194+0.j -0.10247011+0.j 0.14091406+0.j]\n", - " [-0.13063786+0.j -0.10247011+0.j 0.03020384+0.j -0.04153549+0.j]\n", - " [ 0.17964958+0.j 0.14091406+0.j -0.04153549+0.j 0.05711846+0.j]]\n" + "[[ 6.96262776e-01+0.j -3.29640355e-01+0.j 2.06852686e-02+0.j\n", + " -3.19984811e-01+0.j]\n", + " [-3.29640355e-01+0.j 1.56065737e-01+0.j -9.79328424e-03+0.j\n", + " 1.51494393e-01+0.j]\n", + " [ 2.06852686e-02+0.j -9.79328424e-03+0.j 6.14538578e-04+0.j\n", + " -9.50642772e-03+0.j]\n", + " [-3.19984811e-01+0.j 1.51494393e-01+0.j -9.50642772e-03+0.j\n", + " 1.47056948e-01+0.j]]\n" ] } ], @@ -1240,7 +1711,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 20, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:53:27.924758Z", @@ -1250,7 +1721,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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    " ] @@ -1325,7 +1796,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 21, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:53:47.622260Z", @@ -1337,7 +1808,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "损失函数的最小值是: 10.000000010745854\n" + "损失函数的最小值是: 10.000000010746223\n" ] } ], @@ -1447,7 +1918,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 22, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:53:50.904606Z", @@ -1460,8 +1931,8 @@ "output_type": "stream", "text": [ "随机生成的矩阵 H 是:\n", - "[[0.65531213+0.00000000e+00j 0.00378707+2.56639434e-01j]\n", - " [0.00378707-2.56639434e-01j 0.34468787+1.21430643e-17j]] \n", + "[[ 0.4148327 -6.93889390e-18j -0.28540716-3.59066212e-02j]\n", + " [-0.28540716+3.59066212e-02j 0.5851673 +0.00000000e+00j]] \n", "\n", "不出所料，H 的本征值是:\n", "[0.2 0.8]\n" @@ -1491,7 +1962,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 23, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:53:50.916504Z", @@ -1513,9 +1984,9 @@ " \n", " # 初始化电路然后添加量子门\n", " cir = UAnsatz(num_qubits)\n", - " cir.rz(theta[0], 0)\n", - " cir.ry(theta[1], 0)\n", " cir.rz(theta[2], 0)\n", + " cir.ry(theta[1], 0)\n", + " cir.rz(theta[0], 0)\n", " \n", " # 返回参数化矩阵\n", " return cir.U" @@ -1523,7 +1994,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 24, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:53:54.556150Z", @@ -1560,7 +2031,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 25, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:53:59.114893Z", @@ -1572,17 +2043,17 @@ "name": "stdout", "output_type": "stream", "text": [ - "iter: 0 loss: 0.2878\n", - "iter: 5 loss: 0.2202\n", - "iter: 10 loss: 0.2044\n", - "iter: 15 loss: 0.2010\n", - "iter: 20 loss: 0.2003\n", - "iter: 25 loss: 0.2001\n", - "iter: 30 loss: 0.2000\n", - "iter: 35 loss: 0.2000\n", - "iter: 40 loss: 0.2000\n", - "iter: 45 loss: 0.2000\n", - "损失函数的最小值是: 0.2000001964593201\n" + "iter: 0 loss: 0.7704\n", + "iter: 5 loss: 0.6964\n", + "iter: 10 loss: 0.5480\n", + "iter: 15 loss: 0.4297\n", + "iter: 20 loss: 0.3643\n", + "iter: 25 loss: 0.2958\n", + "iter: 30 loss: 0.2372\n", + "iter: 35 loss: 0.2104\n", + "iter: 40 loss: 0.2025\n", + "iter: 45 loss: 0.2006\n", + "损失函数的最小值是: 0.20016689983553002\n" ] } ], @@ -1638,191 +2109,6 @@ "
    " ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 量子机器学习案例" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### 变分量子本征求解器——无监督学习\n", - "\n", - "目前阶段，大规模的可容错的量子计算机还未实现。我们目前只能造出有噪音的，中等规模量子计算系统（NISQ）。现在一个利用 NISQ 的量子设备很有前景的算法种类就是量子-经典混合算法。人们期望这套方法也许可以在某些应用中超越经典计算机的表现。变分量子本征求解器（Variational Quantum Eigensolver, VQE）就是里面的一个重要应用。它利用参数化的电路搜寻广阔的希尔伯特空间，并利用经典机器学习中的梯度下降来找到最优参数，并接近一个哈密顿量的基态（也就是找到一个埃尔米特矩阵的最小本征值）。为了确保你能理解, 我们来一起过一遍以下两量子比特 (2-qubit)的例子。\n", - "\n", - "假设我们想找到如下哈密顿量的基态：\n", - "\n", - "$$\n", - "H = 0.4 \\, Z \\otimes I + 0.4 \\, I \\otimes Z + 0.2 \\, X \\otimes X. \n", - "\\tag{30}\n", - "$$\n", - "\n", - "给定一种常见的量子神经网络架构" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "我们已经学会如何建造这个电路了。如果需要复习，请转到 这里。" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": { - "ExecuteTime": { - "end_time": "2021-03-09T03:54:03.717323Z", - "start_time": "2021-03-09T03:54:03.709869Z" - } - }, - "outputs": [], - "source": [ - "from paddle_quantum.utils import pauli_str_to_matrix\n", - "\n", - "# 首先生成泡利字符串表示下的哈密顿量\n", - "# 相当于0.4*kron(I, Z) + 0.4*kron(Z, I) + 0.2*kron(X, X)\n", - "# 其中， X，Y, Z是泡利矩阵， I是单位矩阵\n", - "H_info = [[0.4, 'z0'], [0.4, 'z1'], [0.2, 'x0,x1']]\n", - "\n", - "# 超参数设置\n", - "num_qubits = 2\n", - "theta_size = 4\n", - "ITR = 60\n", - "LR = 0.4\n", - "SEED = 999 \n", - "\n", - "# 把记录的关于哈密顿量的信息转化为矩阵表示\n", - "H_matrix = pauli_str_to_matrix(H_info, num_qubits)" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": { - "ExecuteTime": { - "end_time": "2021-03-09T03:54:04.655091Z", - "start_time": "2021-03-09T03:54:04.643511Z" - } - }, - "outputs": [], - "source": [ - "class vqe_demo(paddle.nn.Layer):\n", - " \n", - " def __init__(self, shape, dtype='float64'):\n", - " super(vqe_demo, self).__init__()\n", - " \n", - " # 初始化一个长度为theta_size的可学习参数列表，并用[0, 2*pi]的均匀分布来填充初始值\n", - " self.theta = self.create_parameter(shape=shape, \n", - " default_initializer=paddle.nn.initializer.Uniform(low=0., high=2*np.pi), \n", - " dtype=dtype, is_bias=False)\n", - " \n", - " # 定义损失函数和前向传播机制\n", - " def forward(self):\n", - " \n", - " # 初始量子电路\n", - " cir = UAnsatz(num_qubits)\n", - " \n", - " # 添加量子门\n", - " cir.ry(self.theta[0], 0)\n", - " cir.ry(self.theta[1], 1)\n", - " cir.cnot([0, 1])\n", - " cir.ry(self.theta[2], 0)\n", - " cir.ry(self.theta[3], 1)\n", - " \n", - " # 选择用量子态的向量表示\n", - " cir.run_state_vector()\n", - " \n", - " # 计算当前量子态下关于观测量H_info的期望值\n", - " # 也就是 \n", - " loss = cir.expecval(H_info)\n", - " \n", - " return loss" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": { - "ExecuteTime": { - "end_time": "2021-03-09T03:54:17.622644Z", - "start_time": "2021-03-09T03:54:08.611202Z" - }, - "colab": { - "base_uri": "https://localhost:8080/", - "height": 1000 - }, - "colab_type": "code", - "id": "S9fO_sGR64LV", - "outputId": "f1be9cac-5d5e-4944-c13d-32983628fa6c" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "iter: 0 loss: 0.7363\n", - "iter: 10 loss: -0.5727\n", - "iter: 20 loss: -0.7474\n", - "iter: 30 loss: -0.8101\n", - "iter: 40 loss: -0.8154\n", - "iter: 50 loss: -0.8225\n", - "计算得到的基态能量是: -0.8242290080502013\n", - "真实的基态能量为: -0.8246211251235321\n" - ] - } - ], - "source": [ - "loss_list = []\n", - "parameter_list = []\n", - "\n", - "# 定义网络维度\n", - "vqe = vqe_demo([theta_size])\n", - "\n", - "# 一般来说，我们利用Adam优化器来获得相对好的收敛，当然你可以改成SGD或者是RMS prop.\n", - "opt = paddle.optimizer.Adam(learning_rate = LR, parameters = vqe.parameters()) \n", - "\n", - "# 优化循环\n", - "for itr in range(ITR):\n", - "\n", - " # 前向传播计算损失函数\n", - " loss = vqe()\n", - "\n", - " # 反向传播极小化损失函数\n", - " loss.backward()\n", - " opt.minimize(loss)\n", - " opt.clear_grad()\n", - "\n", - " # 记录学习曲线\n", - " loss_list.append(loss.numpy()[0])\n", - " parameter_list.append(vqe.parameters()[0].numpy())\n", - " if itr % 10 == 0:\n", - " print('iter:', itr, ' loss: %.4f' % loss.numpy())\n", - "\n", - "\n", - "print('计算得到的基态能量是: ', loss_list[-1])\n", - "print('真实的基态能量为: ', np.linalg.eigh(H_matrix)[0][0])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "

    [回到 目录]

    \n", - "\n", - "
    " - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -1878,7 +2164,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.10" + "version": "3.7.10" }, "toc": { "base_numbering": 1, diff --git a/introduction/PaddleQuantum_Tutorial_EN.ipynb b/introduction/PaddleQuantum_Tutorial_EN.ipynb index 82ddda5..4150e6c 100644 --- a/introduction/PaddleQuantum_Tutorial_EN.ipynb +++ b/introduction/PaddleQuantum_Tutorial_EN.ipynb @@ -27,7 +27,7 @@ "- PaddlePaddle optimizer tutorial\n", "- A case study on quantum machine learning - Variational Quantum Eigensolver (VQE)\n", "\n", - "**Latest version updated on:** Aug. 18th, 2021 by Paddle Quantum developers.\n", + "**Latest version updated on:** Dec. 3rd, 2021 by Paddle Quantum developers.\n", "\n", "---\n" ] @@ -63,7 +63,7 @@ "|00\\rangle = |0\\rangle\\otimes |0\\rangle := \\begin{bmatrix} 1 \\\\ 0 \\\\ 0 \\\\ 0 \\end{bmatrix}, \\quad \n", "|01\\rangle = |0\\rangle\\otimes |1\\rangle := \\begin{bmatrix} 0 \\\\ 1 \\\\ 0 \\\\ 0 \\end{bmatrix}, \\quad\n", "|10\\rangle = |1\\rangle\\otimes |0\\rangle := \\begin{bmatrix} 0 \\\\ 0 \\\\ 1 \\\\ 0 \\end{bmatrix}, \\quad\n", - "|11\\rangle = |1\\rangle\\otimes |0\\rangle := \\begin{bmatrix} 0 \\\\ 0 \\\\ 0 \\\\ 1 \\end{bmatrix}\n", + "|11\\rangle = |1\\rangle\\otimes |1\\rangle := \\begin{bmatrix} 0 \\\\ 0 \\\\ 0 \\\\ 1 \\end{bmatrix}\n", "\\right\\}.\n", "\\tag{2}\n", "$$\n", @@ -134,12 +134,12 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 1, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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    " ] @@ -218,12 +218,12 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 2, "metadata": {}, "outputs": [ { "data": { - "image/png": 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i2i9IaYNjpV1+6KGH0N/fjzvvvDNmsCOZy3Nm4nn33XflukiOO+443HHHHdi8eTPOO++8sONffvll+Zh4xsbG8Nxzz6G0tBRnn3122nX63//9XwCIuvbxxx8PANi1a1fUOT6fD/v27YPRaERFRQV8Ph++9a1vxSz/9ddfx969e3HmmWeioqIi5qKhdIBIY1woERER0ZzW0tIi6nS6sAUh3377bdFoNIrLly8XPR5P3uqW6qKZ+/btE3ft2iV6vV55265du0SHwxF17K5du8Tq6moRgPjaa6/J230+n9jS0pJw0cxYC1pKfvGLX4gAxH//939PWNfJycmobU899ZSoUCjEI488MuaimCeffLIIQHzwwQfDtt96660iAPHCCy9MeE1RFMVLLrmEi2YeGJLGKOyZISIiov3GjTfeiMsuuwyrVq3C+eefj4GBATz11FNoamrCCy+8MOvryzz00EN48803AQCffPKJvE0ahrV69eqoYVwnnngiurq60NHRIfc4PPnkk7jnnnuwdu1aNDY2wmg0Ys+ePXjppZfg8/lw4403Yu3atXIZKpUKDz30EE455RSsXbsW5513HoqKivDMM8+gq6sLd911V8LejN///vcAEg8xA4CjjjoK9fX1WLJkCXQ6Hd577z1s3boVLS0teOqpp2JmH/vNb36DY489FpdddhmeffZZLF68GDt27MCWLVvQ2NiIn//85wmvSRQmlYhHZM8MERERFYjf/OY34oIFC0StVis2NzeLN9xwgzg1NZWXukg9CPG+LrnkkqhzGhsbRQBhPSdbt24VzznnHHHBggWi2WwWVSqVWF1dLZ511lniyy+/HPf67777rvjlL39ZNJvNol6vF1euXCk++eSTCev87rvvigDElStXJn19GzduFJctWyYWFRWJOp1OXLJkifjjH/84Zo9NqO7ubnHDhg1idXW1qFarxfr6evHqq68Wh4aGkl5TFNkzcwBJGqMIoiimHPdkP5QiIiIiIiKKSUh2AFMzExERERFRQWIwQ0REREREBYnBDBERERERFSQGM0RENCd4vV4EAoF8V4OIiAoIgxkiIpoTVq9ejWuvvTbf1SAiogLCYIaIiOYEjUaDTZs25bsaRERUQBjMEBFR3tlsNtTU1GBqairfVaH91CmnnAK1Wg23253vqhBRFjGYISKivPvoo49w+OGHQxAENjYpJ3bs2CGvUj+b+vr6cO+99+Lkk09GQ0MDNBoNqqur8bWvfQ3vvvtuxuX+9a9/xUknnYSysjLodDo0Nzfj/PPPR09Pj3yM2+3G97//faxduxa1tbXQ6XSorq7GqlWr8PDDD8Pn88UsWxRF/OUvf8Hxxx+PmpoaGAwGLFq0CFdccQXa29ujjg8Gg/j1r3+Nww8/HAaDAWazGWvXrsXzzz8fs/xM6pVunejAwUUziYgo7375y19i8eLF+N73vof7778fa9euzXeVaD/S09ODhoYGXHzxxXj00Udn9do33HADfvrTn6K1tRXr1q1DRUUF9u7di2effRaiKOKPf/wjzj333JTLE0URV155JR544AG0trbilFNOQVFREfr7+/Haa6/hf//3f7F69WoAwOjoKOrr67Fy5UosXLgQFRUVmJiYwKZNm9DV1YWTTz4ZmzZtgkIR/mz7uuuuwz333IOamhqcddZZMJvN+Oijj7B582aYTCb885//xNKlS+X6fP3rX8czzzyD1tZWnHrqqfB4PHjuuecwPDyMX/3qV7jmmmvCys+kXunUifYrSRfNhCiKqX4RERHlxMUXXywODw+Lxx57rPiTn/wk39Wh/cyzzz4rAhB/8YtfzPq1n3nmGXHr1q1R219//XVRrVaLJSUlotvtTrm8e++9VwQgXnXVVaLf74/a7/P55O8DgYDo8XhiHrNu3ToRgPjiiy+G7RsYGBAVCoXY2NgoWq3WsH333HOPCEC89NJL5W1PPfWUCEBctWqV6HQ65e0jIyNiY2OjqNVqxY6OjrBy0q1XunWi/UrSGIXDzIiIKO9GR0dRUVEBi8WC999/P9/Vof2A2+3G7bffjsWLF+Pf/u3fAAA/+MEPsHz5crzwwguzVo+vfvWrOO6446K2r1mzBscffzwmJibwySefpFSWy+XCLbfcgpaWFvzyl7+EUqmMOkalUsnfKxQKaDSamMecffbZAIB9+/aF7evs7EQwGMSqVatQXFwctu/0008HAIyMjMjbnnvuOQDATTfdBL1eL28vLy/HtddeC4/Hg4cffjisnHTrlW6d6MDCYIaIiPLK6XTK8xiUSiV8Ph/Xm6EZmZiYwOrVq/GjH/0ILS0tqK6uhkKhwDe+8Q3s3LkTZ599Nt544418VxNqtRpAeACSyObNmzExMYH169cjEAjgL3/5C+6880787ne/iwpKEgkGg/jb3/4GAFFDsxYsWACNRoO33norKiHHiy++CAA48cQT5W2Dg4MAgObm5qjrSNu2bNkyo3qlWyc6sKT200NERJQjH3/8MQ499FD5/4ceeqicEIAoE+effz62bduGhx9+GBs2bEBtbS0WLVqEhx9+GEceeSSuvvpq3H333VizZk3M8++9915YrdaUr7d+/XocdthhadWxu7sb//jHP1BTU4Nly5aldM62bdsATAf9hxxyCPbs2SPvUygUuPbaa3HXXXdFnef1enH77bdDFEWMjY3hlVdewe7du3HppZdGBQFlZWW48847cd1112Hx4sVh81O2bNmCq666KmwOTHl5OQCgo6MDS5YsCSuro6MDAMLqmUm90q0THWBSGYsmcs4MERHlyH333SePjz/jjDPEl156Sbz33nvzXCsqVC+99JIIQLzwwgtFURTFwcFBEYD4jW98QxRFURwbGxMBiK2trXHLaGxsFDGd+Cilr4cffjitOnq9XnHt2rUiAPGxxx5L+bwrrrhCBCAqlUrxyCOPFN977z3RZrOJr7/+urh48WIRgPib3/wm6jybzRZWX0EQxOuvvz5sfk2kP/3pT2JRUVHYeatXrxbffPPNsOMeffRREYC4Zs0a0eVyydtHR0fFpqYmEYCo0WhiXiPdeqVaJ9qvcM4MERHNbdu2bQvrhTn22GPxz3/+M481okL2+9//HgDkJ/Xbt28HACxfvhwA5HkdkRm8QnV2dqbzsBcbNmxIuX7BYBAbNmzA66+/jssuuwwXXXRRWucC0wvMPvvsszjyyCNhMpmwZs0aPPXUU1AoFLj77rujzjOZTBBFEYFAAD09Pbjvvvvw0EMPYd26dTHXdrr11ltx4YUX4qabbkJPTw9sNhveeOMNuN1urFu3Lizl8gUXXIDjjz8eb7zxBpYtW4bvfve7uPLKK3HwwQfDbDYDiH+v06lXOnWiA0waP6xERERZd9ppp8nfn3HGGaIoiuKXv/xlMRgM5qtKVMDKysrE0tJS+fNz2223iQDELVu2iKIoinv37hUBiF/+8pdnvW6BQEC85JJL5J6jQCCQ1vnXX3+93AsSy/z580UA4sTERNKy/vznP4sAxB/84Adh2//+97+LAMRrr7026pyBgQFRr9eL8+fPD9vudrvFm2++WVy4cKGo0WjEiooK8fLLLxf37NkjAhAbGhpSfo2x6pVJnWi/kTRG4ZwZIiLKG4/HEzOr0YIFC7B3714sXLgwD7WiQjUxMYGxsTEcdNBBEITp5Skie2ZeeuklAMAJJ5wQt5xczJkJBoO49NJL8dhjj+H888/HI488krB3KJZFixYBACwWS8z90naXyxX3GMnJJ58MANi6dWvY9k2bNgEAjj/++KhzqqursXjxYuzYsQN2ux0mkwkAoNVqsXHjRmzcuDHseKnsFStWJKxLsnplUic6cDCYISKivPnkk09iTn5es2YN3njjDQYzlBYpC57L5ZK37dixA83NzbBYLPD5fHjggQegVqtx4YUXxi3n3nvvRVdXV8rXbWpqShjMhAYy5557Lv7nf/4nZlrlZKTG/K5du6L2+Xw+7Nu3D0ajERUVFUnL6u/vB/BFRjWJ1+sFED/V8cjICBQKRdR5sfzv//4vAOC8885LemyiemWzTrT/4ZwZIiLKm+3bt+OII46I2i4FM0TpKC8vR2VlJTo6OvD+++9jcnISHR0dWL58OYLBIK677jp8+umn+OEPf4iampq45WRzzkwwGMQ3v/lNPPbYY/j617+Oxx9/PKVApq2tDbt374bP55O3tba24uSTT8a+ffvw0EMPhR1/5513wmq14uyzz5ZTPe/cuRNOpzOqbKfTie9///sAgNNOOy1s36pVqwAA99xzDyYnJ8P2/e53v0Nvby+OOeYYaLVaeXuseTdPP/00/vCHP+DII4/EV7/61bB96dYrkzrRgUMQRTHVY1M+kIiIKBVXXnklfvSjH6G+vh4AcOaZZ8oTeU899VR5eAlRqn7+85/jBz/4ASoqKrB27Vo888wzWLFiBQRBwPvvv4/zzz8fjz/+eNpDvDJ1880345ZbboHJZMJ//Md/xFxTJtYwtaamJnR1daGjowNNTU3y9ra2Nhx77LEYHh7GV77yFXmI1ZYtW9DY2Ih33nkH1dXV8rXvuecerF69Gk1NTTCbzejr68OmTZswNjaGNWvW4OWXXw5b7DIQCOCEE07A66+/jsrKSpx55pmwWCzYvn07tmzZAr1ej61bt2LlypXyOUuWLEF9fT2WLFkCnU6H9957D1u3bkVLS4tcr8h7kk69MqkT7TeEpEek8eSBiIgoq0477bSwif5SAgBRFMUbb7xRnJyczEe1qMD9/Oc/F5uamkSFQiECELVarbhixQrxkUcemfW6SBP+E33FSu0spYfu6OiI2tfd3S1u2LBBrK6uFtVqtVhfXy9effXV4tDQUNhx77//vnjZZZeJBx98sGixWESVSiWWlZWJxx9/vHj//ffHTYHsdrvFO+64Q1y+fLloMBhElUol1tXViRdeeKG4c+fOqOM3btwoLlu2TCwqKhJ1Op24ZMkS8cc//nHcn99M6pVunWi/kTRGYc8MERHlhc/nw7/927/hueeek7eF9swQzdT555+PJ598EgMDA3JvBREVlKQ9M5wzQ0REebFz504cfPDB+a4G7cc++ugjVFVVMZAh2o8xmCEiorzYtm1bzMn/RNngdruxZ8+epCmTiaiwMTUzERHlxaGHHipP/CfKtn/9618IBAIMZoj2cwxmiIgoL9grQ7m0YsUKpDEvmIgKFIeZERERERFRQWIwQ0REREREBYnBDBEREe1XfvKTn0ChUKCurg6/+tWv8l0dIsohBjNERES0X1m6dCmuueYajIyM4Hvf+x4GBwfzXSX89a9/xUknnYSysjLodDo0Nzfj/PPPR09PT8plvP/++zjttNNgsVhgNBpx9NFH489//nPMY91uN77//e9j7dq1qK2thU6nQ3V1NVatWoWHH34YPp8v6pzHH38cV1xxBVasWAGtVgtBEPDII48krJMoivjLX/6C448/HjU1NTAYDFi0aBGuuOIKtLe3Rx3f1NQEQRBifq1bt27G5dOBhwkAiIiIaL+yfv16rF+/Hi6XCw899BDef/99nHHGGXmpiyiKuPLKK/HAAw+gtbUV5513HoqKitDf34/XXnsNXV1dKWX1e/XVV3HKKadAp9PJZTzzzDM499xz0dPTg+uuuy7seLvdjt/+9rdYuXIlvvKVr6CiogITExPYtGkTvvnNb+LJJ5/Epk2boFB88Vz7xz/+Mbq6ulBeXo6amhp0dXUlrdf111+Pe+65BzU1NVi/fj3MZjM++ugjPPjgg3jiiSfwz3/+E0uXLg07p7i4GN/73veiympqaspK+XSAEUUx1S8iIqKcOuOMM/JdBdqP3H///SIA8Sc/+Une6nDvvfeKAMSrrrpK9Pv9Uft9Pl/SMnw+n9ja2ipqtVpxx44d8nar1SouXLhQ1Gg0YmdnZ9g5gUBA9Hg8Mctat26dCEB88cUXw/b9/e9/l8u54447RADiww8/HLdeAwMDokKhEBsbG0Wr1Rq275577hEBiJdeemnY9sbGRrGxsTHpa860fNrvJI1ROMyMiIiI9kuNjY0AgE8++SQv13e5XLjlllvQ0tKCX/7yl1AqlVHHqFTJB8ls2bIFbW1tuOCCC8LWzSkuLsZNN90Er9eLRx99NOwchUIBjUYT83pnn302AGDfvn1h+770pS/J9ywVnZ2dCAaDWLVqFYqLi8P2nX766QCAkZGRlMub7fJp/8BhZkRERLTfEUURd9xxB4D8BTObN2/GxMQELr30UgQCATz//PPYs2cPLBYLvvSlL2H+/PkplbN161YAwMknnxy175RTTgEAvPbaaymVFQwG8be//Q0AZjw8a8GCBdBoNHjrrbcwNTUFs9ks73vxxRcBACeeeGLUeR6PB4888gj6+/thNptx5JFH4qijjspa+XRgYTBDRERE+50HH3xQbuDv2bMHXq83Zk9FpHvvvRdWqzXl66xfvz6styTUtm3bAABKpRKHHHII9uzZI+9TKBS49tprcddddyW9xt69ewFMN+4jVVdXw2QyycdE8nq9uP322yGKIsbGxvDKK69g9+7duPTSS2ccCJSVleHOO+/Eddddh8WLF+Oss86S57Rs2bIFV111Fa655pqo8wYHB3HppZeGbTvyyCPxxBNPoLW1dcbl0wEmlbFoIufMEBHRLOCcGcqGvr4+sbi4WFy0aJF44oknigDC5pok0tjYKAJI+SvRnJIrrrhCBCAqlUrxyCOPFN977z3RZrOJr7/+urh48WIRgPib3/wmaZ1OOukkEYC4d+/emPtra2tFs9kcc5/NZgurryAI4vXXX590rk4qc2Ykf/rTn8SioqKw66xevVp88803o469+eabxVdeeUUcGhoSHQ6HuGPHDvGiiy4SAYiNjY3i1NTUjMqn/Q7nzBAREdGB5eqrr8bU1BQeeughefhSqkPNOjs703nQiw0bNsQtKxgMAgA0Gg2effZZHHnkkTCZTFizZg2eeuopKBQK3H333TN+vYmYTCaIoohAIICenh7cd999eOihh7Bu3TpMTU3NuPxbb70VF154IW666Sb09PTAZrPhjTfegNvtxrp16/D888+HHb9x40accMIJqKyshMFgwGGHHYbHHnsMF110Ebq6uvDggw/OqHw68DCYISIiov3G008/jWeffRZXX301Vq9ejUMPPRRAfubNSJPWV6xYgdra2rB9S5cuRUtLC9ra2pIOa5PKmZycjLl/amoqaoJ8JIVCgXnz5uE73/kOHnjgAbz11lu47bbbUnwlsf3jH//Axo0bcc011+CGG27AvHnzYDKZsHr1arzwwgtQq9VRKaPjueKKKwAAb731Vk7Kp/0X58wQERHRfsFqteK73/0uGhsb5cn/6QYz2Zwzs2jRIgCAxWKJuV/a7nK54h4DfDFXZu/evTjiiCPC9g0ODsJut2PlypUp11lKJCAlFsjUpk2bAADHH3981L7q6mosXrwYO3bsgN1uh8lkSlhWeXk5AMDhcOSkfNp/MZghIiKi/cJ1112HwcFB/O1vf5MbtwsWLIDBYMDHH3+cUhn33ntvSotFSpqamuIGM1IjfNeuXVH7fD4f9u3bB6PRiIqKioTXOO6443DHHXdg8+bNOO+888L2vfzyy/Ixqerv7wcAqNXqlM+Jxev1AoifHnlkZAQKhSKl67z77rsAwhfOzGb5tP/iMDMiIiIqeFu2bMEf/vAHXHLJJXK6YmB6eNXSpUvR39+P8fHxpOVkc85Ma2srTj75ZOzbtw8PPfRQ2L4777wTVqsVZ599dthaM21tbdi9ezd8Pp+87cQTT0RLSwv++Mc/4sMPP5S3T05O4vbbb4dGo8HFF18cVv7OnTvhdDqj6uR0OvH9738fAHDaaaclvR+JrFq1CgBwzz33RA2B+93vfofe3l4cc8wx0Gq1AIDdu3fHrNPu3bvxwx/+EABwwQUXZFw+HZgEURRTPTblA4mIiDJx5plnckIvpc3lcmHZsmVwOBzYuXMnSkpKwvZffvnlePDBB7F169a0ejCyoa2tDcceeyyGh4fxla98RR4atWXLFjQ2NuKdd95BdXW1fHxTUxO6urrQ0dER1kvx6quv4pRTToFOp8N5552HoqIiPPPMM+jq6sJdd90VNXfk5ptvxj333IPVq1ejqakJZrMZfX192LRpE8bGxrBmzRq8/PLL0Ov18jkPPfQQ3nzzTQDTw/K2b9+OVatWyevhrF69Gt/+9rfl4wOBAE444QS8/vrrqKysxJlnngmLxYLt27djy5Yt0Ov12Lp1qzwETqrT2rVr0djYCKPRiD179uCll16Cz+fDjTfeiNtvvz3j8mm/JCQ9Io2nD0RERDnF1MyUif/8z/8UAYhPP/10zP2//vWvRQDif//3f89yzaZ1d3eLGzZsEKurq0W1Wi3W19eLV199tTg0NBR1rJQauqOjI2rfu+++K375y18WzWazqNfrxZUrV4pPPvlkzGu+//774mWXXSYefPDBosViEVUqlVhWViYef/zx4v333x8zNfMll1ySMA31JZdcEnWO2+0W77jjDnH58uWiwWAQVSqVWFdXJ1544YXizp07w47dunWreM4554gLFiwQzWazqFKpxOrqavGss84SX3755ZivI53yab+UNEZhzwwREc0Z7JkhIqIQSXtmOGeGiIiIiIgKEoMZIiIiIiIqSAxmiIiIiIioIDGYISIiIiKigsRghoiIiIiIChKDGSIiIiIiKkgMZoiIiIiIqCAxmCEiIiIiooLEYIaIiIiIiAoSgxkiIiIiIipIDGaIiIiIiKggMZghIiIiIqKCxGCGiIiIiIgKEoMZIiIiIiIqSAxmiIiIiIioIDGYISIiIiKigsRghoiIiIiIChKDGSIiIiIiKkgMZoiIiIiIqCAxmCEiIiIiooLEYIaIiIiIiAoSgxkiIiIiIipIDGaIiIiIiKggMZghIiIiIqKCxGCGiIiIiIgKEoMZIiIiIiIqSAxmiIiIiIioIDGYISIiIiKigsRghoiIiIiIChKDGSIiIiIiKkgMZoiIiIiIqCAxmCEiIiIiooLEYIaIiIiIiAoSgxkiIiIiIipIDGaIiIiIiKggMZghIqLZFwwCjqnpf4mIiDKkyncFiIjoABLwA0/cDvz1XsA2AVgqga//J/C17wOKLD9fE0VgxyvABy8Dai2w9utA66HZvQYREeUVgxkiIpo99/078P9+Nx1oAIB1GHjwPwHbOPDN27N3HZ8XuPVrwLsvAsrP/9Q9cRtw/o+AS3+SvesQEVFeMZghIqIviCLgcU33ZCiVSQ4VEQgE4Pf75S+fzyd/HwgEwr4w1oem534LBAGIgCiElPXHO9Fx0KmwWq34+OOPIYoiFAoFRFGEIAgQhOmDFQoFFAoFlEpl2JdKpYJKpYJGo4FSqYT2hV9D+d7/gwBM9wZJnrgNOPxLwKHrsn3niIgoDxjMEBHRtFefAB7bCPTthag1wrXuAoyecS38Ki0EQYDH40EgEEAwGEQwGIQgCGGBhUqlgkKhgCAIUKvV8v+VSuX09s4P4AkAAgARgCBO/wsA8IuY5x2HwWBAQ0NDzOqJoih/BQIBiKIo18Xn88HpdMrfVz97PxRuESrl9PUUIqBQAoJCgOsvv4Gregm0Wi3UajW0Wi1UKv45JCIqRPztTUR0AAoEAvB4PPB4PHC5XMA/HkPpIzciCCAoAqLPgeCLD0L56Xb0X/YriADUajV0Oh2qqqqg0WgAAIIgyL0noigmvCaKygB8EcCIIqYjDYm5TP42tGdGEtpDo0zSawSPHSIAX0A6GRC9nwdEDis8Hg9sNhuCwSC8Xi8CgYAckGm1WhgMBuh0Ouh0Omg0Gvm6Mfl9wJY/Aq//eXp421FfAb78LcBQlLiOREQ0YwxmiIj2Y8FgEG63Gy6XC3a7HU6nE36/H4IgQKVSQa1Ww2m3o+ovd8MVnO4tkbtOABjbt2GxaAUOOgYA4HA40NfXBwCorKyE0WiUr5OwwQ8ABx0NVMwDxnqnh5oJn19KAaB+CdB4sHxorOBI2iYFT5HCth+8BvjnX4DA571AAATFdI4BcelqmM3mmOeKogiv1wu32w2bzQafzwefzweFQgGtVgu9Xg+TyQSdTgetVgshGAA2rgfef2n6AmIQ+PAVYNODwC/eAkyWJO8QERHNBIMZIqL9RCAQgNPphN1ulxvigUAAGo1GboibzWa50R4MBtHb2wuNYxwa6+gXBX0eaADTgYaw6205mDEajWhubobX68XQ0BDGxsZQV1eXvKcEABQKiD98DMLNXwVsVkCpgBgIAuYK4PqHgQQBDAD538hAJrR3SPZv10F853ko4J9+PdL1y2qAL10cdn7ouYIgQKvVQqvVhl1LGtrmdrsxPj4Oj8cDv98Py46XUPfuS9OJ2MSgVCDQ8xnw9N3Ahv9Kfl+IiChjDGaIiAqQKIpyb8vk5CS8Xi9EUZSHRZWWlsacByIFBB6PB729vaiuroapojRkIgvCvlcEAbGoLKocjUaD+vp6OJ1OdHR0oLKyMqq3I9a1hfnLgQc/Ad78CzDYCbGmBcKarwFaPYDoQCVymFmsoWwxh7c1HQThzs0Q/+dm4OPXAaUCOPZsiBfdDCGityRRj1Lw83VwBEGAUqmE0WiUe6MEQQCeeBOTAUDhA5SY7vlRKQBVMADx1ScQ/Mb/hVqtTnhfiIgocwxmiIgKgCiKcDgcmJqawtTUFPx+vzyHpaSkBCqVKqp3ItZwLEEQ4PV60d3djebm5i8a2secBbzz3Be9GFLPjEYLHHNm3HoZDAa0tLSgt7cXk5OTmDdvnnydSPI2vQk46eLQy6R8DyL/n3Bo2/zlwC3PAYEAIAiAQpHwevHuV8L6+AMQgtOxn1cElCLg/Tx5WtDmxMCePXKQabFY5CFqRESUHQxmiIjmKJfLBavViomJienhYgrAvPtNVDomoGhcAiw7LmyhyXgN8dDhWT6fD93d3WhqagrvMbjspxC7d0Lo2QuohOksAEolcN0fIJosMYMAqfGvUCjQ0NCAiYkJdHV1oaGhIW4QkCxRQLx96QYaYSKGwIWWFXpvUi4v1IpTgPc2AQAU+HyqkTD9H8Xq9airqwMAeL1e2O12jIyMwO/3Q6/Xo7S0FGazmZnUiIhmgL9BiYjmCL/fj8nJSYyPj8PpdEKlUqGoqAhVVVVQdH06vQjkxCgEqdXctATY+FegpCphuVIjPRgMoqurC3V1dXI2MllJFYR73wLeewnYtx2CpRLB1V+DUFodtzcjsvFfWloKpVKJjo4ONDU1Rc2jSSXjWUrzYZKcn841kpWb6NqCIADHnwfx748Be7d/fvx0HgChpBri2f8hH6vRaKBWq2GxWABMBzcTExPo6+uDIAgoKipCWVkZjEZjZkEVEdEBSkiaSvMLKR9IRESp8Xq9GB8fx+joKAKBAIxGI4qKiqDVar9oSAf8wBWHAuP9Ydm5oBSA5ScC/+cpubxEjfne3l6Yzea4c1vSCRqALzKYRZ7jcDgwODiIhoaGtOeLnHfeeXjyySfTOieRWK8p3deZ9FyXA9j0APDG04DPB6w8DTjjKqCkMuVyXS4XJicn4fF4YDAYUF5ejuLiYiiknje3E3j2v4FX/md6UdMjTwXO+QFQ1ZjR6yAiKhBJf1kzmCEimmUejwfDw8MYHR2FSqWC2WxGUVGR3HCNajBv/ztwyznT8/JDf61Lv5V//y+gvC7hNaempjA5OYn6+noA0UFPolTImXC73ejt7UVzc7PcQ5NKEBEZzCQ7ZyZ1TCS0RyiltNNxygBSS2IQyuv1wmq1wuFwQKPRoLK0BOU/OwfCzre/yJimUAFGM/DrD4Ca5rTrRkRUIJL+8uUwMyKiWeD3+zE4OIixsTEIgoCSkhI0NTUlnCgvN+Qnhqf/H5pxDCH/To4kDGYCgQCGh4fR0tIib4s1mX4mIhvpOp0ONTU16OrqQnNzc8q9I7ECqkQS1TudQCcy8Aj9dya9OKlsi6TRaFBZOd2r4/f74frbY5ja/hY0CkCtnM6WhqAfcEwBf/wv4Lo/ZFQ/IqL9AYMZIqIcCQaDGB0dxcDAAILBICwWS8LJ8ZET0+XjWg6BIEzPx4h6RqVWAzWt0eeE6O3tRU1NzRdDluKIbPxHfi8NKQudNB/Z+A9lNBpRWlqKnp6eqNedcB5KiGwFE6n0sGSzhyfdHiNRFKFQKKLOUavVUO35J0QB8IiA+/MU0GoFoFb4oXr7hazVmYioEDGYISLKMpvNhr6+PtjtdhQXF6Ourg5qtVpevT6WhJm6mpdBPOx44ONXv0idDEz30px5NWAoilkGMD3cC4C8Nkpo+an2zkSme052fCiLxQKv14uBgQHU1NSknc0sWSCTatCQLCiS3ptUAqfI4wKBAFwuF5xOJ9xuN5xOJ7xeL3w+HzweD4LBIAKBQNLXJooilEolVCqVnHZbq9WixuODUSFACIgQAAQ+P83jB4K+ABw9PaiqqopO6kBEdABgMENElAU+nw8jIyMYHByESqVCRUUFqqur5cZ2vNXrJUkb5D98DHjoBuC1JwBfENAbgLOugfj1/wzrrAm9niAIGBoaQnV1dcz9iSTqdZHKjrWuTazehcrKSvT29mJ8fBylpaVxr5lJL0w6QUiyayYLdqxWK2w2G2w2G6ampuDxeOTeKq1WC51OB4PBIK8lI2Uw02g0cgrrZHUJBALw+XxwuVxwu93w+/2wHnQcTO8+Lx8nYDpztigAtkNPw/jnvX96vR61tbWwWCxRmeSIiPZXTABARJQhv98vT3SfnJxESUkJysrKYjYkU+1BiHecvN0xBVhHgIo6QKNLeK7D4cD4+Lg86T9UvIAkdF8q4gUwsY5rb2/HvHnzoNVq4x6X7WxmQPq9N36/HyMjI5icnMTExIQctJhMJhQVFcFsNqO4uBh6vT7lOswovbQoAvdeDrz29HTaZxEIiECgqgld37kfY17IvUF+vx/FxcVYuHAh6uvrodVqmeqZiAoZs5kREWWb1+uFzWbDwMAAPB6PnEY30kx6DLJRRnt7O+rr66HRaHKS8StVUuPc5/Ohq6sL8+fPj3usFMxE9phkI0FBvDkzDocDo6OjGBkZgc1mg1KpRElJCSwWC8rKymAwGMKOjzu3KcY1kw2pixVQxjwvGATefRF4868QPXYIh54AnHihPMRQKm98fBzDw8Noa2uD1WpFbW0tDjroIDQ1NUGnCw9+iYgKAIMZIqJs8Pl88Pl8sNlsGB4ehs/nQ1VVlTwXJXJ4F8b6gcEuoLoJKKuJW26qDeN0OZ1OjI2NxeyVkaSadjjV3pfQ4+NlaZMWBK2ri5197dxzz8Wf/vSnpNcIrXs66ZNFUYTH48Hg4CCGh4fhcDig1+tRXl6O8vJyeVHLXKV8Tla30OBmpnUIBoPo6OjA3r174fF4YDab0dLSgvnz50fNoSIimqOYmpmIaCY8Hg88Hg/cbjcGBwcRDAZRWVkZ92m94LJDvO+7wFvPTk/WVwDiMWdC8d37IOpNUeUny/AVa15KKo320dFRVFVVxdwXGpzEG2oW9prSbFQnmhdUUlICu92OycnJmL1ZqUoUBMZ6PWNjY/K8HWlO0+LFixMuIJotieoX+V4AsdenSUXk+6RQKNDS0oLW1laMj49jcHAQo6Oj6OrqgkKhQFNTExYsWDA97E8Ugb3bAccksPAIwJj5e0NENJsYzBARRQgGg/B4PPIchP7+fni9XtTV1SUcqiOKIvDL7wDv/b8v1oMJAsI7zyMY8EK48Ym065JKOuPI430+H/x+f9y5KbEWzIx8HVIQkwt1dXXo6OiA0WiESpX9P0NST83AwAD6+/tht9thNptRV1eHZcuWRU3Ez3UvTKJMdfFSXUceG2t7smx0of8vLS1FSUkJxsfHMT4+DrPZDLvdjr///e8on+zFipd/DtVg+/TBah1w/o3AN/4PwPk2RDTHMZghIvqclErX5/NBFEUMDw/DbrejuroaJlN0r0qUwU7g7Rengxhxuh0oCgACgPDu34D+DqC2OSpTWDqT7WOJLG9sbAxlZWUplRmvvFTqkU6wE/o6FQoFamtr0dvbi6ampozqE+teBINBDA4Ooru7G263G2VlZViwYAGKi4tzvr5MaC9XvDpL4gVPkWmvEw2fS1TneL1tgiCgrKwMpaWlGB0dRSAQwGELmmD83rmwO53QKgCtElD43MBjGwFLFXD6FUlfOxFRPjGYIaIDnpQKV5rzMjU1hdHRUZSVlYWlNY4U1djs2/vF6F7hi4mG4ueBDfr3ALXNUb0iqfQMpNOwnZqakleQl/Znu5cl3fIieyP0ej00Gg2sVqs8TyVeuQmzuwEYGRlBV1cXpqamUFFRgSVLlshD2NJNJJDu/KDIeqc6byfV/ZkkQUhl/lBFRQVKS0sx9cRdgMsJAYAnOL0wpxqATgUIf7oTCgYzRDTHMZghogOW2+2G1+uVgxifz4e+vj6o1Wo0NzentC5IWKOxsnF6O8JnLCoUnwc2FQ1RZaSbNjiZqakpmM3mtIanpduAT6W8ZI1wQRBQXV2N9vZ2FBUVyemsIxvy8erkdDrR3t6OwcFBWCwWNDc3h/VGxeqdmElq7NmUbk9MKudH7hcEYTprm3MUolKAGPi8/CDgEwB/AFD2dOK9V17BiiOPjDu3iIgo3xjMENEBJzKICR1SFjovJp2GrSAIEOsXQly6CsLOt6Yn/2O6VwZKAEtWAY1Los7LdsN5fHwctbW1YeUna9ymEsjE6xmKlVY4dF9kGdL9lq5bWVmJ/v5+NDQ0hJ0f69xgMIienh50dXUBAJqamnDQQQclnJMyE5kkPkj3/cxFr1kq15PrWd0EIRBSZ8Xnn9kgEKioRVNzM958800YDAasWLEiteGWRESzKPFjRyKi/YQoinC73ZiampJXVpfS9La3t0OlUqG1tRU6nS5pNqlET86F6/4ALDwy5FgAC44Arv99zONn+poi/x8MBuUV55PVNfLfZNeKl245Xp0ig6TI70VRhNlsRjAYhN1uj9krI71HH3/8MV555RVMTU1hxYoVWLNmjRwAxboHubi/yY5J535KZrsnKOr9WnsOoNXLrQFRnO5VFARAPOsalJaW4thjj8W8efPw6quv4q233oLX6521+hIRJcN1ZohovxaamQwIb2iOjo5icnIybFX6mT4pl59879kOYbAdqJsPtB6WVhmppOaN1QienJyEw+FARUUFgsGg/CU18GP9H4D8vTT8KN6XQqGI+X+lUgmlUgmVShX33iV6TX6/Hx0dHViwYIG8aCYw3cu0a9cueL1etLa2or6+PmY65li9Q6muO5NMroKNRPWfdZ+9B/x8AzA6MP2XXiXAfcq30X/iFaiprQ0L8Pv7+7Fr1y4sXLgQS5cuzW+9iehAwEUziejAFAwG5eFkoQRBgN/vR09PD/R6PSorK6OGRsXLBpVMpo3SZHNMAoGAnG5ZWrxT+j4QCMjH9fX1obq6GlqtVg40FApF1PehQYlSqZT3SXWRAp7I7yN7PUIDpEAggEAgIAdIEpVKFfNLrVaHBT9jY2MIBAL47ne/i7vvvht79+6F0WjEokWLUFJSEj08KoFsBiDZCjRmowcmVlAX75pRrysQAHa+Dbhs0z2JJZXw+/3o7u5GcXFx2HykYDCIzz77DIODg1ixYkXChVmJiGaIwQwRHVik4WQ+n09ueIc22lwuF3p7e1FbW5uXVdBjNTCl3iO32y0HYKFBikKhCAsA1Gq1/CUFI6Iooq2tDfPnz89JXROlE47X2JeCH5/PJ78mKTCTgkxpm1qtxo4dO/CLX/wCd9xxBw499FAUFRVFXUMKqpJlgct2b0ey1znTa6V6fzO5VqpZ3OINSezv70cgEMC8efPCFvh0uVz46KOPoNVqccwxxyRcg4mIKEMMZojowOH1euUUy7EacBMTE5iYmEB9fT3UanXCskLPD23Qz4TP55MDltD1bABAq9VCp9PJX1J2r3giG5+Tk5Nwu92oqqqaUR1zKTRrmvS93+/Hrl270NvbC4vFgv/zf/4PHnvsMXnBUmm4mHRf1Go1dDodNBoNgPipi+dCVjLJTIKdREFGOmUmmvOUyn2amprC0NAQ6uvrw4IWURTR09ODvXv3YtmyZWhtbU362SUiSgODGSLa/0WuExOL9HQ51SExiRqLyRqAoijC6XTC4XDIyQYAQKlUhgUsoRP1k10zmd7eXpSXl2f8dDzZHI5Yw+9Ce0ikoCNW4Bc5h0Ua6rd7924MDAxg/vz5aGhogFKpxFe+8hU8/fTT0Ov1YdeUAkBp/pOUjU6lUkGv10Ov18NoNIYNl5POjZWtLZXenXTNtKyZnp/toClym9frRXd3N2pra2EwGMKO9Xg82L59O1QqFVauXImioqKkqc2JiFKQ9JcaUzMTUcHy+/1hmcniPcGW5seEpiyW9iWbsB5re2SD0+v1wuFwwOl0wu12yz0JJpMJpaWlUKlS+1U7k54fj8eTUiATr5cpMviIV7d4x6WaPS0QCOCzzz7DwMAAFixYgBNOOCEsANHr9RgcHERTU1PYvZYCwMj77/f74XA44HA4MDo6imAwCKVSCYPBAL1eD4PBkPD1JAtK0+39mIlsBDKp9uTEml8TKXKbRqNBc3MzOjs7UV5ejuLiYrkcaahZZ2cnXnnlFRy+fDkqJ7qhG+mAYt4C4KBjP0/tR0SUXQxmiKjgBAIBeV4MEH8CfTAYRFdXF4qLi1FaWhpWRswJ0NteBj57FzBagNX/BlRG9+IEAgG518XlciEQCEClUsFkMqGsrCytnpFsDRXyer1Jh81Jcp19KlYdpZ6YvXv3YmBgAC0tLTjxxBOhUCjkhAHSeQqFAkqlEg6HA0ajMaq3RzpeOlelUsFisaC4uFi+nvQeOZ1OjI2NyQGOVquFwWCAwWBIKcCcrQQQ2ZAomIy1PVkvTDxKpRLNzc3o7u6Gz+dDeXl52P6mpiZUqET4f3QKPL174QOgVQG6BYcA//VizJ8pIqKZ4DAzIiooLpdLHmIEhD9hD22QBYNB+Qly5OrlUQ03uxXYeDaEfR9CVCkhBgPTD5Gv+R2C674Om82GqakpeL1eCIIAg8EAo9EIg8GQ0vyAXM/fGBsbgyAIUQFbNmSaQSx0GFdHRwf27duH5uZmNDc3Rw0/Cj32nHPOweOPP47u7m60trbK+6VrpJKUIJZgMCgHOE6nU046UFRUhKKiooTBTT6DlGzLZna2rq4uGAyGqIAGG89C8KPXocR0w0EQAQiAcfFhUP12O3toiCgdHGZGRPuH0Mn9ksiGbGhg09nZiYqKCjkjVkKP3wJ0fDj9xCYQgIDPV0H/9ZXoKZ4Hff0CVFRURPW6pDrhPBuBTKLy7XY76urqZnyNWFKte2SAIQgC+vv7sXv3blRVVYUNJ5OOj+xNkMpQq9UwmUyYmJhASUlJ2JyXWAFTKhnNFAoFTCZT2Ar2Ho8HNpsNvb29CAQC0Gq18jGhwU0hBjLx7kumryVWsNrQ0IDu7m6Mj49/EUj37QM+eh0KfPEEVPz8kvZdH0K14w0YDlvN+TRElDUMZohoTgudFwN8kRErkZ6eHpSWlsYNZCKHl4mv/BFCAGHPfwRxujHW2PU+cMSqsPNDexKkRl62FmmMJ1FQ4ff7U56Xk8p1Unkd0vwXaY2Z0PVmxsfH8emnn8JkMmHBggXQaDQYGRmRe89ifQHT74vb7UZvby9EUcS+ffvQ1NQk75P+DQ1QpDVzpDVrQtfNUSqVYcdIpPdMq9VCq9XKPQtutxs2mw09PT0IBALQ6/UwmUxzdjJ7ovcqNPjLxucy3uevvr4enZ2dEAQBJSUlwFj/590xiP5XAPyDnZiaOkSeA0VENFMMZohozpLSGAPhT/wje0RCV6/v6emB0WiExWJJWLbH48HU1BQc46NoilhYc7pgQBAUgG08elfEROrIbbkS62m7y+VKuVEY63y/3x/3KzRQkc4HvggoIwOJQCCA3bt3IxAIYPny5WFBQGjwFxmYhAaFWq0WFRUVACDPiTGbzVE9M1IAKX1J6wpJX1KwJR0XOQxRFEUolUoolUqoVCp5LR+NRoOKigqoVCo5S974+DiCwSB0Op08LC1bPRwzkUodkgU7qQauiebiNDY2orOzc7pHrW4BoPj8YYAwPaIsKH7xnGDEWI4KQH5AodVqU57vRUQUC4MZIppzpPVYpIUjUxlKJIoiRkZGoFQqw1YrDz3O6/VifHwcTqcTarUaZrMZDQsWAU1LgO5d8rgYMQgICgCBILDoqFy9zLRFNsgBwGazhQ2dko7z+/3wer3yApU+nw9+v19u4EsBhNSTEboQp16vh0qlgkqlCpsTJN3nWJmx9u7di97eXixduhTV1dUZv0aFQgGtVgtg+ql/R0cHqqqq4gazMxEMBuXALRAIwO/3ywGMtC30Mzg1NYXh4WF4vV5oNBqUlZWhtLRUXv8mlXrlcu5UOvcmnWAsVq9WKIVCgcbGRrS3t6OpqQnqNV+H+MZTgDg9XFMQACgAcflJ2Gn1obm7Gw0NDfI9VqlUcbPOERElw2CGiOYUp9MJj8cTs/cj0RNip9MJu92O5ubmsOP8fj/Gx8cxNTUFtVqNsrIy1NTUhJ0rXvBjCHd8Qx4SIygAKAA0HwYc+eWE9U3WgMz25H+pJ8rr9cLtdqOnpwfl5eWYmJhAIBAIC1I0Go28yKTZbIZarZ7RgoaxnuYPDQ3h008/xbx587Bu3bq0hmPFy0InfS/Nc7FarXJPW6b3MtZnR6FQQKPRyAtwplKGz+eTA56xsTF88skn8Pv90Ov1KCoqku+xRqOBVquV/5V6H3KZDCKXgVKyayiVStTX16Orqwst3/kFFGo18OoTQECc/lk6dj2Eq/4ba3RGvP3223C5XFi0aBGA6flwgUAgbDFUIqJUMZsZEc0JUuNcapDHa+jG4vf70dnZiebmZiiVSgSDQVitVkxOTgIASkpKUFxcHBUghTVu390E/PG/gK5dgEYLnHA+cNHNgLE47Fq5yGwVq8xgMCgvEul2u+XeFWk+iFqthlarRV9fHxYvXgy1Wp3TeR2R74G0SKIgCFi+fDm0Wm3UMK5M7tN5552HJ598Uv5/MBhEe3s75s+fn3a5kYkF0jk/3Uxpk5OTsNls8tApnU4HhUIhv4dSj5j03klBjvQVq04z/azlIwvb5OQkpqamphennRwFBjshVDVAtFSG9axt374dBoMBS5Yskc+VgnC9Xj+joJuI9itJf4kxmCGivBJFES6XCx6PBwCiVmtPpUEmZS4LBAKwWq3w+/0wm80oKSmBUqlMr1HncQEqDRDRmMpVwzAQCMDlcsHlcslr50jzOaReA51OF3Nugd/vR19fHxobG2dcj2AwGDdlcqT29nZ0dHRg2bJlqKysnPG1Q0UGM8B0749Wq006DypXks0Zify82u12TE5OwuPxQK/Xo7i4GEajUT7O6/XKQY7X65VTjUtD7HQ6HfR6fdwgJ5ty0VPU29sLs9kclRI90rZt26DX63HQQQdF7ZNePxEd8JiamYjmrtB0y1IQE2s8frzgRhRFDA8PY2xsDIFAAEajEdXV1VFDVdJqEGr1YeclmiidSkMwdIic2+2WgxapASst5ig1etMZZuNwOKDX6xMek2pjNXSifuRrlu651WrFhx9+iMrKShx//PGzluGroqICHR0dCYOZXPZCJCo31mdTShIATA9/tFqtGBwchE6nQ2lpKfR6PTQaTVRjX1oM1u12Y2xsDG63W+6JCw1yspkFLHQOVLbuYW1tLdra2mAymRJ+Ro444ghs27YNO3fujApopJ8Ro9E4JzPJEdHcwWCGiGZdMBiUJ1lLjanIoEUSuU1qdE1OTmJ0dBQDAwNYvnx51CT4yOMzkWqgErlNWqDR4XDA7XbL2dakdLRlZWVZeerucDhQXJx4GFw6rz1RkoVPP/0U4+PjWLFiRdx7na5YjedYdVAoFDAajZicnIx6vZJ8TB6PlVkvksFggMFgADAd2IyNjcHj8aCoqAilpaVhKbWVSiWMRiOMRmNYGdLPixTkSL2YGo1GLl/6PGUy1C90OGc2KBQKVFdXo7+/H/PmzZO3x6qPFNB89tln8hwa6dhgMAibzSYHckREsTCYIaJZJc0BiUy1K82VSSQQCGBsbAyTk5Mwm83QarU49NBDEzaucz3ZWhom53A44HK5EAgEoFAooNfrYTQaUVFRkbPx/x6PR24oS2bSII117vj4OD788EM0NTVh6dKlGZWbyTyXSJWVlejs7IwbzORDKokpQkmBhxSM9/T0AIg9pyuUFMxFBjlutzssQAKmAxzps5fKMK1kwX6mvTVFRUVy75IUiMQr54gjjsDbb7+Nzs5OeV0h6drAdPpxr9ebtKeHiA5MDGaIaFYEg0F56EhkqtdkPB4PhoeH4fP5UFpaivnz58Pv96OnpyfpuPx4Mm3Eud1u2O12+Um5NGHZYDBEPWlP9VqZyuXQqkAggE8//RSTk5M4+uijo4KmdMQbwhRv0nss0sR5p9OZUV3ipZXOhmTlxerBsVgssFgscra99vZ2aLValJaWpvz6Yi08GSvA0el0MJlMMYOBZJ/Lmdyr6upqDA4OhgUokaT346ijjsJbb70FtVqNurq6sGOkXlu73c6MZ0QUhcEMEeWcz+eD0+mM6o2JFDlXw2azYWxsDAqFAuXl5WGNvJGRkRlNPk+1EedyuWCz2eB0OhEIBKDVamE0GlFVVZVWSt/Q7zNpIEae5/V6YwZO2TA2NoYPP/wQra2tOOSQQ7JSZjYCiMrKSgwODmaU8CDR3KdUz483FDLVa8eiUqlQWVmJyspKOJ1OTExMYGBgACaTCaWlpWkvKBkZ4IiiKKctHx8fh9/vh06ng9FohMlkkhc8zUSyz7KU0c3lcslzuyLPCR3iduyxx+LNN9+EVqtFeXk50LcPeOV/II4NAo1LIJ54IZzF5fD5fFG9VER04GIwQ0Q55Xa74fF4UnoqrlAoEAgEMD4+DqvVCr1ej7q6uqgGnTRROnK9mJmShoxJwYsoTq9IbzKZUFZWlpXhYpk2HCPPC20gZosoiti1axfGxsZw7LHHJi1/tlP/SumfpUUrZ1MmvWvp3p/QYWhTU1Po7+9HIBBAaWlpwmFoiSbwC4IQNURN6l2UypcWrSwqKoo5NC3ea0/ltVVVVWFgYEDunUmUglqpVOKoo47Cm2++iTWqcWj/+woIIiAKAF4HhL/eC/HWl+BtWoJgMAiDwcAUzkTEYIaIciMYDMLhcMDv94dlypJErgESDAYxOjqKqakplJSUoKmpKW5DZXR0FGVlZVmpp8vlwtTUlBy8hM51SWV8fqoN1mw1/KVyXC7XjJ9Oh9bJbrfjgw8+QG1tLdasWZPS+fmYdF9RUYGRkZGooUhzUTrzhCKHoRUXF6O4uBiBQACjo6Noa2tDUVERysvLo34u0p3AL/XelJeXA5juObXb7RgeHobH44FWq5UzskmpzTMlBaB+vz9uT2JovXU6HY44aCFU3z0CYvDzjUEAAiA6JoH7roZw16sIBAKw2WxM4UxEDGaIKPv8fj/sdjuA+E91Q4ecjY2NYXx8HOXl5fLiiInYbDZUVlam3ZiWMiRNTU3BZrPB5/NBp9OhqKgo5eAl0kwntserZ7xzpG1er1dujGZKKktaN2bFihVzaoJ9LEajEQMDAwgEAgX/VD60RyVym0SpVKKqqgqVlZWYnJxEZ2cnNBoNKioqspbhS61Wo6SkBCUlJQCm56hNTU2hp6cHwWAQOp0OZrMZRqMxowC2uLgYVqs15c+rZe87EAL+8I0ipoOafR8CQ10QKxsgCAKcTqc87CwfwTUR5R+DGSLKKmlYWSyRaWMnJiYwPj6O4uJiLFiwIKXyPR4PNBpN7IZLMAh8/DrEj16FoDcBq88GaufD6XRicnISLpcLCoUCJpMp5no0uZTOnItUGmWJnnSnyufz4f3334fBYEh73Zh4KYAzSQ0c757EC4TLy8sxOjqKqqqqjOo7VyQKVkNJdS8pKYHFYoHL5cLw8DACgQDKysoyToIRWb5Eq9WioqICFRUV8pwbm82G4eFhObNa6JpIye6txWJBZ2dnysGM4HZHbJAq+vn3HldYb5TP54PNZoPRaCz4AJeI0sdghoiyQmr0+P3+uMdIDRCr1YrR0VGYzWa0tram1ci0Wq2xF0/0uiHcfi7ED18HlAJEEcAfb8foGd+D79TLYDabUV1dndcGbSbDdWI16FNZ/ybZ6xwbG8OOHTuwbNmytIKC0Hql830mZcV7nRaLBfv27Uurdy7fgcxMginpvND1ihoaGuD3+zE6Oorh4WEUFxejrKws5uKnqZQfr36CIMBkMslDGqXhXYODg3KPiMViSdhLpFAooFAoUg/AD/18mKMUvCDkv5YKoO6L3tvQe2O327kmDdEBiMEMEc2Y1JCQGlvxGlFTU1MYGRmB0WhES0tLRsO67HY7KioqouvwzC8gfPQ6BACCX5QbQRUv3AuccDZgqg07PpXGZbbnuWR6biRpXkM8ya61e/duDA8PY82aNUnnG8zFHg0AMJvNsFqt8tCouW6m9zBWwKdSqVBdXS33cra3t8NgMKC8vDztXsdEPUKhn0GlUimnlRZFEQ6HQ15PRqvVwmKxxBzyZTQa4XA4YDabk9+L6mbg1G8Cm/4gxzOiAhACgHDpTyAqv2i6RA7Rc7vdCAQC0Ov1XJOG6ADBYIaIZiTWIpiRQ6qkycV6vR6NjY0zGh4llQ1MD7WyWq2w2Wyof/lhqD6fKBz6NBdKBfDqk0BzeIrhVBqXkcfEW7E+lXVGssnpdGb09Nnj8eC9995DWVkZ1q5dm9I5czGQAYCysjJ0dXWlFMxEJpvIh8jAIN37Kj0oiEUQBJSWlqK0tFTOUgZMJ0swGAxZy6AXa7+0fg0wnUxjcnISQ0NDUKlUsFgsKCoqkod2TkxMpD4n67KfA/MWQdj0AIKj/bCVNcK8YSNw5JcT1kfKduf3+2EymTjsjOgAwGCGiDLmcDiiFsEEvmhUeDweDAwMQKVSoaGhYcZzPDweDxQKBYaHh2G326FUKmE2m9HQ0ACl2xEexEiCImAbn9F1JanOccg1r9eLoqKitM4ZGRnBRx99hEMPPTRmz1ahUSqVUKlUYSvMx5PPIEaSaChXquenQgouvF4vhoeHMTIygoqKillZl0Wv18vpvL1erzycVK1Wo7i4GC6XK/XCFArgK5cDX7kcCgB9O3diUKnEopBDIu9naKAoLbKp1+u5yCbRfo7BDBGlTUq7HPq0OHLi9/DwMBwOB2prazPqRQh9ih0MBjExMYG+vj74fD6UlpaiqakpfBjJkqMgfvgqhMh2qygCS45JeK1EjcxcD7NKVn6s/R6PJ61MZnv37kV/fz9Wr14tvxeZrJuSqtCy0+2JSKdOUprm+vr69CuZppner9kOejUaDebNmwefz4ehoaGooCad3qpUXntkeRqNRl4M1Ov1YmJiAj09PdBqtSgpKUk7uFqyZAlef/11VFdXy707oUkA4mVMlBa7zfaaTEQ0dzCYIaK0+P1+OByOsMaqIAhyw0KaHFxeXp7RxHKJKIqw2WyYmJiA3+9HcXExampqoFKpUFJSEnV9nHMDhI9fm85oFgCgwPTT3ep6YM2/JbxWooZmrhuhyTKcxbq+tNBhMoFAAO+99x4MBgPWrl2b0uT6TIO30PNCg9x05yWlEzDo9Xp4vd6cpGmOlTJ5JvLVO6RWq8OCmuHhYVRWViYNJiIfTiST6BiNRoOqqio4HA6UlpZiYmICg4ODMBqNKCkpSWmdGEEQcMQRR+CDDz7Acccdl7BHJpLH40EwGJyV3ikimn0MZogoZdL8mFBSo8Ln86G/vx8KhQItLS0ZNy7dbjfGxsbgcrmiUigPDw9HLeInN2qWrARueRb4n1uBzz4AVEpg1deAS24F9PlpxKSaZCAX7HY73n33XSxatAjz5s1L+bxsDINKp4zIY9OdtG2xWGC1WrO2iKok3pP+RBPlQ+Wy5yuW0Dk5seooBTVerxdDQ0MYGhpCVVVV3Ab+TIfFxaJSqaDRaOQFT202G4aGhuDz+VBUVITS0tKEQbrJZEJ9fT0++eQTLFu2LOb8tXhC0zczMQDR/oXBDBGlxO12y4FM5FPR0dFRTE5Oora2FgaDIe2yA4EAxsfHMTU1BY1Gg9LS0pgrvAeDwcQ9EkvXAD/9O+D1AEoloMzvr7h0GoKpNhyDwWBYYyzWeQMDA/j000+xcuXKGa9BMteVlJSgo6NjxsFMKusAJZqAH6u8TGUSCCXrCZM+JxqNBvX19WFzaiorK2P+3GaS7CJZHYPBoPz/oqIiFBUVQRRFTE5OoqenB0qlEmVlZWFBVuj9aG1txRtvvJEwk12swE4QBHkxX5PJxICGaD/CYIaIknI4HPLke+CLhprT6UR/fz+Ki4tjrheTbJiKy+XC6OgofD4fSkpK0NzcHDZkLWOa5MNW0pFpBqp0xEsuEHnv3G532ITmyPN2796NsbExrFu3bsYJFwqBQqGAVquF0+nMKJCWzEZPSqrzo3JRj8gHENKcGqmnRhp+lugezjSQCc1EGLlPSvfs8XgwNjaGwcFBmM1mlJSURH2ODzvsMGzfvh3HHXdcwnpGvubIxABqtTrj10NEc8f+/5eOiDImrSPh9/vlp9aCICAQCKC/vx/BYBCNjY1yoyDR/IfQxoTVasXExATUajXKy8ujJufGa9BJC++lItVGYT5SK6dal1j193q9MbMzBYNBvP/++zAYDFi1alVO6znXVFRUYGhoCA0NDXGPme1hX/HqEEvkvLPQbamUmWkvDoCwnhopqKmqqsr6hHlRFBOml5ZotVrU1tbKvye6u7uhVCrlNNPAdI9OeXk52tra0NramrC8WHOfpN9rer0+pfk6RDS3MZghopikjGWBQEDeJggC7HY7BgcHUVVVFZUeONEwHJ/Ph9HRUTidTpjNZjQ2NsadVxOvcaZUKsPqIx07k2E+c2kdlch5J7Eafx6PJ+rpudvtxjvvvIOWlpaoBn2+GvGRQ3ykRqT0/2zSarXw+XwJEwHkO5CRxJtfEynVnrp0Xleiz0JoUDMwMABBEFBbWwulUpm19ytez0w8JSUlKCkpkefR9ff3w2KxoLS0FEuWLMHWrVtRV1cXni3xs/eBrU8DXgewbA3EY9fH7al1u90IBoPMdEZU4BjMEFGUQCAgZywLbYj29/fD7/ejubk55Qn+drsdIyMjEAQBZWVlqKmpybheKpUKXq83bNtcCkYizWSOQbxzvV5v2FyB8fFx7NixA8uXL0dpaWnMckJls8cqkXjZplK5bmQ50ucvdNhiZFklJSWYmJgIS1mdagKGdBMW5CswiszalW7dU6m3RqNBY2MjHA4Hurq6YDKZUFlZmZWfs1TrGznnRafToa6uTk7R3t7ejqKiIixevBgff/wxVq5cOX3iH28D/nwXoFRAFIMQ/vG/wHO/Bv7rBcBkiXktr9fLTGdEBY4z4IgoTGggI315PB60t7dDr9fH7FGJ1UCZnJxEe3s7rFYr6urq0NTUlPZCj5H0en16C+/lWTafaEv8fr88rK+3txcfffQRVq1aFTeQybThna8gMV6GqmTZ0iwWC6amphKWlcr1kplpIJOtoCBbZcVjNBrR2toKtVqNffv2wWq1zqi8dAKveMkMFAoFysrKMH/+fOh0OrjdbgwODmJoaGi6R+bPd00fGAhCCGJ6Ed2ufwFP/SyqLtK/oijC6/XCbrfP6PURUf6wZ4aIZD6fD06nM6zBNjY2hsnJSdTX18ddSTu0cTAxMYGJiQkYDIa4Q8kyfbqt0WhSnjMTq47ZbPxlu7xEQq8jDT3bu3cvhoaGsHbt2ri9ZNnOsjWXKRQKqNVquN3ujBZp3V/NtCeptLQUFosFw8PDaG9vR01NTdrDsgRBiEpcMdMeseLiYhQXF8NoNOK1117DKX2vwawUIAREQMR0IAMAQQCvPglcentYWZH18Pl8sNvtMBqNc7q3l4iiMZghIgDTgYzL5ZJT//r9fnnFbinLWDyiKGJsbAxWqxVmsxnNzc0Jx8ZnI21tug2ObA/3Cp2wncsAIdb1d+zYgWAwiNWrV8/aNQtBaWkpxsfHUVtbm9H5+cpolsv7nY3Xo1AoUF1dDa/Xi8HBQQiCIC9gm2odpAn3kmz1iFVVVWHBggVA+yZAFACI04FMaEDjcYadE/o+h/4+CQQCckDD1M1EhYM/rUQkD7OQ/qjbbDa0t7ejoqIi4RyXYDCIoaEhtLW1QRAEtLa2orKyMqcNAb1eD5vNlrPyIyUL4mbSWEzl3NDr+3w+7NixAwaDAUcccUTG103nmrNtJvfTaDRG9SymU/Zs9FqlOtl/LtJoNGhoaEBpaSm6urowNDSU8j212Ww5W/No6dKl6ClughCyho0cyAgAlq1NeL5CoZCDmkAgAJvNFpVohIjmLgYzlBOBQADXXHMNbrnllnxXhZLweDxwOBzyk8mBgQGMj4+jtbVVnhQb60myNOxEo9GgtbUVZWVlM+r9SPT/UCUlJTMev59ILua5ZONaHo8Hr776KhobG7Fo0aKUypqNXoZU9qdbj0zqLZ1jMpniBruFEjQkMtPXkI3PhDSfRqPRoK2tDRMTE3GPlbLyBQKBnK17pFaroTj2LLjrFwGKkCFkCiCoVMG5/vthx8f6fRP6YEIURdhstoyHtBLR7GIwcwDr7OyEIAhYt25d2PatW7fG3J4OpVKJTz75BLfccgsGBwdnVlHKGbfbDZfLBUEQ4PV60dnZCa1Wi4aGhqhV5qV/x8bG0NbWBpVKhfnz56OkpGTGDaxUUtVKpDS8uWqoZ6vcyAVGZ8LhcOCtt97CokWL4q6lEus6uW68p7o+T7o9dZnUWzqnvLw8buN6pj1psyVRHYOhvQ8ZyOZnoqSkBC0tLfB4POjo6IjKNChdz2azwWQyzahOiY4RBAGLli7DO6feBPHMq4DiMkCnh7DiFARu24RRcy06OzuTJg+JvIa0xhYRzW2cM0M5s379erz++ut47rnncMUVV+S7OhTB6XTC6/VCFEW4XC709/dj3rx5MSdPC4KAyclJjI6OoqioCK2trQkX+Iu1UJ20PRtMJhOmpqZQXFyclfIylWiuQ7Zes9VqxbZt27BixYq0h77kM41wqNlIBS1RqVRyT0C85BMzMRv3NFnDfa6Q1o2prq6Gx+NBb28vTCYTKioqwuaTTUxMoK6uLmE5od+n28soiiKUSiWqWxaibeFBmL/hJ/I+NYAGTPdsDg0NAZieZ5PKYpnBYBBOpxN6vV7OIEhEcw97ZijKypUrsWvXLjz22GMzKmf9+vUAgGeffXbmlaKscjqd8Pl8AKYby4ODg2hubo4ZyDgcDrS3t8PlcqGpqSnmmhOR/498ehw6WT7W8UlNjgIv/A54dCPw2p9RVmTE6OhoemXkQK4bliMjI9i2bRuOOeYYFBcXw+fzpdWomguBTKqyeS8tFgvGx8dzco1UVrFP577n+z2aSV1D74NWq0VLSwsUCoX8+wIAXC6XnGku1xYsWICurq6YvVdSj3NlZSUGBwfR3d0dt9dF6sFTKBTy4sHS70simnvYM0NRDAYDFi9ePONympubccghh2DLli2w2WwzXmOEskPqkQGAgYEBeRHM0LUdpLVlBgYGoFQq0dDQII93T/ZkOpOFERP66DXg9vMArxuioIAQDEJVOQ/G7/4BdntVwuErM5XPno3+/n589tlnWL16tfwU2efzxU2PTV8oLi5GR0cHKioqsl52Kp+JVIbfzcZaMalINz1yMuXl5SguLkZvby90Oh18Pl9a70MmWQql4EOpVGLevHno7OxES0tLzON1Ol3YoqBFRUVhPUmhdQh9j5xOJ4xGY87m/RBR5tgzQ1GyMWdGsn79eni9Xrz00kszrxjNmBTIBINBdHV1QaVSob6+PuwPuZQEYGBgADU1Naivrw/7A54sU1RWG/9uJ/CziwCvezrjqvTEdbQXlU/diuHh4exdK4Z8BTJdXV3Yt28f1q5dGzYcJnTBzGzKd+9Atkk9AR6PJ99ViTJXhv5Fymad1Go1mpuboVQq0d7entN5J5FB4fz589HV1ZX0PCmJgVKpxL59++SkEfGGuImiCLvdzjk0RHMQgxnKKQ41mzukQMbn86GjowMlJSVRT0wnJyfR3t4OvV6PpqamlMaV59QHLwMOGyACYujIkSCg+PhN6N2TOUvTnK8GZ3t7O/r6+rB69eqoOR/SGkDZVgjpgtOtT0lJScxEAPl+XXMhkMnk/U633lJvxpFHHomJiQn09vbGnPM108n/kXVTKpUoLy9HT09PSueUlZWhpaUFU1NT6OrqShoA2+12pm0mmmMYzFBOLV++HI2Njdi0aRPHHOeR0+mEx+OB0+lEV1cX5s2bFzbsz+v1oqOjAw6HAy0tLbBYLGlfY0ZzYuKxfTHvIVaRlQYNhoaGZpzhKZZkC2WmKrShlezczz77DMPDwzjmmGNiBi2z1RDOZtav2Ux1HXqs0WiE3W6P2h6rnLkQYMxUrufppPs+Tk1NQa1Ww2g0or6+Xh76Nzk5mXZd0h3Wt3DhQrS3t6d8jlKpRG1tLaqqqtDX14fBwcG4v1OkHppc/M4hoswwmKGcO+usszA5OYktW7bkuyoHJJfLBY/HA6vVioGBATQ3N0Or1crDXQYHB9HX14fq6mrU1tZm5cl/NhooACAcfEzIfyJ2FlmgrFuA8vJyOUtRrmXSyI/M+hbPzp07YbPZcPTRR8dtOKa7PZl49clm70W6C1gmyw6XyvGCIEChUECn04Wl4832/ZtLcvUaMilXFEUMDQ2hurpaLqOoqAgtLS1wOBwJJ99ng1arhdGYXpIQQRCg0+nkRCjt7e1RQ8+kpAAAGNAQzSEMZijnONQsfzwej5ySVOp1kYYu2e12tLW1QaPRoLm5GXq9HsDMnlKnc25KiQIaDgKOOTM6kAGA824E1BpYLBZ4PJ6ka0jMpB659vHHH8Pj8WDFihUJj0unoZ+N4Tu5lMlE71iSLbAaOtSs0Hpg5kKAkkmPT19fH8rLy6OGSSoUCtTW1qK8vBxdXV05Xfx2wYIF2LdvX9i2VF93SUkJmpubYbVa5eFxUq+s9EAjGAwyoCGaI5iWg1K2YcOGpMc88sgjUdukRf6SjWGm7PJ6vXC5XOjr65Oz/ADTDY7+/n4EAgF5km6oeBNg89Y4vvYB4MkW4OXfT8+fqaoHvv6fwJcukg+RMhjFej3J5LuB+9FHH0EQBCxfvjzhcYFAIK1es9CEDHMhYMsHo9EYtmhvod2Hub4wbCSFQiEHj4mGqhoMBrS0tKC/vx82mw11dXUxP9szSZZQXFwMr9cLt9stp5wXg0Hg1SeB//c7YLgbaFkGrP8esPyEsHOlzGj19fWYmppCe3s7KisrYTabw44LBAKw2+1R24lodjGYoZQ9+uijSY+JFcy88MILAIDTTz8921WiOPx+vxzIqNVqVFZWAgDcbjd6e3tRVlaGkpIS+fhspFvOGY0WuHgjcOH/AXweQKOLmkCjUqlQU1ODnp4eNDU1zdmMUZE+/PBDKJVKLFu2LOmxfr8/o7SwhdaAzza9Xg+HwwGj0ZiV8nL12SqUz2wiHo8HY2NjcdMihxIEAXV1dXKwUFdXJ/cOS2Z6P5qamtDW1oalS5dOl/XHnwBP3TPd0ysC+OQNCB++AfH79wPHnRN1bUEQYDabYTQa0d/fj6mpqaihuFIPTS5TxBNRYhxmRimTutcTfcXy7LPPQhAEnHXWWbNc4wOT9LSwq6sLWq0WlZWVCAaDGBoawsDAABobG+VAJifplHNAEARAoQC0+tiZADD9FN5gMGBoaGjGE9hn44n4jh07Ug5kgMyDmVTrUwgyqW+8rGazWYd8ljtbAoEAenp6MG/evLQCaLPZjKamJgwODsZMtT6TYLy+vh6Dg4PT93a0D3j6nukd0q0OAqIAiA/fBATC5/BEJgior6+H2WxGe3s77HZ7WDIQv98flWyCiGYPgxnKqbGxMbz55ptYuXIlampq8l2d/Z70lLCzsxNGoxHl5eXwer3o7OyEUqlEc3Nz2Dol+X5qn+o8iFQbepWVlfB4PBgfH5/Ra8v1XIUdO3ZApVKlHMgA0w2mdIfQpVqfXEq3kZ6NHsLQMvR6PTweT8EHC3OZKIro7u5GVVVV2uncRVGESqVCc3MzAKCzszMsOcBMHrgIgoCKigr09/cDn7z5RRATeZx1DOjeFXXNSGazGc3NzRgfH0dvb2/YPp/Px4CGKE8YzFBOvfDCCwgEAnISAMoth8OB9vZ2FBcXo6ysTP6jW1dXh/Ly8oTn5qOxl4tsWtI498gUsHPFjh07oFar0wpkgNz0zCSTjWAnWxP9Z1KGwWBgQzMHpPvc3d2NkpKSjIZahWYKq6ysRGVlJTo7OzE1NRXzuHS1tLSgs7NzerhqImpdStdSKpVoaGiAwWBAe3s7vF6vfE4wGMw4EQkRZY7BDOWUlMGMwUzu2Ww2tLW1oaSkBBaLBb29vXC5XHIq5mTy3UuTLYIgoLGxEWNjYzltwGYS/H300UdQqVRYunRp2uemG8xkYw7GXOvNyPQzWlpamtWhZjRNFEX09fXBYDBktDZVKOm9lZIDWK1W9Pf3p51NLfJ4k8kEn88H78FrAK0u5NjPv1EAqF8I1M2PWV68upaUlKC2thZdXV2w2WwQRRGBQGBGmRUpf/bs2YMrr7wSTzzxRL6rQhlgMEM543Q6sXnzZixatAiLFy/Od3X2a3a7HXv37kVJSQmMRiM6OjpgMplQV1cX8/hsLoqYL8mGI0nj8KW1IrIt3Yb1p59+imAwmHaPjCQQCKQ1zGx/zGKW6WdWq9XC5/MV/Gc+22bye0AURfT09ECj0aCioiKr9VIoFGhoaIBer0d7ezs8Hk9K50Uuaiu9toaGBnSNjAPf/fX05H+lYvpfBaYTilxzX8y5eMmGwWq1WrS2tmJiYgKDg4PyAwS32y332FDudXZ2QhAErFu3LuMy5s2bh8ceewy33npr9ipGs4bBDEVZt24dRFHE1q1bZ1TO5s2b4XK52CuTYw6HA5999hmqqqqgUqnQ1dWF2tpa+UlptlayD5WrbE7pXCtZ/RUKBVpaWjA6Opr3p/KfffYZXC5X0vTLktD1LCS5mDNzIDEajXA4HPmuxpyS6e+BYDCI7u5uGI3GrAcyoUpKSlBfX4/e3l6MjY1F7U9Wd+n11dfXT8+bWf014JdvA6ddDuGY04Gv/yfEX70PLEq8vlO860qLszY0NECtVqO9vR1+vx+CIMDlcsHn86VVLuWPwWDASSedhN27d2PPnj35rg6licEM5QyHmOWey+XCzp07UVVVBafTiZGREXkF61zKxRP/XMyfUSgUaGpqgs1mw8jISMblzERbWxsmJiYSLogZK+FBrKfMDGYyZ7FYsrZI42z18My1njVpXkh3dzeKi4tRWlqa82tqNBq0tLTA5/Ohu7s7bJHKVN4HKcGAWq2eHnbasBj41h3AD/8HOP8mCBXzYp6Tzv8BoKysDNXV1ejs7ITT6YQoinA6nWHJDGhuk9oqf/3rX/NbEUobgxnKiUAggBdffBE1NTU46qij8l2d/ZLX68WePXtQUVGB8fFxBINBNDU15azBW6hDdARBQENDA3w+nzwGf7YaiZ2dnRgaGkr6M5BKfYLBYEEGM3Plc6PT6VIerhQp8jXM1udnrtw7idvtRltbG8rLy2c8RyYdgiCguroaxcXF6OjoiOrxSOU+1dfXo7u7O+XrJfp/vHMMBgOam5sxMDCAqakpiKIIh8Mx595Hiu2MM86AUqmUH8RS4WAwQzmhVCoxOjqK/v7+Ofd0cX8QDAaxd+9e6PV6jI2Nobi4GFVVVTGPzTTNcaRCfx9ra2uh1WrR2dmZleEfyYbF9fb2oqenB0cffXRW7t1sDu2Ld91438/0GvGul8r2dMrR6/VwOp1plQMU3mc/F58Vm82G3t5eNDY2wmQypZRgItv1KC4uRl1dHbq6usKGDKby/tTV1cVcxyaV15BKunDpXynN9Pj4uDw0jpn0CkN5eTlWrVqFd999F4ODg/muDqWBwQxRgQkGg2hra0MwGITNZkNVVRWKi4tjHhurF6LQGmbZVFZWhqqqKnR2ds54/kSiYXHDw8PYt28fjj322LDVwueaVBqboZ+XeN9nU7xys5Hiubi4OO/zp2ZDtt+b4eFhjI+Po7m5GRqNBkBqCSZi7U93OGnk8TqdDs3NzRgZGcHo6Ggq1QcwPeRUq9VGBRaZvIZQ0rC30PuhUCjQ3NwMl8uF/v5++P3+jIJomn3r16+HKIp47rnn8l0VSsPc/StLOWexWLBx40Zs2LAh31WhNPT09MBqtcLj8aCurg5FRUVxj83kqfhcCHZyWQdpKMjIyEjMJ7UzZbVa8a9//QurVq2atWFhcy073Vz4DMViNBrhdrvzXY2C4fP50NHRAQBobGzMSmCejUQf0lw4n8+H3t7elD/78+bNS3moWbI6RO6L/BkMBoOYN28elEoluru74fF4mOGsAEjzZjjUrLAwmDmAWSwW3HzzzQxmCsjQ0NB0Vh5MpxvV6XRhf0DjZSdKdc2RbKxNkmvZqJ9SqURTUxMAhC18N1N2ux3vv/8+jj76aKjV6qyUKUk21GUuBRAzeY9yPXRJq9XmLaDJ9s9WLn9WrVYruru7UV1djcrKyqxee6bnSkFVTU2NnIo+lYn21dXVUYlAMv25idXjHfm7GAAqKyvluT42m40JAea45uZmHHLIIdiyZUvO0vpT9jGYISoQVqsVu3btksdkS8M9QgWDwZgNhUx7XPLVQE5ljHo2VFZWora2Ft3d3WkNWYnF7Xbj3XffxdFHHw2DwZClGn5hLgUruTTTYT/JFBcXZy2rWbpSrXuu5iOlIhAIoLu7Gw6HAy0tLdDr9Vm/9kzPDb0/JSUlqKmpkbOIJaJWq6FQKMIeXsxknZ1YdYu1zWKxyMNbp6amwjKy0dyzfv16eL1evPTSS/muCqUo9eWkiShvnE4nPvzwQxiNRrS2tsp/0GdjPsxcGXqWKunJbaqNFJ1Oh9bWVgwPD6Ojo0NOFJAOv9+Pf/7znzjssMNgMpmS1q9Qh//lU7bugclkysnwwmzK13s9Pj6O8fFxVFdXJ/0cZ9NM3ltRFKHX69HU1ITu7m6UlJSgpKQk7vHV1dUYGBhAY2OjVABgtwJa/fQCmjmoHzA9xLGqqgodHR2YP39+3HmOlB27d+/GnXfemfCYxYsX44Ybboja3tDQAGB6SDcVBgYzRHOc1+vFBx98IDe6Mxm3nukf41lvRHd8AvHpuyB89BqgNwEnfAM4+z8AXeo9HZkMlRMEAVVVVXC73ejv74dOp0NVVVVK91oURbz99ttYsmQJysrKkl4nE4FAoCDTMmdTtj6HgiBArVbD6/XG7N0sJNn6+XS73RgYGIDBYJAflszm9bPRyyP1WPf19cHpdKK2tjZmuXV1dfjoo4+mg5m3X4T4+C0Q+vYBSgVw7NnAN28HSipjXmOmTCYTRFFEW1sbFi9enJMeXJo2ODiIRx99NOExxx13XMxg5oUXXgAAnH766TmpG2UfgxmiOUwURWzfvh0AsGDBArnHIRuZneac9o+AG06B4PcCQRGwTwJ//hnwyevAf70AKDP7dZXO/ZIyJVmtVrS3t6e0nsb777+Puro61NTUpFSXTASDwbTew0SveabzokLLzkWwm2gieKK0zenUScpqFi+deaLyZ5P0muNdP1GdUqlzIBDA8PCwnEwk3eBurv1eEQQB8+bNw9jYGDo6OtDQ0ACVKvz3hsFggMfjgfje3yD89CLIL8EfBN76C9D+IXDvPwF17HuR7s9P5PFSwpadO3fi0EMPzfrcOpq2bt26jH7POZ1ObN68GYsWLcLixYtzUDPKBc6ZIZrD/vWvf8HhcOCggw6SewmytW5HvkW9jj/eBkiBjEQEsPMd4N3Mxy5n0uCyWCxoaWmB2+1GR0dHzLH4oihi586d0Ov1aGlpybh+oeXFEwwG0+qRS9bInYlcp2dON9tVJnUqKipKKzV3ZJmz9TMlza3I9nw3URTlYZUGgwFNTU0F30sVqqysDJWVlejq6oq5plRRURH8j/8XIGD6dwww/X1QBPragLfjp+XNxnpHRUVFqKiowL/+9S8EAoG0yqPc2rx5M1wul5zVjAoDgxmiOaq/vx89PT045JBDoFKpojJWpfqkNt9PT1NeBPHDV8MDGYlSAD7eOuPrpUuhUKC6ujrsSa/L5ZL3d3d3Y2pqCsuWLcvK9Wb6lD3eeYVmNuqsVCohCELGDclcBoupXifTssbHx9HW1galUonW1tb9du6GyWRCXV0dOjs74fF4wvZVV1ZC3b3zi0BGIgJQKoG922Z87+MlYpEUFxejpKQEO3fuLMif0/2VlJKZwUxh4TAzojnI4XDg3XffxTHHHBM2DCHZCuyZDNFJRao9A7Guk3KjQKMH/LFSYQppz5nJVKygQa1Wo76+Hh6PB0NDQ/JxnZ2dWLNmTcbXSqdOgUAgo7lS+Q5k5ypRFFFUVISpqamEk8Uzkco9l35G4iXyyDZRFDExMYHx8XGYTCa0tLTkbTHX2Ryyp9Pp0NjYiO7ubtTW1spzVCqrquDT6qH2uMJPEACIQaCoLKs9mPG2WSwWBAIBtLe3o7W1dUbXo5kLBAJ48cUXUVNTg6OOOirf1aE0sGeGaI4JBAL4+9//jsMPPzxuWtR0zfQPc6oNnxld57ivA4rP/9iHFhMIAqu/mnm5aUjUyNJqtfLaPps3b0ZdXV1O1iuJFQzOtXVksilfT6WLi4vzto5E6PuZyyFsoihidHQUbW1t8Hq9aG5uTjmxRTbrE6tHebY+zxqNBk1NTRgcHJTfb7VGg4GlJ0GMWQUROO7c8C05/IyWlZXB4/HM+Qx7B4I33ngDY2NjOPPMM/fb37f7KwYzRHPMm2++idbWVhQVFWV1AcE5P5Th/JuA2pbpQEbAdHYhAPi3a4H5h0cdno8GvtfrxSeffILzzz8f9fX1GB8fR3t7O6ampjIuM5WerEAgsN/+cc3X61Kr1fD5fHPu5yIbw5uCwSCGh4fR1tYGAGhtbY0bxCR7/dl4f5L1Iuf6PVCpVGhqasLY2BgmJiYAAFOnXg3vwpXTByjxxe+c7/4OqGoIOz/Xc8NqamrQ398Pu92e9etQ6jjErHBxmBnRHPLZZ59BFEXU19dDEISoLFahw1NC/5X2xXrKO9tPQjNmLgPueh1442ngo9cBUxGw9hzgoGNiHp7tuQnJygsGg3j77bexbNkyeQ2OefPmwe/3Y3R0FCMjIzCbzSgrK0sr61wqxyQb5jfTYYTAgbmWjcFggNPphNFozHdV0hLvvXK73RgZGYHP50NJSUlKaZbnwns+G3VQKBTykDOfz4eK+kbsvfAuLBWtwM63AGMxsOpsiCVVyFVtIrPuhdatvr4ee/fuxdKlS5nhLE+ee+45mM1mnHDCCfmuCqWJwQzRHDE2NobPPvsMq1evBhC7wZLoj/5sTv7PWcNXZwBOunj6axalEghs27YNDQ0NqKwMX4NCpVKhuroawWAQExMT6OjogEajQXl5eVaHCSYKZrI9FCib5kKQFBnUS/fLbDZjamqq4IKZyIcYVqsVExMTUKlUKC8vz/v6JbP5nqcTyAuCgMbGRvT39yMQCGDCagXWrAEO+WLuW65qnSxphFKpRE1NDfbs2YMlS5bkbU7TgerDDz9EZ2cnzj333P0qs9+BgsEM0Rzg9Xrx5ptv4qijjor6IxavYZCswZDLBkWq5Wajx2Au2LNnD9RqNZqbm+Meo1AoUFZWhrKyMrhcLoyNjcHj8cBisaCkpGRGjZN0UzMnk8laMZl+nvIdyETWIfTzaDQaMTg4mFIZcyEoA774mXK73RgfH4fT6YTZbEZjY+OcWFg1l/cpXu9zumprazE8PIyBgYGkPdqxhP5eS+fnJ9k1dDodioqK0NnZmZV075S6ww47bL/4W3WgYuhPNAe8/vrrOOigg6DT6aL2JVr8MJ5Y80my9Ys6nYaKtE5GIevv78fw8DAOO+ywlM/R6/WYN2+eHPx0dnaiq6sLk5OTGb0PyXpm0pXJWjFzoSGfC2q1Gl6vN+lxmTRYs0Uq1+/3Y2hoCPv27cPIyAiKi4sxf/58VFZWzolABsjt5ySbZVdWVsprvUT+nkp2ndD3OdM6xTuvuLgYHo8HVqs1o3KJDkTsmSHKs127dsmLqEXK5voi0jyOdMuZSVBUKA3gyNcp/X9qagq7d+/G2rVrMyo3tLfG5/NhfHwco6Oj0Gg0KCkpkefeJBM6dypy3hRlThAEOUVzeXl5VspLJt2f6UAggMnJSUxOTkKhUKC4uDiluTCFIp+9t01NTZicnERnZ+ec6tmqqqpCZ2cnli5dCpWKzbRkLBYLNm7ciKampnxXhfKEPyVEeWS329HW1obVq1enNEdmJkM4Mmkw5KvBNJMgLhtDoQRBgN/vxwcffICVK1dmpUGhVqtRVVWFqqoquN1uWK1WDA0NQaPRwGw2o6ioKG7vS2jPTC6HhM1UoQ0rFEURZrMZPT09WQlmUhHZKxaZ5AMAfD4frFYr7Ha7HHA1NDTkrbE9V4bYZVtFRQVGRkbk4KGpqWlO3GNpwd729nYsXLgwL/UpJBaLBTfffHO+q0F5xGCGKI/eeecdHHzwwWlNYJ2rstngyfbQjUy8++67WLx4ccq9J+nQ6XSorq4GAHlIydjYGBQKBYqKilBcXBwWQKV7b/MZhM7UbNddqVQiGAxmfV5SKkLfV5fLhampKTgcDiiVShQXF6OxsTGtzHi5ksvFPfMZ/JpMJjmbnRQ8tLS0ZDWgSTeroXSv9Xo9rFYrxsfHUVpamrX6EO2PGMwQ5Ul7ezu0Wi1KS0tzOtY+140g6RqpXieTCbezbefOnSgpKUFtbW3C47JRb61Wi6qqKgDTcyKmpqbQ19cHv98PvV6PoqKimGP6C6UHZK69t7EYjUbY7XaYzeacX0t676T32m63w+fzyZO/Kysr08piOFvyUYfZ+OxIvWNGoxG1tbXo6upKa8hZKskC0hGaWKCqqgrd3d0wm80cbkaUAH86iPLA7Xbjk08+wZo1a5IfPAOz0QDJxjWyVc9sNH76+/thtVpx7LHHJj02MiPYTK+vUqlQWloqB7gulws2mw09PT2wWq0oKytDUVER9Hr9nGjgpkKhUMjBWD4n0SdiNpsxPj6e02DG7/fDbrfD4XDA7XZDrVbDaDSipqYmJ+uKzFYQmeusidkqP6ycgB/Y+ifgjadw+NgoPD2nQn/WVTAWlaCysjJuQBPrIcJM65bo9QmCgMrKSnR0dGDBggUzug7R/ozBDFEeSMPLkk3KL4Sn2umay9mObDYbdu3ahXXr1mV03Wy+NkEQYDAYYDAYEAwGUVRUBFEUMTExIacT1uv1MBgMMBqNOXlym43P31weIifVTa/Xw+VyZbVsj8cjBy9+vx9KpRIGgwGlpaVZW39IkotGdjrXTkW+U3t/EcgEgDu/Aby/GRAAkwig91PgzT8Dd/4DJst0IpbOzk40NzeHDT1MJdDO5PMeeU7o+6nX6zE2NgaHw1Fw6yERzRYGM0SzbHBwEF6vN6UJx7GGY8UKgKT/p5KxLB9DlAohKAsEAnj//fexcuXKrI2Zz9a9lhbVk4adSdtcLhfsdjusViv8fj/UajV0Oh0MBgP0er38OjJZV0aq//4s9PVpNBr4fL6Mekm8Xi+cTidcLpccFEk9L9XV1TlfhK8QhhzG+izl5ffCuy9OBzIAIH6+SKYIYLgHeOYe4Ft3wGQyQRRFOSlAOnOpUknrnEqil1A1NTVoa2vDIYccknI9iA4kDGaIZlEgEMD27dtxxBFHZHR+vMZxZNreRPLR8CmERvEHH3yABQsWyMFCNuTyXof23Eh8Ph+cTifsdjtGR0flSe16vR46nQ56vV5uWKfzmdnfiaIIk8mEqakplJWVxT0uGAzC7XbD5XLB4/HA4/FAFEWo1Wro9XoUFxejuro6pxPmZ1OuX0Nehpe+8/8AhQAEP//ci5iOaIIi8PZzwLfuAAD594A05GymySHSnVsYSqlUQq1WMxkAURwMZmi/5nK5sj6kYyY+++wzlJSUQKvV5rsqc9psNwTb29uh0WhQX18/a9eMJ1bAmur9UKvVKC4uRnFxsbwtEAjA5XLB6XRiamoKPp9Pvo5Op4NWq5X/nQvrbOSDIAgwm83o6+tDaWkpfD6fHKx4PB54vV75PdDpdNDpdCgpKYFOp0s43yGZeOsbzRVzqS6JpFVPMWIh39BTA4Gw90Aa2pmNgGam91KayzPXgpm59jeWDkwMZmi/5XQ6cfbZZ2PdunW45pprsvrEPRN2ux3d3d04/PDD81qPdOWjgZXLFLCRT80nJibQ3d2d8cKY2RavpyTTe6JUKmEymaJSTAcCAXg8HrjdbkxOTsLr9SIQCMjXUqlU0Gg00Gg00Gq1UKvVUKlUBdPAlUR+fgOBAHw+X9iXx+OB3+9Hd3c3gsGg/Nq1Wi1MJhO0Wm1OXnc2spbNtQAoX1Ie0rnyy8Drz4QHMQBEhQDh2DOj7qWUFKKrqwtNTU15u9dSD+vg4KCc1j2fPv30U9x222045JBDcMMNN+S7OnSAYzBD+y2DwYC//e1veP755/HVr34VJ510Eq6++uq8TKIURRGffvopKisr5WE+hbKS+1yvXyzJxqVL3/t8Pmzfvh3HHnts0qeumcx/yWYmpmyTJqSHDlMLvZ7H44HP54PX68Xk5CT8fj/8fn9YXRQKBVQqFZRKZcIvhUKR8hCbVHqlpHVhRFFEMBiE3+9HIBBAIBCA3+9HMBiUv/f5fGHnKxQKOTCT5rWUlpbK840sFkvMezJXpTJP7kCQ8j045izg0MeAj9/44lwBCBZXQvnV78c8xWw2h/XQZDvRR6zkDbG2VVZWoq2tDZWVlbO+JpJk165duO2226DVavFf//VfaG1tzUs9iEIxmKH9miAIOOuss3DGGWfg2WefxVlnnYVTTz0V3/nOd2a1wTI0NASn04mlS5fK9UqnAVJI64rMBak2Nt577z0cfPDBKQ2TSOX+R75PcynldDpCh1MlEgwG4fP5ooIJj8cjBxShgUcq99DlcqG9vT1qe+icA+lLoVBAoVDIAZPUo6JUKsOCrFQbfkVFRbDZbAUVzPD3QppUauDHTwF/fxR47SnA64J1/kpMrT4PjWU1cU+Temi6u7vR0NAQ82FJovci3v7I3xeJfk4UCgXMZjOGhoZQUxO/rrmwZ88e3HbbbRAEARs3bmSqaJpTGMzQAUGhUOCrX/0q1q9fj2eeeQZnnHEGzjjjDFxxxRU5H+8bCATQ3d2NkpISOVNSvJ6DeE/ogsFg9tdaOMDt3btXnrCdrnjZwbL1Ps0FiRpf0mtUKBTQarUJ54ClG4gbDAa0tLSkX+EsMJlMGBkZycu1aRZptMBXLp/+AhAYHcVEby8aE5wiCAKKi4vh9/vR19eHefPmhe1P9hnPVnKWsrIy9Pb2oqKiYlYW0ty3bx9uu+02BAIB/OhHP8KiRYtyfk2idOWnn5IoTxQKBb7+9a9j8+bNqK6uxumnn45f/epXcLvdObtmX18fACRNxRyv4ZjNAKQgGtpTY0DXp4DTlrNLTExMoK+vDwcffHBG58cashb5fbbN9nsnLXQ503oUUs9BaFCaSKqvqZBeey7N9ftgNpvhcDhSOrasrAwqlQpDQ0M5rlVsUgBjs+Xu9yMwnRTl29/+Nm6++Wb853/+Jx577DEGMjRnMZihA5JSqcR5552HzZs3o7S0FF/5ylfwm9/8Bh6PJ6vX8fl8GBsbg0KhiJqAnapM5hkUJKcN+MXlwIYFwH+sBi6ZD/zhRxAC/qxexu/3Y/v27Vi5cmVKa0LMFXOpLvszk8mUtKGY6HOTi2GGc0kmn8O5dB9i1V+j0cDr9aZcRnV1NbxeLyYmJjK+5kyUlZVhaGgIfn92fzcC04uFXn755fjxj3+M733ve3j88cdx0EEHZf06RNnEYWZ0QFMqlfjGN76Bc889F3/84x9x6qmn4txzz8Wll16alYXuurq6YDQac/JHJ9Rcaixk7K5LgB2vTq/7AABeL/DCbyAGfcC3f5a1y2zbtg0LFy6MmheRymJ2+ZLrCcfpXFOacO/1euV/pQxhoRPwpXkygc/T3UZO2o/8V2K1WvH222/Lc2KkuoR+AZDny0hzZlQqVdg8GWmSf+RXsvkzZrMZo6OjYemt05Hqe1UoCUAiZbu+giDM6vDMeNdJd0L9vHnz0NnZKSeRSFT/bL+2oqIieR6mNJdnprq7u3HHHXdgYmICN954Iw499NCslEs0GxjMEGG66/7iiy/G+eefj8cffxxf/vKXccEFF+CSSy7JaEVwAHC73XA4HBAEAVVVVRmVkYs5LnNy3kzXp8D2V79YwA6f/ysC+NsfgHNuAMwzX1+hq6sLKpUq5noyc+WeSI076ftsk4IHt9stf3m9XjlNs/T/QCAQM1OWIAhRwYL0vZTOOHRyfuj3ib4kZrMZy5cvl4MfAGH/xtomBVJSumkpIYH0OkK/YjWcFQqFnIZao9FgaGgIoihCq9VCo9FAp9NBo9FkNYPUTN7bfCYEyfbvj7kyz0yhUMDv96c8D0UQBDQ2NqKjowN1dXVJk2UA8efaxTsmEaPRiImJCfnzmane3l7ceeedGB4exo033ojly5dnXBZRvjCYIQqhVqtx6aWX4sILL8Sjjz6KU045BRdddBEuuuiitCdbtre3o6qqCn19fRn38szG2hZzQsen0//Gqpo/AAzsA8wrZ3QJm82GtrY2HHfccTMqZ6aSPZFP1MhJxuv1wm63w+FwwOl0wuVyycFJ5PAnqeEuLZhpMBhQVlYmZzHL1uTidBu/CoViRo2zTPj9/rCgzmq1wmazYXJyUl400+fzyfdQFEWoVCro9Xo5vbVOp4PRaITBYMhq0BPr/uVzyGGmvz/iBWCpDPWcjd9ZBoMBdrsdFosl5XMUCgUaGhrklM3JHnxFzq+Ll/Qlld6q8vJyDA4OwmKxZLQOUn9/P+6880709/fjhhtuwIoVK9I6n2guYTBDFINarca3v/1tXHzxxXj44Ydx8sknY8OGDbjgggtSauTZ7XaIogi3242ioqK5GUDMJeW1X3wf2jsjKanFTIiiiG3btuGII45IaZX7XD75Dv0spNpQEwQBfr8fLpdLDlQcDgfcbnfYPK/QBrbRaERZWZnc0M7XuhSpiPXEOt79z0XjVqVShc1pU6vVUCqVKCkpiXuO1+sNex9GRkbQ1dUFt9sdFrBqNBoYDAbo9XqYTCYUFRWlNX9uf/ndkenPk/RZyKgXY3wQePUJYKQbqFsIrDsPKIr9nhoMBjgcjrSCGUEQoFarMW/ePHR3d6O5uVnuzZzpXMdk56tUKng8HvnvTKpZOQcHB/HTn/4UXV1d+OEPf4ijjjoqpfOI5jIGM0QJaDQaXHHFFdiwYQN+//vf45RTTsE3v/lNnHfeeQkbxZ2dnaiursbg4CAqKioSXiO0EZeJ2RhyMtMGZNLzDzoWqG0BBtuB0ERSCgWw/Higcl7cUyWJ7sOnn36Kurq6lOdBzNaT78h74vV6MTU1BZvNJn/5/X4MDw+jrKwMxcXFcqBSUlISd9HLQhP5xDrdRl62A5yioiIMDw8nDGaknq1EjV9pOJ/dbofL5cLExAS6urrCAlCDwQCTyQSj0Qiz2Qyz2TynA8/ZlCiQkfbH9dEbwO1fB7weQKEEggHgzz8Dbn4eaF0WdbjBYIDL5UpYn8i6SJ9TnU6HqqoqdHV1oampKelQsmRSndOm1WrlxAVarTbh52Z4eBg/+9nPsG/fPvzwhz/EMccck3a9iOYqBjNEKdBqtbjqqqvwzW9+Ew888ABOPvlkXHbZZTjnnHOi/oCMj4/Lcwm8Xi+0Wm3CP2qxhhOk80cwk8Uc05XOH+SMJtIrFMBNf4L4X1+DMNT9xfbWQ4Hv/jbl68YyOjqKiYkJrFmzJqVycs3v94cFLHa7XW7cKpVKmEwmmEwmVFdXY+HChdDpdOjr65OHgM0lqXxOZ6NnIdvXCG0kzoRCoUgYcAaDQdjtdkxOTsJut2NoaAgul0v+LGu1WpjNZhQXF8vBa0b69gED7dMPDGrnZ/pyZl2i31kJP3s+L3DPpdOBjAggEJje7pgE7v028N/vABHn6nQ6TE1NJaxPos+ZyWSCz+dDT08PGhoakh4/E9JrN5lMmJqaQnl5OZxOZ8wev9HRUfz85z/Hrl278IMf/ACrV6/OSZ2I8onBDFEadDod/v3f/x2XXXYZfve73+Hkk0/GFVdcga997WtyUNPb24u6urqwICXRE8ZE21JpLKZ6zGxL96mkWNcK4TfbgY+2AiM9QMNiYPFRUY2OdPj9fnz00UdYtWpVxmVkKhgMYmpqCpOTk5iYmMDU1BREUYRSqYTBYEBRUREqKirQ0tKStJGa6Ml0Ic6fKARqtRo+ny/mPIhs9QRJK7rHy0hlt9ths9lgtVrR09MjB716vR5FRUWwWCwoKSmJH+ROjU833re/+nm9AeHw44Hv/14ebjUnE4KkIGGdP3kDmByL3h4UgZ49QPcuoDE83XAqPTORIu9dSUkJvF4vBgcHM1qMN1XSNYuKitDb24uysjI5o6D0eR0bG8Pdd9+Njz/+GNdffz1++tOf5qw+RPnGYIYoA3q9Htdeey0uv/xy/Pa3v8XJJ5+Mq666Cscdd5zc3e9wOMIaqZkMPUh1PkWuZNLQCQ3g0j5PqQQOPzGt8xLZvn273LuRbaH3xu12Y2JiQg5apEanwWBAaWkp5s2bB4vFktJ8q5kkAJhthdoQToXRaITNZkNpaXQWvdmatC710tXU1IRtt9vt8ueto6MDPp8PwPTnzWKxoLi4GKWlpVD94tvAh6+G1BvAR68Cv/gW8H//ktJrKUSiczJmLhFZjAV5DQZD2r1xsea/VVVVobe3F+Pj4zE/O9mkUqnCsg5KQxrvuecebNu2Dddffz1uu+22/fI9JgrFYIZoBoxGI66//npceeWVuO+++/Czn/0M3/nOd3DmmWfC4XDAaDQmPH+uNwZnu27Z7Gno6+sDgJhpmGfC6XRiZGQEY2NjcqIHpVKJ0tJSmM1mNDU1zWgeS6q9d0DqAc5M52UlK3d/VFRUhMHBwYwapLm+L1KQE0oasma1WjEwMICOf/4dR+14NfrkIKZ7avrbgNrWnNYzX4QlR3+R2j2SzgA0LY3arFQqEZCGo2VyzZD3vK6uDh0dHdDr9SlPzM+UVquF2+2Gy+XCb3/7W2zfvh0/+MEPcOutt+7XP59EoRjMEGWByWTC1VdfjeOOOw4vvvgizj77bJx99tm48MILo46NnOxMX8hWY9vj8WD37t0zTsPs9/sxNjaGsbExjI+PIxAIQKPRoLS0FA0NDSgtLS2IydpzsVdnrtNoNHKPR6S5+BBCqVTKQ9YaGhqAXX9LeHz/9reg05XAYrHk7TOcs2GSZbXAGd8Bnv/t9NA6AV8EN+fdAOgTP2SKVU9JqnMUGxoa0NnZiebm5pjJYjJ57bHO8Xg8+NnPfoYdO3bgO9/5Dm666aaMF3wlKlQMZoiypKenB01NTbj++utx+eWX4/bbb8fXvvY1XHXVVTjppJPmXONnf7Zt2zYsXbo07bVSrFarHLw4HA6o1WpYLBaUlZVh/vz5Ga8XlA2zmWGNwc+0ePNm5uLPcth79pd7gSfvTHh8sLIJHR0dsNvtAKYfyFRUVKCysjLtYZnJ1k5Kqc4pHJtW+Rt+AlQ0QHjxN8BI73Tig69eC5xwflp1lK6d7vBglUqFmpoa+e9C5P5MfsZCz7HZbLj//vuxdetWXHzxxfjxj38sl+vxeKDVatMun6hQMZghygKpm18a2242m3H55ZejpKQE999/P+6//35cffXVOP744wHEXjBtNhuRc/HJcrb09PRAq9Wiqqoq4XHBYBDDw8MYHByUJ+ebTCaUl5fjoIMOSmstkFC5uLfSmPjZkKvrxEprO9c/g4nmzWRDzu7BsWcD//uTL7J4hVIIwGHrMG/lWkgJz6VkFSMjI9ixYwfcbjeMRiPKy8tRXV2dcYKKbEr7GgoFcMaV018RQtcySrWnPJ3PrvQzZDQa4XQ6oxICpPozFus6drsdDz74ILZu3YorrrgCV199NcbGwpMduN1uBjN0QGEwQ5QFPT09YevJSJnMSktLccMNN2BiYgK/+c1vcN999+G73/1uzOFPs/k0fK43IjPl8Xjw2WefYd26dVH7/j975x0mVXU+/s/02d77sg2QXqyIgIom9kIVEQvq1xoVAWuMiSZGo7KKgF3sYEPAGGPiL0aNAooNFAGBrWzvfWan/v4Y7zi7O+3O3JmdZe/neXiYnbn3nHPPPfee9z3nLTabjaamJhoaGmhpacFut5OUlERWVhaTJ0+WzNQm0L71JSDZbDaPvw0FxITrDnXSUn/LDsZvxt+2hAL7F++isFodZlVK+vqOTD0Vlq/vc7xSqSQxMZHExERGjx4N4AwV/cMPP9Db24tWqyU9PZ20tDSP0dcCamsACl2wSqCnICUqlcqvXQ0xdaelpVFZWUlHR4fofnOtp6enhxdeeIGPP/6Y//u//2PZsmUolUpsNhsWi6XPsUJ+o0gL5S4jEypkZUZGJkhMJhNtbW2MHj3aOcmazWa0Wq1TaEpKSuKee+6hubmZtWvX8uSTT7Js2bI+Mf+Hwkp1pPPtt98yefJk1Gq1W+UlISGBjIwMxo4dK9oELdSESrgPZlwNlslZKOsUU7Y3v5mI5et/o3j9L47PChw+IrMWQE0pZBdizxrp13gQggyMHOkIEiAEvti/fz/d3d1otVpSU1PJysoKSrkJZGyG6j2p0+kCMtHy9Yzl5uZSVlaGXq8XbapqMBh48cUX+fe//81VV13Fli1b+iy8CAqNKwqFwnkd8pwiMxyIrNlcRmYIIiQ0dMVsNrsVllNSUrjvvvtobGxk3bp1rF27lltuuYUZM2YcMZPOYCllFRUVWCwWmpqa2L9/f8QrL55w13/BmJkFcy9k3xmH34zJZOojhEbswsPhn+Gxq379OykNLvgdRMU6I5f1b7WgsPq6pujoaPLz88nPzwccpkwNDQ3s37+frq4u4uLiyMzMJCsrK+KeNX+Vcq1Wi9FoDGoHxR1KpZLc3FwOHz5MYWGhUxnx1udGo5GXX36ZDz74gKVLl7J161aP7wFXZcbVhE5I2iwjc6QTWW8cGZkhhhDtSli9FCYmk8nkNtmeQFpaGvfffz8NDQ088cQTrFu3jltvvZVp06aFpd2hJJxCns1mc4ShLSvjyy+/ZMaMGcTFxXHUUUdJKlCFc4fCU2hmWbEYHGJiYujq6upjahaRikxnKzx0MRh6QKUEqw0W3e1QZLwQqPO+Xq8nLy/Pme1eCAm9bds2FAoFqampZGdnk5iYGNDleGkwNNU4QpSlZPmVVNffZ0etVmOxWIJtoVt0Oh1paWlUVVU5+8xdn/f29vLaa6/x97//ncsuu4ytW7f2iYbm7hzXnRrX3+VAADLDBVmZkZEJgvr6emJiYvrYYNvtdmw2m1/CdHp6On/961+pr69n9erVrFmzhltvvZXjjz8+1E0fsvT09FBdXU19fT1Wq5W0tDSMRiOXXXaZT6f/QAmnIuFutVahUAx5n5mhSmxsLA0NDSFNgBj0To/VAsVXQk05ZIyA362DzzfBby+TrI2+EHxuxo0bh8Viob6+noMHD9LZ2UlsbCyZmZlkZmYOMLMSde37voRnVkLFXsffBePhumIYd6Ik16DRaCRRZjxdU3x8PD09PTQ1NZGamtrnN5PJxIYNG9i8eTNLlixh8+bNfeaQQBY0bDbbgF1FGZkjEVmZkZEJEGHCFswuoO8qp+t2vyvuJrqMjAweeughamtreeyxx3jiiSdYsWIFxxxzTOgvJADCaWZjs9lobGykurqa9vZ29Ho92dnZnHDCCWi1Wmpqaujq6gqZIhNKPCku/QlUmfEUtUnGf3Q6nejM8GIJ+t68fC/s+gx0erhrAxROgsknS9O4AFCr1eTk5JCTkwNAR0cHtbW17Ny5E6vVSmZmJiNGjCA6Otrttbsdr4cPwB8vBIvLvSjfC3+8AB7fBrmjJWm3J2VGbGhmT+dnZmZSXl5OVFQUMTExmM1mNm7cyKZNm7jooovYsmWL37vKdrvdZ+ASg8EgKzMyRzyyMiMjEyDt7e2oVCq3CdG8+Th4+y0rK4tHH32UqqoqHn/8cadSM2XKlIDb6U2xCqbMUCHY79fW1nL48GEMBgNJSUnk5uYOUO4sFgv79u1j1qxZbsuJRAHetV3+tk+pVAaUnVxsPTJ9Ee6VkB3e3bM+6PzndXj/GcfnW57BXjBxgF/MYCMk8xwzZgwWi4Wamhp2796NyWQiNTWV/Pz8PqHQ3Y7X958Cq7lvZDY7YLPCP56G6x8T1SZPvmmeFNdgnyHX80eMGMHBgwfZuXMn77zzDgsXLmTz5s1eTZPdvbtd/Z08Ie/OyAwHZGVGRiYALBYLDQ0NJCUluf1dqVR6zR7ui9zcXIqLizl8+DDFxcW0t7ezYsUKJk2aJLqtQn2R7nNhs9moqamhsrKS3t5e0tLSGD9+vFdn3N27dzN69Gi3E/VgCPD+KFCBRm8a7mZmwSinge5QCcdGR0fT1dUVeZnV938FzyxzfF50J8y4MOIUmf6o1Wqnr43NZqO6upoff/wRg8FAeno6ubm57v1sDnwDtl/eYXZ+jWRgtcHB70S3w9040Gg0dHd3uz1eqsURi8XCO++8w+uvv87s2bN59913JVc0+rfVaDTKyozMEY2szMjIBIDRaKSrq4vMzEyPpkK+Vsz8YcSIEaxevZrKykpWrVpFV1cXt912G+PHjw+qXH8Ih9O5zWajvr6eiooKDAYDaWlpTJw40a9oQo2NjRgMBqczbSQQKgXqSA4A4M4B3fV6hefLk+mOP5He+u9Oir1PsbGxtLW1RZYy01gND18GFhuceC4sukOacu12qK8ElRrScqQp0wNKpZIRI0YwYsQI57vgwIEDdHd3k5SURF5e3q++Smk5ULnXodAofm2qQgWkZkmibKjVao87oMGWbbVaeffdd3n11VeZM2cOmzdvprW1lc7OzgHRMMXizVRVWAixWCwRF2VORkYq5JEtIyMSm81GZ2cnUVFRXm2jpVxJz8vLY82aNZSVlbFq1SpMJhMrVqxg3LhxktXRHymEZ3dCuCC0HD58mO7ubr92YNy17YcffuCkk04SdU4kmVuJtcEXez+kut5Q95unZ8jb766/+dsvnkzu/Lm+qKgo6urq/KonLBh74G9LoLUR8sfBsmccGe+D5bv/wvO3Q22p4++Rkx3mW6OPDb5sHyiVSrKyssjKynL6yZWUlLB7927S0tIYecrFRH39UZ9zFArABvbfXCnJGA3FDqjVamXLli28+uqrnHvuuWzatMmZzDIjI4OSkhLi4uJCvnPS29srKzMyRyzyyJaREYnRaKSlpcWjiZlCoXCbyEwKCgsLefLJJykpKaG4uBiLxcJtt93GUUcdJXldgdBfMHQVNFtaWigrK6Ojo4O0tDTGjh0bcLK9ffv2kZeXR1RUlN/nRJIiA+LaIzbPjJTXGmn9JjX+XJ+wMxQRARXsdlh3M5TshvgkuPsNn+GXveFUCA9+C39dAFb7r2ZcZT/CvefDE19CRmh2QD35rmRkZJCRkeEMv76rM5Os6YvJ//INR7uFNl7yexTHnyFJW1QqVdDvbdfFrPfee4+XXnqJs846i7feemvA+0qhUDBixAiqqqooKioKql5PCPfXbDZjs9l8BgyQkRmKyMqMjIxIzGYzBoOBnJwc56TVfzLW6/U0NTWFrA0jR47kqaee4uDBg6xatQqlUsltt93mzHczWPTvB5PJRFlZGdXV1cTExDBy5MgBIUnd4U1Y7O7upr6+nlNPPVWKJg8JxO7MHKkmaYNJVFQU3d3dxMbGDq6C9+7j8MVmRy6Z21+BzHzf53jBOVa2Pvmrc72CX5zr7WAywr/Xw+X3B1VP/zr9DU6hVCqdkdFMxx5L5e5L6N3+PmqNmpiT55Ix8TjJ2iXFIpTdbufvf/87L7zwAmeccQZvvvkm0dHRHo/X6XTExcVRX18vOiKjQqHAbDb3CUzR/93pOj+ZTCbnrpCMzJGErMzIyIjAZDLR1dVFTEyMW1t/1+hHgeYrECO4jh49mmeffZb9+/fz8MMPo9FouP322ykoKAiobleCWX2ura2lvLwcs9lMfn4+J598sigTB2/1fv/990yZMuWI3zFwRYimJTN4xMTEOJUZKQjID2rnh7DhL47P1zwKkwZG8QuYkm9/dbCHXx3sbXYo+V66egh8t0+r1ZJ//Ew4fiZdXV2UlJSw5+OPSUpKoqioKOgEncH4ptntdv75z3/y3HPPMXv2bN544w2/x0paWhqlpaUYDAa3uzee2mS32wckaPbmPyMrMzJHKrIyIyMjgt7eXpqbm8nIyPCYD6T/Z3fOzN4IZDIdO3Yszz33HHv37uWBBx4gKiqK22+/PSjneLG+BV1dXZSWljpXGCdNmhS84Ge3w2dvwYcvQksNPTljST1mLsnJM4MrNwIQoyx6MzOLNF+gI5WYmBhJd1tFP+eV+2H1NY4dkzOXwllXSdYWAFJyHY7//ZulVEJyrsfTBmv8xcbGOkPWNzQ0OAMH5ObmUlhYGJB/iFhzTnBc/7///W+eeeYZZs2axeuvv05cXJzoukeMGEFFRQUjR470aKrbH4VCQW9vLzqdzmPb+pclh2mWORKRlRkZGT+xWCxYLBa/Jw+NRjNg4gi1Q/b48eN54YUX2LNnD/fddx/x8fGsXLmSESNGBF2vuzptNhuHDx+moqICjUZDfn4+kydPDrj9A3jlXof5yy9mL/rGasb88F/IyYBjfxPAVQwugeSYAe/mL5EagjqQYyMVIWraoIXH7miBv12MvbsbxaST4P8eBiSOcnfWlfDT9oHf22zw28s8nuZuZ9on1YegtgyyiiAneNPY9PR00tPTsVgsVFRU8PnnnxMfH8/o0aNF+eWJWTSw2+385z//4emnn2b69Om8+uqrAfsAgmO+SElJoa6ujqysLL/OEZQTb2Zsrsg5Z2SOVGRlRkbGT3p7e2lvb/c7PKtOp5Mk+3J/gcUfYWHixIm8+OKL7Nq1i3vvvZfk5GRWrlzpzMjtC19CidFo5NChQ9TX15Odnc2JJ57o93X6LdjWljkUGXCuFisdjYP1d8Ax3/4Szsh9myMxnHGgQn0gK8ahJJBcLUMZ4Rr0er1bU6CQYrVA8ZVQU4EicwTc9jJoHM+apGNi5nwo/wneXf3rdyoFXPkQjJ/uVxGu49TtO6SjBVb/H3z3ya/fHT0bVqyHOPcBVbzRvw61Ws3IkSMZOXIkDQ0N7NmzB4vFQmFhYdALOkI9drudTz75hCeffJLjjz+eF1980a15WyBKfFJSEpWVlU5TZk/nu5bd29vrNRhN/7+tVqscCEDmiENWZmRk/MBut2OxWGhtbSU317PJhevkERUVRU9Pj0/lx9ekF4zAMnXqVF5++WW+++477r77bjIyMlixYoXfK3/9aWlp4cCBA5hMJgoLC5k4caLHNgctxH7/8a+OyH0KB2rKsNdXoMgscH4dbqE53DsOkaTMiEGKfhJbRqh2jmJiYujq6gqvMvPyH2D3/0AfBXdvhMQ0v04T3e8KBVz2JzjjSvj+P448M8edCUn+O6X7XHRZ/X+w69O+3+3+BB6/Gv642f+2eqvjF4Tdmt7eXg4ePMiBAwfIysqiqKjIo9+It2fMbrfzv//9j7Vr13LMMcfwwgsveFQifLXNGzk5OZSVlVFUVOSxDNfvzWazqAUzYTdH9p2ROZKQlRkZGT8wmUxYrVbsdnsfZ0tvREdH09jY6PO4cAjExxxzDK+++irffPMNt99+O7m5uSxfvtxj9Jz+0XCqqqooKysjKiqKsWPHDliJdLcrEjRqjVORcU347axD7X0CD7XwfyTsOIQDqfJ/+CJQEz4xx8bExFBbW+v38UHzn9fh/Wcdn5c9AwXuFw/cEXC/Z+RJ64/T2eoII73rP44dmX4Ps90Giu8+gZoSyA7e5Kz/u0in0zFx4kTGjx9PVVUVO3fuRKPRMHr06AGRFT0pgF988QVr1qxh0qRJPPvss0EnufRWn0qlIj09naqqKp8+j729vaJ3/gU/G1mZkTmSkJUZGRk/MJlMdHd3+22bDI5JSQjdHClb+scddxyvv/46O3fuZPny5RQUFLBs2TK3So3JZOLQoUPU1taSlZXF9OnTPU6cIRHsjz/LYeZitfdVZJQKGDkVUrOlrzOE+JutXiYwwqFcajQazGYzEIaduX1fwjO3Oj4vugOmXxCSakJmjvnWw/DpRqit7Fdhvz9tjk0hu0TKjKd7olQqycvLIy8vj7a2Ng4ePMhPP/3EqFGjnOa3/cPsb9++nTVr1jB27FieeuopUWHl/elXT22Nj4+no6ODjo4Or344nZ2dooMNCG2SfWdkjiRkZUZGxgcWiwWbzUZnZ6fo0J8xMTF0dnb67WcD4TFfOuGEE9i4cSM7duxg2bJlHHXUUdx8882kpaXR3d3N/v376ezspKioiNmzZ4dNGetz7UkZ2K58COXzd2FXKVHYbA5FRhcNNzwelvZISST68MiIRwiT7ZrbQ3IaquDhS8FihRPPg0V3hqyqkI3J7vZfFZnULOhqA6Nh4HHKXzZgs0KTNNIdiYmJHH/88RiNRvbv38+BAwcYOXIkCQkJKBQKvvzyS5544glGjRrFmjVrSEtL82ry5c68Lth+zc7OprS0lNjY2AHvX6HO7u5uv/0g+yMrMzJHErIyIyPjA7PZjN1ux2Aw+OVr4jq5JSQk0NDQIEqZkVqR8aYcTZ8+nenTp/PFF19w3XXXkZ6ezvnnn8/xxx9Penq6pO3wh/7t3F80i/hbXyR3z8fQUgujpsIZV0FaYBO4t3ojRdFwzTAfKW2S+RUheWYwkas8oVAosBu64W9LoK0ZCsbDsqcd4ZGHGqdfClNPhx8/g/fW9c1h44oSmDobckYB4Y2Up9frmTp1qnMX+u233+b999/npJNO4vHHHyczM9OvNkiNQqFAqVSSmppKfX39gHlHqNNisfgMQe3pPSIHApA5kpCVGRkZH5jNZiwWC0ql0q9oWa7f6XQ6TCZTWNrpCVfh2B0dHR1otVqWL19OW1sbL730Et9//z033ngjycnJzuPC7fDe09NDfX0942fPhdlzQ1pXJCkNrtGgZCIPIQhAKJQZu80G634HpT9AQhLcvRG7PmaAv9iQQKGE1//suBaAvHFQuc9pOupkymxYvv7X0wYhUt6ePXt4/PHHSUxMZOnSpeTl5dHa2kpqampA+WqCRXj2ExMTaW1tdZsOoKenx69AFO7eI8Kc0NvbG95gFjIyIUJWZmRkvCCYmLmzXXadJLwJ+mLCufqzGh+I74W7tnV0dLB3716sVivjxo1zKi7nnXcen376Kddccw3HHnssN954I4mJiWF3eN+9e7fHaGlHMoEqjfJOTniIjo6moaEhNIVvegy+2AoqJdz+GmTkR7wiM2Dc2Wzw/tPw+v1gMkN8Asy9Fd54wPH7zU/DUcdBTSlkF4n2k5FyUWX37t089thjpKWl8fDDD6NWq6mrq2PixInOfDVpaWkcddRRg2aSlZ2dTU1NDYWFhX2+b25u9suHxx2Cb5DZbJaVGZkjAlmZkZHxQm9vL+BwtPRmYuZtck1ISKC1tTXgVTR3dQUjtLa1tbFv3z4Axo0bN8APSKFQMHv2bE499VQ+/vhjrrrqKqZNm8b1118vylzOFbECSFNTE3a7nbQ0/8LQRhLB3h9vDszezEJkRSY8hMwsZ+c/YeMvAv81q2DijNDUIzF9xl19Jay5Afue7Y4UUMecCtevhlVXgtkKx58Bp1zk8PgP0NlfCkVm9+7drF69msTERB544AFnDpq6ujrUajVKpZLCwkIKCwuprKxk27ZtpKamMm7cOEl2asS8D3U6HXq9nra2Nue7Wkh+GWxEMjmJpsyRgqzMyMh4wWKxOP8P9IUfGxtLXV3doNsnd3R08MMPP6BUKhk/frzPYAYKhYLf/OY3nH766Xz00UcsXbqUk046ieuvv150BB2xAsiePXs4/vjjRZ0TblwFkv6fQ4EvZcZb+wYTscqdvxnYBwOhDRqNxq3pT8BU7oPHr3F4wp99FZx1pTTlhgu7Hf67EdbfCT3dKHQ6uOpBOPNKRyCA+BSIjoXrHu+T6Dbc7N27l+LiYmJiYrj//vsHhD4WzIldESKgVVZW8umnn5Kfn8/IkSMHHNd/fHobr2LHcUZGBqWlpcTHx6NUKmltbXUGKxCDa6Q1AVmZkTkSkJUZGRkPCI7/RqPRL6HF2+SVlJREa2ur6PwEgQpwrucZjUZ++uknDAYDEydO9Dsim+vEd+aZZ3LGGWfw4YcfsmTJEk499VSuvfZaYmNjRbfNF5WVlSQlJRETEyN52VIieV4dHyiVSqxWq98rw6EIJBFIaGmxx0slAPpbl9eM9R7aEB0dTXd3tzTKTEczPHQxGHpg0gy4+m/Bl+kDMeGDfdJaD08vg53/dvw94ii4cwPkOhz6iU2EP7wN9RWDFk59//79FBcXo9PpuPfeeykoKHB7nM1m8xilLj8/n9zcXEpKSvjkk08YPXp0H2Wov2+ilONVqVSSlpZGXV0d2dnZtLe3e7wGb7hrk2BKLQcCkBnKyKNXRsYDriZmwk6EtwnK229JSUm0tbWJbkOgE6KQ32bv3r3s2LGD3NxcZs6cKSq0dP+6FQoF55xzDu+99x6jR49myZIlPPHEE3R1dQXURnfYbDYOHjzIhAkTJCtzMJFyl0YICTwYdUN4fXIC9RkSi8+M9R6IjY2lp6dHdH0DsFqg+EpHCOOMEXDby45ksQEQiON80MEmtr8PN53wqyIDcPgAPLzEEV761wohs0BU0VIoAwcOHOD6669nzZo13H333axbt86rEmCz2TwuFgjK/OjRoznllFPo6Ojgk08+6ZNENZg2+zo3ISEBo9FIW1sbGo3GL+XDk/O/62e73e7MnSQjM1SRd2ZkZNxgs9mw2WyAQ5kRJkB/nPPdTUoKhYKoqCi6urpCspvRn7KyMkpLS515YjwRyM6PQqHg/PPP59xzz+Xvf/87l1xyCWeccQZXXXWVqKSi7jh48CB5eXmDEkEoFEi9OitGmRlskyyBQMZYIMJ1OH2GvEUpFHW9L90Duz8HfRT8/g1ICMyhW6g3UESPla42eP4u+Owt97/XHILHroa//dv9734QzPWUlJRQXFyMzWZjxYoVHHXUUX6d580PxVWZV6vVTJw40bnrffDgQSZOnNgn+qNY/Lne3NxcvvnmG6ZOnepXme7uq7vANZKaTMrIDAJHhsQgIyMxwta78OIP1hZaoVCQmppKbW1tSJWZuro69u3bR0ZGBqeccorfOQgCEXyVSiVz5szhggsuYMuWLVx88cWcffbZXHnllQE5pppMJqqqqjjttNNEnyuGSPC9CASxOzORQrj62p/7KuW99/Ts+J0j5d8vo3j/OVAAy56F/CGyG7n7M1h7IzTVONruTga32mD/TscuzQj/FAkpKCsrY9WqVVgsFlasWMGYMWNEnW+xWDwK9e6UDb1ez7HHHktXVxd79uzBbrczZcoUUYs6YsakQqFArVZjNBqDXjhyxWazhT4RrIxMCJGVGRkZNwirrkajkaioKEn8IwQnS6PRGHQUmv50dHSwe/du9Ho906dPH1C+NxOhYIU7pVLJ/PnzmTNnDps3b+aiiy7i/PPP5/LLLxe12rdnzx7Gjh0bcuE3khUZb/dpqCoz4cKf+yrlvY+KiqKnpycw3669O1A8f5tDGVh8F0w/v8/P4VbM/MLY4wi3/I/nHH9n5MFvLoMNf/V8TkttWJSZiooKVq1ahdFoZPny5YwfP97jsd76rbe3N6Bd4djYWE488USampr46quvyMzMZMyYMX6Zgom5h3V1dYwfP566ujoSEhLcKh+BjguTySSHaZYZssg+MzIy/bDZbM4oZt3d3X0Ug2BNWTIzM6mrq+vzna8yvU1MNpuNH374gV27djFlyhSOP/54t4pSoO0Wc55KpWLhwoVs3ryZ2NhYFixYwIsvvtjHHMdTeT09PXR2dpKTkxNQO6VkMEMce6t7uCszkRZ6WggCIJqGw/DwZWCxwknnw8LbBxzS/5n35fsQcg58AytP/lWROWsprN4Gsxb80kA35ygVMGJsSJtVWVnJsmXL+POf/8x1113H888/71WRAe/95i1qpT/jLzU1ldmzZ6NWq/n0008lzUfU29uL2WwmNjaWjIyMAfOIgKfr89Z+IeeMjMxQRd6ZkZHpR29vr3OFvKenh4yMDOdvwQoQOp0OjUbTJwmnPyuw7qivr2fPnj2MGjWKyZMnB9UuTwRyvRqNhsWLF7Nw4ULefvtt5s+fz/z581myZAkajXvn5h9//DFinP6DvcehWjGPBGVmME30Im1HLTo6mtbWVr+Pt9vtKHoN8LdLoL0ZCiY4EkhKvHofCB7DilvM8M4qeOdRsNkhOQNuXAvH/dbxe1QszJwL27aA3RGhWaHAseN0+qWO40NAdXU1q1atoq2tjeXLl0vy/hMEek/KjJh7MHr0aEaMGMGuXbsoKSnh6KOPDno3XohkBhAXF0dzczMmkwmNRhP0rqTdbsdut2OxWI4Yf0WZ4YU8amVk+iGEZBZe7sGGZe5PZmYmJSUlxMXFBSSkGI1Gdu3ahVKpZNasWRGXI0DoC7VazSWXXMLChQt58803mTdvHosWLWLRokV9lJr29nbMZnPA2awHC095ZkIleKpUKmdQisFCzLW5eyakUIYixedJrVZ7VC7d+tIArPsdlO6B+GS4eyNERUb4cbcLJpX7YfV1UPqD4++Z8+DaRx1td+XmJyE2Af7zOgqLBTRaOPtquOy+PuVLcc9qa2t57LHHaGho4NZbb+Xoo48OukwBq9WKxWLxuOAiFr1ez4knnkhDQwPbt29nxIgRjB49OqCyenp6UCgUfRSijIwMamtryc/Pl6S9gjInKzMyQxF51MrIuGC1WrHZbKLD0Ppa9XI9RqVSkZSURHNzs2gBvrS0lLKyMiZOnNhnxyjScO07jUbDZZddxqJFi9i4cSPz5s1j8eLFXHTRRajVan788UcmTpwoquxIEGbDnWcm3Dszwfazp6h+wRIJ917oGyHCXH/fBbdtfGcVfLEVVEq48zWHz0kkYrPB+087/GPMZohLgGtX/WpS1h9dFFz/OFx2vyPnTEqWY8fGhWDvWV1dHatXr6aqqopbb72V4447Lqjy3CHkUJI630p6ejqnnnoqP//8M5988gmTJk0S/d6vr68fYIIr+LdI5YMpLN7JyAxFZGVGRsYFwW7YbrfT29srya6Hu4k8NTWVkpISkpKS/Iog09HRwa5du0hOTmb27NlDMsGZVqtl6dKlLF68mNdff525c+cyZ84cxo4dG1T+m+FCuHdm3EXpijS/FSnwV2lzlz09KioKg8HgO0LhVx/Axgcdn68thgknBdPkPu2RlLoKx+7Rnm2Ov485DX63zqGg+GpDTLzjn0i8XUd9fT1r1qyhrKyMZcuWMW3aNNHli22LlGUJ16VUKhk3bhz5+fl8//33VFVVMXnyZL/e462trej1erdzkeCD6e/ujK9nWE6gKTNUkUesjIwLrs7qPT09kkV36T+BKBQKp5mAL/bu3cuuXbuYOnUqEydOjJiJJtCJX6fTcfXVV/POO++wb98+HnzwQd555x3nrsNwVVZ8oVQqRSkzUvdjuBSZQOsJJsGsmONc2ydENPNKxV5Yfa3j8zlXwZlLA2mmx/ZIgt0O/3kdVkyHH7eBTgfXPwb3bvKoyEjVBncCdmNjI3/84x9ZtmwZ559/Phs3bmTatGlDKtKhu7Kio6OZMWMGCQkJfPbZZz4TKZvNZlpaWsjMzHT7u06nQ6lUDhiDYs1BXc+TAwHIDEUiQyqSkYkAXBNlAhgMBrex/APxA3D3e1xcHHa7nY6ODrcCXFdXF5999hkajYaTTz7ZGTDAU3nhJtg2tLS0sHjxYjZt2kRjY6MztPNgO7lHMmIE/aG6ixLouBqM642OjsZgMHg+oKMZHlqMvacHJs6Eq/4Wvsb5wNlfrfWOoATrboYeA4w7Hh7fDmdd+Ys3f4jr59d73tzczH333cfvfvc7zjzzTN58801OPPFEt+eEoj2hfK+6tr2wsJBp06bxww8/sG/fvgHHCcdWV1eTnZ3ttV2ZmZnU19d7rMvX9/3L9pQMVkYmkpGVGRmZX7BYLH1e7J5skd3tsgQ6yebk5NDQ0DBgV6KyspKvv/6aKVOm9HEaFeqJFL+RYDhw4AATJkwgKiqKG2+8kbfeeovq6mrmzJnDe++9J5lJ1ZFkHjXU7/mRhrcgAFjM8OhSqKtEkZUHt78Eammcy6VAoVDAjr/DrSfBV/8CtQou+yP89UPILnJ7jpTPketYbmlp4YEHHuC6667j9NNP5+2332bGjBmS1dUfd9fR29srmfO/O/q/h6Kjozn55JNRKpV89tlndHZ2Oo9TKBS0tLSg1+t9WgdoNBq0Wi1dXV2StNM1WbSMzFBBVmZkZH7BdUUqkMhUgQiaSqWS7OxsqqqqAIdZwY4dO2hqauKUU04Z4EviWkc4JpxQCc81NTXEx8f3URajo6O5+eabeeONNygrK2POnDn84x//CPo6jwTFTyZyEYIADOCl38OPX0BUNNz9BiREULS+rjZ4/Dp4+Apob4GC8bDqU5i/HLz48En9HLW1tfHQQw9xzTXXMHPmTN555x1mzZolaR3ucHcdBoMh5JEh3dU7ZswYjj76aL755htKSkoAxzzQ2trqd5CXjIwMyXLa2Gw22dRMZsghKzMyMjgEXiEkMzh2ZcRObIEK3dHR0URFRXHgwAE+++wzCgoKOOaYYyLCN8afawrkmAMHDnhMbhcTE8Ott97Khg0b+Pnnn5kzZw4ffvihz3r6R42TkQkHQhCAPnz0CnzwguPzrc9BvvdEjoEQ8Djf9SncOgM+e9shAcy/FR75LxT4H1EQgltMaW9v5+GHH+aqq67ihBNOYNOmTZx66qmD+uwajUbJfCTFEh8fzymnnEJ3dzdffPEFhw4dIicnx21/uOt3tVpNVFQU7e3tQbdFoVDIpr4yQ47Bl5ZkZCIAs9ncZ+IwGAwDTMxCtRNis9lobGzk+++/59hjjyUry7PDbTjaIxZ/Mk67HlNdXU1iYqLPcKJxcXGsXLmS1157jT179jBv3jw++uijAdftVGLaGmHzamxrb4LNq6FVuuzbvnBtUyjvi8ddAJlBY0AQgL074LmVjs+X/B6mnStJPZ7Gva/vnBh74Pk74L650FQDWfkOk7LL/gTavrm0/BnDgSgenZ2drFq1iiuuuIKpU6fy7rvvcvrpp0fEAkT/d74U+ZDEoFQqmTx5MikpKezdu5eOjg63x3lqV3p6esC7M/3bKu/MyAw1ZGVGRgYGxNfv7e0dIGxLMeH2nzR6enr4/PPP0Wq1zJs3j+bmZr99RaQWAKQuz9PO0oEDBxg3bpzf5cTHx3P77bfz8ssv89133zF//nz+85//9N2J+Xkn3Hg0vHY/ik82wmv3ww1TYd+XotsdiDISrpwzXn00jhDEOC97+z7YY/2lTxCAhsPw8KVgscKMC2DhbZLVE2iWd7vdDj9/AytPhg+ed3x51lJ47AsYd+KA4/2tSwxdXV0UFxdz2WWXMWHCBLZs2cKZZ54ZEUqMQP+AL8GOlUBMlNvb24mJieH888/nwIEDHDx40O8yVCoV8fHxPiOkuau3f1utVusR/56RObKQlRkZGfo6/wsmZ57MzIKZ5FwnjaamJnbs2MGkSZM46qij0Gg0pKenU1FRETG7LsHg7hoOHz5McnIyOp3OzRneSUhI4K677mL9+vXs3LmThQsX8umnn2K3WqH4/6C3B+yA1eb432SAx/4PRE7KkSRg9UelUgWV2C6QcRXuseip/8V+H+yx/XFnxmi3239VMA3d8NAlDh+Uwolw01Meo4GFrU8tZhQbH4K7z4DqEkjOgHvfwX7dYwMSW4aC7u5unnjiCZYsWcKYMWPYsmULZ599dkQ+Yz09PW6jV4YDu92OwWCgubmZESNGoNVqmTlzJgaDgR07dvitWKSlpdHU1BSwgi9EUlMqlXICTZkhhazMyAx7bDYbVqu1z0vdmzITyETc/5yysjJ++uknZsyYQXJysvP7+Ph44uPjqampEV1HsG0Mh4B16NAhv3ZlvLUlKSmJ3//+9zz33HN8/vnn/OGisx0r4v03tKxAYzUc+Dq4Rg8S7vogWGVGirF7JOJPYA13eWacK9uAbe2NULYH4pPh7o0QFeNXfSGjcj/c8Rt451Gw2WHmPFi9HY79Tcjr7+npYd26dSxevJiCggK2bNnCeeedN7DejmbY+FdYNh1WnAzvPu5QCgcBg8FATIznexYKhP6wWCxUV1eTl5fXp48mT55Mbm4un3766YBoZe7GqVKpJCEhgdbWVp/HCt/331UWoq7JOzMyQwn1YDdARmawMZvNKJXKPiuvNpvNr9wx/ioAwnE2m41du3ZhtVqZNWsWKpVqwMpYSkoKtbW1NDQ0kJ6e7rE+b/VH4s5OTU0NiYmJfgVW8EfYSk5O5t5776X9f1vgMTcKi1BEjzQhS8ONuz6IBDOzSI4OF2gYbk/+Xf6S+tkrKLf/3RHe+K7XIX2E17pc3zeSY7PB35+CDfeDyQLx8SiufQz7rPmhqc8Fo9HISy+9xIcffsjSpUvZunWrW3NTu92OorMF7jwN6g87lC07UPYjbH8PHvwQdNIlLPbnntrtdlReIrmFAmEnpKKigpycHNTqgSLZiBEjSEhI4KuvvmL8+PE+fSpTUlIoKysjKSkJ+FVB8Ya758ZkMg3aTpWMjFjknRmZYU//XRnwT6ARK4yYTCa2b99OQkICxx9/vNdoZVlZWRiNxj7RafxxAPbFYAqhYn1l/CXhmNnQPz+E0DVqNYw+RvI6B4tgd2akIFIVGRgkJf7LfxD33hrH5+seg/HTvR4e0rxHdRXwx/Ph5XvBbIHjTofVX4Zckent7eX5559n4cKFpKamsnnzZubNm+c9IuP7T/2qyIBj8cEOlOyGTzZK1rZw+bMFyuHDh0lJSfEaSU2IdlZeXs7evXsBz9eiVCqJjo6mq6vL7+v1NB4He+FERsZfZGVGZtjTP3KLzWaTPCxyR0cHn3/+OUcddRQjR450fu9NqBkxYgTNzc19IiVJkXNlMKivrycuLs5nBLOAiE2EBX0drQWLs6rpFzvMfo4QImFnJhAicadQEip+gieuA6Bj1sXw28sHpx12O/zndVgxA/ZsB30UXP8Y/OEdSPEvOmIgmEwm1q9fz4IFC4iLi2Pr1q0sXLjQ7Q6DKwqFAr58/1dFxnkdOJSanf8MSXtdkw67jkmr1Tooik5tbS06nW5APjF3qNVqpk+fjkKhYMeOHV4DxaSkpNDc3Oy1PH+i4clRzWSGCrIyIzOscbcrYzKZJM0EXV1dzTfffMP06dP7mI35QqFQkJ+fT01NDb29vc7vwo0Udf78888h2ZVxctHt8Ls1kDsKu1qBMqeQtiX3s7Y+iksvvZRvv/3WZxFDQeBWq9WDvjMTCJG4Ih407U0Oh39DD0yeRdMFtw5OO1rr4aHFsO5m6OmGcdPg8W1w1pUeAxAEi9ls5pVXXmHevHlERUWxZcsWLr74YnFmWgo3xwrNVXovR4pIY65jsru7O+w5Zurq6lAoFH4nxhQYN24cOTk5fPHFFx7fBVqtFqVSidFo9FiOOz+x/s+pv5E1ZWQGG9lnRmZY426V22w2+1xZ9GaH7fpbRUUFlZWVzJo1KyAFSaVSkZ+fT0VFBbm5uX12NsLlu+DOBE+MMNHU1IROpwut/bVCAb+9DH57mVMeSgQeXujw1Xn88cdZvXo1K1euZOrUqaFrR4gZqjszRxwWM6xaCnWVkJkHt70ETe3h9yfa8XfsT9+KoqPV4a9zyR/gwpshRL4fZrOZt956i7feeotFixaxZcuWwBd+ZsyBqr8NDNxhB0483+upoQgdHU7/kLq6OgAyMzMDOj8vLw+dTsf//vc/TjrpJLc73mlpaTQ0NJCXl+ezPHf9qVAohuTCiczwRN6ZkRnWuHtZm0wmn07q3iZT4beDBw9SU1PDjBkzgtrp0Wg05OfnU1VV1SfTuD/JKkOBmPIVCgX79+9n/HjpM6D7S3Z2No8++igPPfQQr776KkuXLuWHH34YcNxQ2D1QqVTDRpkJxkcs5LtsL94NP26DqGi4ayPEp6DT6byuhEtKVxusvh4evsKhyBSMh1WfwrxbQ6LIWCwWNm7cyLx587Barbz77rtceumlPt9rXu/DeTfAiHG/7sYI/088CU5ZJEm7/aW7u5u4uLiw1FVfX4/dbu+jyAQyXjMyMpg6dSrbtm0bEOkMHMlcrVZrQAqJsGAlRzWTGSrIOzMywxp3L3qz2UxcXFxQq6z79u2jq6uL6dO9OwP7i0ajoaCggIqKCrKysryuIopx+gy1AN/W1oZSqQyboOCN3NxcHnvsMSorKykuLqazs5OVK1cyYcKEwW6aKCLJHC6UY6h/uVLmkwmq3f9+Gf653iF8L38eChzjJyoqCoPB4NVcSZL+2vUprL0Bmuscy5HzlsNFd4LW/9xN/u6uWq1WNm3axIYNG5gzZw6bNm0SlSPK67XGxMPfPoL/vObwkVGrYfocmL0YNL4jHkpJZ2cnKSkpIa+nvr4eq9VKdnZ2n+/Fjgnh/iUnJzNt2jS++uorjj76aGeYf2GcJScn09zcLNqUzdW3yGq1hj3Km4yMWGRlRmbYYrfb3doECzsz/ScYfwWRH374AYvFwvHHHy9ZW8FhYiSYnPlSaPwhHDsR+/fvZ+zYsSGvxx2e7ldeXh5PPPEEFRUVrFq1CoPBwMqVK0Pr0yMhkaSsDoXdLHcE3O4fv4BnVzg+X3IPnHCO86eoqChaWlpCUy+AsQdeuw8+eN5hipWTDzc/6/CREYkvRcZqtbJ582Zee+01zjvvPN5+++3QBO+IioXzb3D8kxgx499gMBAbOzCJqJTPUH19PRaLhZycHI/H+Ktkuh4TGxvLjBkz2LFjB+PHjycjI8PZ5oSEBBobG0lPTw841YDFYvErnL6MzGAiKzMywxZX53/XvA9ms9mt+YQ/k9q3336LTqfjmGPchwMONiyrWq2moKCA8vJyMjMzw57kTQwGgwGj0dgnKagYghUkfJ2bn5/P2rVrKS0tpbi4GLPZzMqVKxkzZkzAdYYTX+NoqCoaEUt9BTx62S8JKOfCgpV9ftbr9c5AHZJz4BtH1LTqUsffZ10JS//sUAYkxGazsXXrVl5++WXOPvts3nrrrbA6xkupPIgpx5PALlVbqqurUSqVHhUZ4boDnRv0ej2zZs1i+/btmEwmRoz4Nc9RYmIiLS0tfXae3PWzHJ5ZZigjKzMywxaLxeI1q7c7PE04NpuNr776iuTk5JALwyqVymlylpKSQkJCQkjrC5Sff/6Zo446KmABRejrUAvlRUVFPPnkkxw6dIjHHnsMu93OypUrGTVqVEjrDRQhqavU4cNlvGDohoeWQEcbFE2Cm9YNiBQW6I6Z1zFuMcPbj8KmVQ4lKiUT+w1PoDjujECvxG19NpuN999/n/Xr13PGGWfw5ptvDkrCxFA+654idrn+JjU2m43Dhw8TExNDamqqx+OkuG61Ws3MmTP5/PPPUavVzuSaycnJlJWV9VFmxNQnLPrJiyMykYyszMgMW9ytOPma1Dz9/tVXX5GZmUlhYaHzuFBOmiqVisLCQiorKzEajaJtosUidtXQYrHQ0tISdOSwcE6go0aN4qmnnuLAgQM8+uijqFQqbrvtNoqKikJet+t48SU4aDQazGazKN+FcOLafldH4kDNNsUieVJKmw3W3ADlP0FiCty1AfTuBX0hdLa3aIi+fIGc/VKxD564Hkp/CVYxaz5c8wiKIPMm9VekPvjgA55//nlOO+003njjjZDs9rrek8ESjD3VaTAYQmJGZbFYqKioIC0tjfj4eED8tfdXwHydr1QqmTFjBtu2bUOpVJKRkeFMotnZ2emX76K7OiwWi6TpCmRkpEZWZmSGLe6UmUAEoW+//ZbU1FSnIiOUEwhiJjshD019fT2VlZWMGDFCciEhUPOHQ4cO9emPUCOlgHTUUUfx7LPPsm/fPh566CH0ej0rV66koKBAkvLdISZLuSAwR6oy40/+Ck/fSYHkq+zvPAo73neEPr7jNUgf4fFQnU5HT0+PU3gNBIXdDu89CRv+DGYzxCXAtcUOZUYi7HY7//rXv3j22Wc5+eST2bBhg1ufEX/L8ifggkCwpqNS39+Ojo6g7ld/7HY7vb29VFVVkZOT08dMLxBHf29/u0NIrrlt2zZUKhWpqamkpqZy+PBhv5QZd3XIyoxMpCMrMzLDEpvN5nFSFDPh7NmzB61Wy+jRoyVpVyATfUZGBm1tbZSVlZGXl+czR44/BKMc2O12ampqOPXUU4Nuh7+EQjAeN24czz//PD/99BN/+ctfiImJ4bbbbvMrbwNIo2C5K2OoJs4cbAK6Hzvehzf+5vh83eMw3nt0wujo6OCUmfpKWHsj7Nnm+PvY0+HGtZCSNeDQQK7Hbrfz0Ucf8cwzzzBjxgxeffXVoAX5cO6yhMIcrK2tzWMfBNLHXV1dNDQ0kJ+fP2gKgFardSo0xx57LImJiahUKnp7e0UvgghmrTIykYyszMgMSwRlxt/Jyt1xJSUlGAwGyaOWBUJiYiI6nY7y8vIBq4Fi6H+dgQgqhw8fJjMz0+nTEYrV1HAyYcIE1q9fzw8//MCf/vQnEhMTWbFiRR8nW3f4k1TVF+6OU6vVmM1mv86X+RXRY7niJ4fTPcB51zqSsvrAn4hmbrHb4eMNsP5OMPSAPgqufBDOuGKAb46AWHOl//73vzz55JNMmzaNl156icTERPHtjCC87fqJoaury6OZrtgIYM3NzXR0dFBYWOi3T1uozO70ej3Tp09n+/btnHDCCSQlJdHW1ibKJFm4NnnxRCbSkZUZmWGJ8HL2Zccv/N3/uMOHD9PQ0CBZHhl3iJ3koqKiyM/Pp7KyktTUVFGBAaRQYgRKSkqYMWNGn7KPBCZPnsxLL73Erl27+MMf/kBqaiorV64ckDPCF8EKLhqNJnRRsyQi2J09T98FUmZAbWlvggcXg9EAU2bBlX/16zS1Wi0++lNrPTy9DHb+2/H3uGlw89OQHbyZpt1u59NPP2Xt2rUcd9xxvPjii4OqxEi5sCGVAhBMwkzhWmw2G1VVVc58YGIWMkK5sxUdHc2JJ57Il19+yfTp090qbt7uiauvjpxvRiaSkZUZmWGJoMz0n1xsNptPob6+vp6ysjJmzpzpPMafwAFiVuPFHO96rEajoaioiKqqKrq6usjOzvZajpRKDDhWJmNiYo7ovARTp07llVde4dtvv+XOO+8kOzub5cuX98noHUrE7swMhsO11CG1QxmiewAWM6xaCnWHITsfVr4EKrXf/Sjq+d32Hjy3HNpbQaOGxffAhTeDBELj559/zpo1a5gyZQovvPDCgISKg0EkLmzY7faghHSDwUB1dTUZGRk+laJg3u3+lOuO2NhYTjjhBL788ktGjRpFd3d3nyAP3u6Ja/2yMiMTycjKjMywxJMNsKeJTXipt7S0sHfvXmbMmOE0I/Bngg4kgo2/uFvpGzFiBG1tbZSWlpKTkzMg4Z3USozAgQMHJE8+GalmasceeyyvvfYaO3fuZOXKleTn57Ns2bKQR5bTaDRhzf0w7MKyrr8LftwG0dFw9xsQ7whp628faLVajEajd1PPrjZ44S749C3H3wXj4NbnoGBikI2Hbdu2sWbNGsaPH8/TTz89ICRwuKLKRRKertFsNvsU0L31T1NTEx0dHaL8Y8T0tRilxxvx8fFMnDiRn376CaVS6TFiXf93rWv9cvJMmUhGVmZkhh12u92pzLgLQenO1lmhUGA0Gvn++++ZMWOG3y91MYK4mGP9EUASExOJjo6mqqqKhIQEZ56B/qFz/cVXnQaDAZPJJLkZS7gUmUCFuhNOOIENGzbw1VdfceuttzJq1Chuvvlm0tPTQ9BKR/hVMTbswQqqUgi6Q0Zg/vBFxz8FsPwFyBOvmEdFRWEwGDwrM7s+gXU3QVMNKIF5y+GiO0EbXHS6L7/8kieeeILRo0ezbt060tLS/DpvSNwX3Iwhux12fwY/fALaKJgxF0b0zfHl653a2trqMwCCu/4RzMq0Wi2FhYVh68NgniMhUMzu3bvJzc11W07/vnI1s5aDAMhEMrIyIzPs8Laq7S0Z4TfffMOUKVMG7HJ4Q4wgLuZYMavEhYWF1NfXU15ezogRIwI2FfBlInHo0CFGjhwputxQCrrBOtuLYdq0abzxxhts27aNm266ifHjx3PTTTd5TZYXKENFABUYEu3d8zk8v9Lx+ZI/wAlnB1SMXq+nra1t4A/GHnj1Pvjn89jtoMjOh5ufhfHTAm0xADt37mT16tUUFhayevXqkO8MDhZ9xpCpF/52CXz3X1ApHYrNmw/Dkj/AwpXOw3z5WrW1tYlefBFjViY1wfihKRQKxowZQ2lpKXv37mXChAl+nSN8DudusIyMWGRlRmbY4a8y4/oy//HHH0lLS3MKplIJ4OFYsVYoFGRkZNDT00NZWRmZmZkB55Tw1FabzUZDQwMTJ4o3k/F1/cH0kVgbdSmYMWMGM2bM4PPPP+f6669nypQp/O53v3P6LMhIh2T3tr4SHl0KNmDmPFiwIuCi9Hr9wAANP38Na66H6lIAFGdfCVf8BaICT1D57bff8vjjj5Obm8tjjz0WNp+tYJHknr23Fr7/r+Oz1WXHYMMDMPlkGONfhMn29na/+81ut1NfX4/RaCQvLy9gk6tAEmdKubs6e/ZsNm/ezIgRI7zuSrkzR5T9ZmQiFVmZkRl2WK1Wj+YHrgEAhP9ra2vp7OzkpJNOch4nlXAcLiFboVAQExNDYWEh1dXVdHR09AmfHCxVVVU+gw0IiJ2cI8FMKhBmzZrFzJkz+eyzz7jmmms4+uijufHGGyVRagZDSQsXnnYoQxYJytAFDy2G9hYomgQ3rfUYDtkflErlr9dgNjmSbm5aBTawJ2WguPlJOOb0gMpWKBR8++23zh2YRx55RHQ0vcHCU2RIf3E1dVJ8/Bq4GyYqJXz6pt/KTE9Pj1+7Kz09PdTU1JCcnBy00ij2+qV6xoX+1+v1TJ06lS+//JJTTz1VlMm0rMzIRCqyMiMz7PBnZ0Z48ff09LB3715OOeUUSdswWIKoSqUiLy+P9vZ2SktLSU9PH7A6F4jDfWlpaR9lzxtHogDuCYVCwamnnsopp5zCf//7X/7v//6PE044gRtuuEFU6Oz+CBHNjkSHXE/jIyTjxmaDNTdC+V5ISoO7NoI+OuhiFQoFtvKfUK65EUp/cHw5az6Kax6B+MCU2R9++IHi4mJSUlJ48MEHyc3Ndf42FBTbYNvX5xq72rDjcG3qdxB0tUvSLiEPWV1dHRaLhYKCAp8JiSM1WAn0vU5BAd65c6czKqcvXH1NZWQiDVmZkRl2eFNmXBUZm83G119/zbHHHota7X9oVn8YbB+RhIQE4uLiqK2tpa2tjezsbOdELXYybm9vR6vVehSsh4KgFWoUCgWnn346p512Gv/v//0/li5dykknncR1113n0wHZXf9pNJojQpkZDJObPrz9COx4H9QquOM1SM/1fY4vrFaSv3gDxd9Xg9kMcYlwXbHDfC0AfvrpJ4qLi4mLi+PPf/4z+fn5A44ZTs+XQqHAPv4kFN/8G2z93lU2uyNPjx90dXV5jTjX3d1NXV0daWlpfi889A/t74tQKT++npOEhASam5tJSUlh3759fkeglP1mZCIVWZmRGVYIk43rBNI/upew+rRr1y7y8vKcDqLhjFgTaH1iJ9KcnBx6enooLy8nMTHRL2f1/hPloUOHGD16tCRtGlRsNuhsgeh40IRGSVAoFJxxxhn89re/5cMPP+Syyy7j5JNP5tprr/Vo7uKu/8TmmgmWUCmkg2pys+PvDqdxgOsexz72hIEr/WKpq4C1N5Lw03bH38eeDjeuhZQs0UXt27eP4uJioqKi+OMf/0hBQUGwrQsKT2Z+4d6JsNvtcNHt8N3/A7v1V3MzBZA2Ak692K9yWlpa3Dr/W61WampqACgsLBRlVuXqMD9YSrq/Pog6nY7s7Gy+/vprcnJyfC6qgKzMyEQu0hjMy8gMEWw2m9N8QMD15S/4kDQ0NGAymSgsLASCDw/cv05vBGJXHkj7hDqio6MZOXIkVquV0tJSjEajX+eBY3Jrb2/3OwxsoIRUIbLb4f1n4OqxcMVouDQf1t8NvYaQValQKDjnnHPYunUrY8aMYcmSJaxevZru7m6/zhd2ZgKlvzLvT3uPJBTle+CJ6x1/nH8d/PYyv0LVesRuh//3GiyfDj9tx66PonXJn+AP74hWZH7++WeuvfZa1q1bxz333MPatWsHXZEB92MgmPdiUO/UUcfAXz6AcSc6/larYNZCeOgjiPYvwlhzc/MA/7WWlhbKyspITEwMOvKjPwSzcOWrTE8IdSUnJ9PS0sLUqVP5/vvvfZ4bySZ0MjLyzozMsMJisXhdBVMoFFgsFn7++WePDv++VtHcvfTDEbEs2PMzMjIwmUzU1NSg0+lIT0/3OZlXVFT0sd0PFSGdRDevhtf+/OvfvUb4xzPQWAl3bQi6eF/j7bzzzuOcc87h/fffZ/Hixfz2t7/l6quvJjo62nlM/+vXarX09PQE3CbX9hxpiopP2hrhb0sc93nKybD0AY+H+tU3LfXw9C3w9UdgB/v4adhvWkdrr5IkEX176NAhVq1ahVKp5I477mDUqFF+nzsUCXrcjZsGD34IFjMolOAl2bG7vzs7O53KjGBSFhsby8iRI8PyTAy2iWV0dDS1tbXk5OSQnp7Ozz//zJgxYzwe72p+LVXgGBkZqZCVGZlhhS+bZqVSyaFDhygsLPSYT0bwqzkSfUG0Wi0FBQW0t7dTVlZGQkICqampHq+zsrKSGTNm+F1+xPVZrwHeWTXQmdgOfPlPqPgJe974oNrsz7lKpZILL7yQ888/n61bt3LxxRdz1llnceWVV7q16w92Z2bYYjY5QjDXH4bsfFj5EqiCmAa3vwfPLIeOVtCoUFxyL1xwEwqVCntJSZ9DhbHf/xkoLS2luLgYq9XKihUrOOqoowJvTwgJ17Mruh61xuNP3hah7HY7FouF2tpalEol+fn5Ph38pWSwTCxd0Wq1GI1Gxo0bx2effUZOTo7XsP1CEABZmZGJNGRlRmZY4SsaS3d3N42NjV6jl/kyDRCr6EScgI/DQTQ+Pp7m5mZKSkpITU0dYF/e2tpKVFQUGo1nYaI/kXad1JWCscdNVCQc2s2Bb1Hke08uJxV2ux2lUsm8efO48MIL2bx5M4sWLeLcc8/liiuu6KNcq9Vq2X49ENbfCT9th+gYuOvNgCOL0dUGz98Bn73j+LtgAix/FrvLWFGpVH0Ev/4h38vLyykuLsZoNLJixQq/nbBDQSS9g/q3IxRt6+zspLu7m+rqajIzM70GAuhPJPVVsCQkJNDe3o5er+foo4/mu+++4+STT/Z4vBzRTCZSkZUZmWGFrxfxrl27GD9+fND1hDOPSjD4MoFKTU0lOTmZhoYGSkpKyMzMJCbGkeivtLSUoqKicDY3YDxeZ0yS+xOEQ+NSHH+GwV7ctX0qlYqFCxcyb948Nm3axEUXXcSFF17IpZdeik6nA0JseseRJbQB8OEL8K+XHff21hcgb2xg5ez6FNb9DppqHF6n81fARXcOCBqh0+kwGo1Oc0GByspKVq1aRXd3NytWrPCaiT1c98CfOgZrLHhbNArkPdvc3MxPP/1EVlaW0ydSivYMRWJjY2lqagIgPj6e1NRUDhw44HF3UKlUysqMTEQi7xXKDBtsNpvXF3F5eTlJSUlOYT3URIIzpb8mUJmZmeTl5dHS0kJFRQUGg4G2tjbRjv/BXHNITL1Ssx1+E8p+vyuAhGQ45jfA4N0rlUrFokWL2Lx5M1FRUSxYsICXX34Zk8kU8rqlyAsS6HGSC4w/fg4v3OH4vOReOOEs8WUYe+D52+G+uQ5FJrsAHvy3ozw30e8EZUagqqqK5cuX86c//YlrrrmG9evXe1Vk4MgSnKVGbN+0tbVRUlKC1WolOjrabYjrcBGq94nYPlEqlSiVSucu79ixY6mqqhoQBEZor7wzIxOpyMqMzLDB20vYZDJRUlLC5MmTwya4Roqg4m87NBoNI0aMICMjg88//xyTySRaqA7mmkN2X256CjILHJ9Vv7wSo+McCRS1uoCKlLqtarWaSy65hM2bN6NWq5k/fz5bt24Ni1ITKP39E/w5zp/jRVNXAY9eAVY7zJoP85eLL+Pnr2HlLPjgBcffZ18FxV/A2BM8nhIVFYXRaKSmpobbbruNe+65hyuuuIKXXnqJSZMmBXgxww93Y0HM+BCUmN7eXgoLC0lPT6e7u5ukJA+7shK10RuhzDMmti2xsbF0dHQADuVmwoQJ/PTTT32OcfWRkZUZmUhENjOTGTZ4e8nv2bOHcePGOe3cI4FATUzE+uuIRa/Xo9PpmDRpEjU1NSiVSjIyMpzmT0OOtBxY8xV8/SFU7IWUHJgxx2eIV18melIi1KXRaLj00ku56KKLePLJJ5k3bx6XXHIJF110UUidl0MxFgMpU/Q5hi546GKHg/7IydhvfELc+WYTvPMobFoFNiAlE363Do453eepbW1tPPDAA3R2dnLrrbdy7LHH+l+vxAxWPphA86644u4813I9Hdfa2kpLSwuxsbEUFhY6BXIhPL+U4zJSFqZAXORNcPjN1NbWOpW7jIwM9u/fT09Pj9NEUmwodxmZcCMrMzLDBnfhku12O0ajkc7OTo455hjn95GAlJO/lHX09PSgVCpJTk4mOTkZg8FAfX09AGlpaaKcaSMGtQamX+D45wZPCQPDRf+6tFotl1xyCUuXLmXLli3MnTuXJUuWsGDBgpAoNcGORW8CacjaYbM5cslU7IekNLhrI4qogSak7u6t3W5HUbkfnrgWSvc4vps5H8V1j0Kc9xX9+vp6nnjiCSoqKli4cCFz5szxv80hIhwCaH+FKRzhv4XIkgJ2u522tja3SoyAp2SZoW5rpOIuMuKECRPYs2cPJ5xwwoDnw2KxhLuJMjI+kc3MZIYN/aM/CZPg/v37++R0EGvWECpBIVJXwEpLS/s4zkZFRZGXl0d6ejqNjY2Ul5e7zYESSDLQSCFc/iNiEJSWq666ik2bNtHZ2cncuXN55513hn2kM7vdDm89Al9+ABo13Pm6YwfODQPurdWK4r11cNspDkUmLhFuW4/ithcgLsnjvWxoaODee+9l+fLlXHjhhWzYsIEpU6ZE7HMsNYNxna6+HK2trZSWljqTHWdkZLgNIdzU1ERKSoqo8qVmsEyZPdUbHR3dJ2FvamoqZrOZjo6OPn0ovMMjxXpBRkZAVmZkhg3u7IlNJhOtra3k5LgXdAS8xdUPlQlHpAr+DQ0NbvtLr9eTl5dHdna2M5N2V1eX8/dA7LmlIBL6MVQ5IoQVVZ1OxzXXXMM777xDc3Mzc+fO5d133x22Qodi+9/hrYcdf1y/2qtvSx/qKuCPF8DLfwSzGY77DazeATPn/Vp2v3vZ1NTEfffdxy233MLZZ5/Nxo0bmTZtGuC4R729vVJcUlAMVYXKV7utViv19fWUlJRgNpu9KjECzc3NfgcuCdW7I5zvJG+meALx8fFOvxkBwXfGnYnZUB1PMkcusjIjM2zonzDTbrezb9++AWEoA3E4FZvJOVgGazJpamoiISHB6/VqtVpyc3PJzc2lo6ODkpISmpubB02wPhImXnf9rdVqBwQA0Ov1XH/99bz11lvU1tYyZ84ctm7dOrx2asp+hDXXOT6ffz2cvsT3OXY7/L/XYPlJjjw0Oj3cuBruedvhJ+OGlpYW/vKXv3DjjTfym9/8hjfffJOTTjqpzzH9I5oNFhEZeMMPPLW7t7eXqqoqKioq0Ol0jBw5kvT0dL+SOZpMJvR6/aD4EA0G/tz7mJiYPjszgNMUr6WlZUB5R8I7VebIQlZmZIYN/V/AZrOZlpaWAbsMKpUqpC9rKVblBmu3obS01O+QphqNhuzsbAoLC7Hb7ZSVlVFTUzOoEbiG6iTsrt0ajcaj/XpUVBQ33XQTb7zxBpWVlcydO5f3339/yF6/37Q2wEOXQG8vTD0Flv7F9zkt9fDgxfDkLWDogfEnwurtcMYV4OY5a21t5cEHH+Taa6/l5JNP5q233mLmzJlui9bpdKJ3Zgb7Hg2mb5gvOjs7KS8vp76+nuTkZIqKikhMTPS7jZ2dnQ6fvqqDKJ6+FW4+0bET9/kmh0IbQiKpH92hVqsHvJsnTpzIvn37+nw3WDvsMjLekAMAyAwbrFZrn1Wln3/+uY+vjIBarcZsNqPVDswdIXDEJRT0A5vNRldXF6mpqaLOUyqVpKamkpqaSldXF7W1tdhsNlJTU4mL8x4xLFj636dgV6hDFaUsEPxJYBcTE8Mtt9zCVVddxXPPPcecOXO49tprOeecc4688Ws2waNLoaEKsgpg5Uug8jHFbX8PnlnuiHamUcPiP8CFN4FKNeDQ9vZ2nnrqKb755ht+97vfcffdd/vsQ71eT2trq6jL8BSq+oi7X25wt+pvs9loaWmhvb2d6OhocnJy0Gg0AZXf0NDACGMjrLgQrBaw2qD6Z/jhc9i/E655JOB2+ksgyT6l2s33Vm9CQgIdHR193u9CzjXXyGYgh2eWiTzknRmZYYUwKdhsNurr6xkxYsSAY9xFd+mPt7CeR+qqVU1NDRkZGUGVERsbS35+Prm5uXR1dVFSUkJjY2PIJkcpBcBQCJPhElBjY2NZsWIFr7/+Ovv27WPu3Ln8+9//HjBWI2Xsim6H3e5IaLl3B0THwO/f9B51rKsNHrsWHlnqUGQKxsOqT2HesgGKTEdHB48++ihLly7luOOOY9OmTZx22ml+3Ttvu2diCGVeEl/fhXNMuNZlMBiorq6mrKwMgMLCQrKysgJWZMChzGR+8ARYTNgtNrDjCLkN8MHzULlfVDvF9I23yH7e6pGq/33VGx8fPyBwi0qloqCggEOHDg1ol4xMJCErMzLDgv7CclVVFdnZ2W6PdbfdDr4nA2HlayisoAYisFRWVkqWNVuj0ZCVlUVRUREqlYry8nIOHz7cJ2BAKDjSJmFPq7aerjMuLo7bbruNV155hd27dzNv3jz+85//OI8Pxc6TFOe5U3b7HPPhevjoVVAAy9fDiDGeC//+E7h1BvzvHccMuHAFPPoJ5E/oc1hnZyfFxcVcfvnlTJo0ic2bN/Pb3/52SD7fnvDnWsJ5vVarlcbGRkpKSmhqaiIpKYmRI0eSmprqlz+Mz/Lbm1Ed/BZsv1gQCpdm/+Xz1x+KKi/UvpLh7HulUjlgEc9ut5OTk0NjY6PzbxmZSEQ2M5MZNrhus1dUVHhMYqfRaNw67fYPINAffyYeqc1FAi3PnV28t7IsFgsmk4nY2NiA2umtHUK+GqPRSGtrK/X19cTExJCcnOzV1E9ATB8MBUFUDBqNBpPJNCBhqT+J8u644w7a2tp45plnePrpp7nppps49dRTvSYCDSTTeSBjtL/g6k6QdZb5w/+wr7/DIZdeei8cf+aAY+12O4peA7z2R+wfrHccm1UAy54dEOmsu7ub559/nk8++YRrr72WFStWBDVuVCoVVqsVlRvTtVAx1MZ5Z2cnra2tWK1WEhIS3OaHCRaDwYBWr3f/o6DYDIF+c2c662tu8na+azkqlQqLxTIgV1VaWhpVVVXk5uZit9tlMzOZiEPemZEZFthsNufkaDKZsNvtfWyAXXE1DZHC30JMGYOZedpbWYcPH/YZvjpY9Ho9WVlZjBw5kpiYGOrq6igtLfUZCS3cglskrU4KykygJCYmctddd/H888+zbds2Fi5cyKeffhpQRD9PhPT+1JXDqqUorHaYtQDmLXffhp+/hpWzQFBkzr4KHvuijyLT09PDmjVrWLx4MUVFRWzZsoVzzz03aJ+FYCOa+Vt3JI1Lf+65yWSirq6OQ4cO0d3dTWZmJoWFhSQnJwekyPiqs66ujtS8Ipg4A5RujrUB084TVWck9HkgPjiecBfVDGDUqFFUVFQ4zx9W0RFlhgSyMiMzbBAmnvLycnJzcz0e56rMSBGSWcyEN5iTo7e6q6qq3PoXBVOmN+Li4sjLy6OgoACAsrIyKioq6OzsDKg8KdokEEmr3u7CM3vCW7uTk5P5wx/+wLPPPsv//vc/Fi1axBdffNHnmEgQ3PrQ0wkPLnb4vIyaCjetGbiybjbBxr/C3WdCdakjzPIfN8F1xRDlcG42GAw89dRTXHzxxYwYMYKtW7dywQUXDEgWGCjBKjOh3nUMhZ+fp/IsFgtNTU2UlpZSU1NDdHQ0o0aNIjMzs88ubCDtcZcPxZW6ujqHz9/VD4Eu+leFRqlwmJktXAE5AwPCeCOU7wJPfRDKOj0pM9HR0djt9ogIMy4j4w7ZzExmWOA6MdTW1jJjxgyPx6rVar+ddiNOwAsCT5Ok2WzGbrej92Ci4W1lMNjoYUqlkpSUFFJSUjCZTLS0tNDQ0IBOpyMxMZGYmBiPJhODIQyEG61WS2dnp18+L/6M1ZSUFP74xz/S2NjIunXrWLduHcuWLWP69OmR1W82G6y53uGwnZwOd74Ouqi+x1Tug9XXQemP2O2gOHkBXPuIMzCA0WjklVde4YMPPuDyyy9ny5YtkpuC2e12dDodbW1tkpYrJf1zbwl/S2USa7FYaGtro7OzE4VCQUJCAgUFBT4TEQeDu/ONRqMjOlfhJEfo7Q+fc0QwS0xH8ZtLsR93VlB1Ss1gPG9RUVHU1ta6vff5+fmUlJQwYcKEI2rekzkykJUZmWGBYKbU1dWFRqMZYBMs4xlvwRIgNE7j7gIpaLVaMjMdCQwNBgPt7e3U19ej0WhITEwkLi6ujyB2pOBNqNRqtZjNZsnvQVpaGvfffz8NDQ2sWbOGNWvWsHz5ck444QTfJ4eDN/8GX/7TEU75ztcgzcUE0mqF95+CDX8GswXiElFc/xjMmAs4Ei6+9tpr/P3vf+fSSy8NiRIjoFAo0Ov1fXbPIjnMslRhzN0pMPn5+V4VmFD2S0dHhzPMMAAZebD0gV/rDkmt4SHYfnM931sAm5ycHEpKSpznyMhEErJEJzOsKCsr8zsiVyQJHYPZlsOHDzNt2rSw1efPdUZFRTmS3+EQTtva2mhqakKtVhMfH098fLxbwSmS7qm/eGuvkBMpVKSnp/PAAw9QX1/P448/zhNPPMHy5cs57rjjQlanT7ZtgbcfdXy+4QkY46Jg1VXA2hvhp+2Ov4/7DdywFlIyMZlMbNiwgS1btrB48WI2b94c0kUNYawplco+PgZiI2ANlfHqqsAAfikwroTyOuvq6pwLIYNJKO6n1LtYOp0Og8EwwKdUqVSiUqkwmUwed+llZAYLWZmRGRYIK0lNTU1MmDDBx9GOF3egE4+Y8/w9drAEGmFFuX+0rEhCp9M589+YTCba2tooLy9HpVI5FRth5X2wExIK5m9S1RmudmdkZPC3v/2N2tpap1KzYsUKjj766LDU76TsB1hzo+PzhTfCaZc4Ptvt8J/X4cW7wNAD+ii48kE44wrMFgsbX3mFd999l0WLFoVciRHov8sRyD2PlPHqiZ6eHjo6Oujp6UGlUjl93ZRKpWS7BVLQ2NgoqQIeaCjzSFdM7XY7sbGxdHd3O5UZ1zGQkpJCXV0deXl5Q0rRljnykZUZmWGBazjJ/iuF7l7Ker0eg8HQ1zThF3xN8FJFlokEqqqqQh7FTEq0Wi3p6emkp6c7V4oPHz6MzWYjOjqauLg4oqOjvZrT+Jqkg5nEQ5XPRWo8jfGsrCweeeQRqqureeyxx1i9ejUrVqxgypQpoW9UawM8tAR6jXD0qXD5/Y7vW+rh6Vvg648cf48/EW55GktqLm9t3Mibb77JggULePfdd0UlXOzfB8HcdyERrz+hxv1pVzhwd/+tVisdHR10dnZiNpuJiooiPj6ejIwMydoVivD1ZrNZ0gWZSH9+xeJq2hsTE9PHx8t1HGRnZ3Pw4EFZmZGJOGRlRmbY0NTURGJi4oDv3b2QhQhE7pSZcNsLD+akUVVVxYknnjgodQeLWq0mNTWV1NRU7HY73d3ddHR0UFdX51xFjo+PHyDgBhs+O9z3SwhYIeVug68xnpOTQ3FxMRUVFTz++OO0t7ezcuVKJk6c6DzfUx8E1D9mEzxyOTRUQVYhrHgRVGr4Yis8eyt0toNaCZfci+XcG3j73XfZsGGDU4kJRIno3wfB3FOtVktvb68kyky4EK7XYDDQ0dFBd3c3SqWS2NjYAdHH3J0bKaG8Gxsb3b73BaTwOYHIUHCkyDumVqs9hl5OTEx0+kHJfjMykYSszMgMC+x2O01NTaSlpfl1fFRUFM3NzSFulX/0n5xCPZEIE6IQxSySBTB/BQmFQkFsbKwz6afFYqGjo4Pa2lrMZjN6vZ64uLg+QQS81SmYIQp/S+U4HQhCrplQmU55E5Dy8/NZvXo15eXlFBcX09PTw8qVKxk/frzH8kT3j90Oz90G+76C6Fj4/ZuO7x+7Fv73juNz4USsNz/Ju9/s5/WFC7ngggvYvHlzxJhH6nQ6ent7iYuLE3XeYCxkmEwmOjs76e7udj4b8fHxpKenizKfHUxc35G1tbVkZWV5PTbYugaLUL17hAUSjUYz4F7qdDq6u7vdLvTJyAwWsjIjM2xobm5m5MiRfh3bPwKRK1IrE2IFFm91SyH8COfX1tYG5DQbbpv+QFCr1SQnJ5OcnAz8uvrc2NiIQqEgKiqKmJgYYmJiBkS66n//B3tFVlj195QENlj8ub6CggLWrl1LWVkZxcXFGI1Gbr/9dsaMGRN8Az58Af7fa44M7SvWQ1M13D8HmmpBCba5K9isPYpXb/0D55xzDm+//XbEOSjrdDp6enpEnyfFs+zrXdXb20tnZyc9PT1OU7iYmBiysrJEmeVFEq7X3NbWxqRJk8JabyjfCf2jj4WCqKgouru7SUhIGFB3dnY2tbW1fi8MysiEA1mZkRkW2O12rFarqF0G16zz/fMvuCs/0IlFyglJSrv1qqoqpk6dGlAbhoIZgus9E6KjZWRkYLfb6enpoauri+bmZmw2GzqdjpiYGGJjY30LeN3tjtDBn74BPV0weRZc/HsYc3xIrkNYKXW9LhgcJauwsJB169ZRUlJCcXExNpuNlStXMnr06MAK3P0/eOFOx+fF98B3H8E/1wNgyy7gvQlLeOmd/3Hmmcm89dZbzgh3kYZOp/M7uamUuHsGjUYjXV1ddHd3Y7FY0Gq1xMbG9lFejhR/CIPBgFqt9hhRTerrDEefia0jEB9AvV7vVplRKBSkpaXxww8/RPz7XWZ4ISszMsMCIc+AmIlAsB1WqVQB+VGEUyAIhdOsyWQKeLV/KEx0nvpLcIJ1NaMQBEDBLE2j0TiVmz6mTGYT/PECKPsRbL/0we7P4MfP4a8fhkSh0Wq1tLa2+ryucDJy5EieeuopDh48SHFxMUqlkhUrVjBqlIgM63XlsOoKRz8ePRs+3Qg1Zdjs8I+803ihvJffjNXyxhtvRKzJi6DU9w/PHEgZgWC1Wunp6aGnpweDwYDVanUq5jk5OR5NEyNhDEmBr5DM7q5zKCzEiEHs3CUkSG5paRlwrBDtrLe3V9I2ysgEi6zMyAwLGhsbSUpKEiX0CxHNBD8LsYRTIJA6hHRdXR2pqanBNuuIQa/X9zFdMplMdHV10dDQ4Mzzotfrif/xY2JLfuh7ss0O2ODNB+FPW3zWJVYx1Wg0WCwWv48PJ6NHj+aZZ55h//79PPzww+h0Om677TYKCgq8n9jTCX+9GDrbIDkDdn+C3Qr/NCfyXO8ITi2aycaHrgn42QwXUpgj+itYCzuK3d3dTsVFqVSi1+uJiYkhNTU1ZMlBpUDqsOXgMJUVu7s82IpMKEL7i0GhUDij77n7Tfh/sPtJRsYVWZmRGRYYDAa/nLtdEZKHRbrAFCje+qKqqipw06AAGGpmLVqtto/Pjd1ux2g0oti7A7tSicLFRBFwKDQ/fuFX2WJ3+cIhWFgsFiwWCzabDZvNhtVqxWq1Oj+7fi98dkWr1XLXXXdRUlLCnXfeSXR0NFdffTXZ2dkD6urp7qbrr5cSe/hn7EolNNfzUQus60hhyplzeOCyK4iNjaWhoYGGhgbneUqlss8/hULhTPQnfKdWq53//NlxlRIpo84J403YdTGZTE7FJTo6muTk5EEJCBEMNpvNaaIqVXnedpcj9Z0jdWh/X9cZyPtDqVRisVgiJsCGjIyszMgMC7q7uwdEtPH1Eo+KiqKrq8vtbzabze/M1lITjkm4u7ubpKQk0edJERp0KCIEDSA51eGo7garVk/ZoUNERUWh1Wqdfjr+rJb7E2FNDDabDbPZjNlsdioqrv9clRGFQuFUCFwVA5VKhUajQafToVKpnP+E390xcuRIzjjjDH788Ucee+wxEhISWLlyJSNGjHAeE91aTexPZdjt8HGTjadqVZx45nlseHAN8fHxXq/J9V9/JctisdDb2+v8bLVaB+ycCNcgKDsajQaNRoNWqw1aOdBoNPT29ooqRzD3NBgMGI1GDAaDU+jX6/VOP69QRxwMh9O51OXW19eTkpIibX0NVbBlNXz7EWh1cMoiOO8GiIpMM0d/3see3h0qlcppZt3/+JiYGDo7OyPWvFNm+CErMzLDAoPB0GeFzh/hT6vVenTaHSxFBkIv+Le2tooOISsw1JWSoDl5AWxZO/B7pQLV6ZcycuRIent7nT44zc3NTl8KjUbjNGfT6/WiIkkJZiHCOWazGZPJ1Oefq9mIsEuh0WicwntUVJTzu1CP70mTJvHSSy+xe/du/vCHP5CamsqKFSvI2fUB1JbxiRLWVcHxYwt58f+9SWLBUT7L9KZE+YugzFmtVmcfClG+XE35lEqlU8lx/d/bPRPCM3sSAF2Vlt7eXsxmMwqFAq1W6wwdnpaWNiimYoNp9hQo1dXVFBUVuf0toN3M+kq4YzZ0tjp2Wu3Axr/C1/+CBz5wKDeDhKd+D2ZHJioqym2uNSHMfXt7e0DRLmVkQoGszMgMCywWSx8hwB+TnUiZlMNNTU0N2dnZQ8ouOmLaWjgZltwDG/4Kql8Ea6sNCibBxXc5V9TdhQ4WlJyenh5aW1udwrNarUan06HVap3/q1Qq5/G9vb00NjbS3t5OdHQ0CoUCtVrtFLCjo6NJTExEq9X6bZYSKGKF2SlTpvDKK6/w3Xffcdddd2H//mO+aoMJcfDCqgdJnHMdCpEKSjACtWCC5qscq9XqVBAFJcRV4VEqlWi1WqciIty3lpYW1Go1vb29zvOFXTBBmY2OjiYlJUXyJKiRGGkrlHR2djrNQPsT0Bh/txi62n4N7KHAodAc+Ba2bYbZiwNtqt94es8F6jPpDW+Jo+Pi4ujs7BRdp4xMqJCVGZlhQX8zCeFvXzlb+tu5D4bQ7NrWYIQFf89vbGxk7NixkaEc+ElEtXXhbXDcGfC/TWDohIkzYdr5oPnVFMjdvdDpdOh0uj7hUM1mM52dnXR1ddHU1ERXVxdmsxmr1eo08YqLiyM6OrqPyVEgq/dCm4IZY4EKVd3d3ZhMJpKmn4vq/c30zLyI3pPmilZkXNsQ7LPq7VpUKpXTTNAVi8WCyWTCaDTS2dlJa2ur89pMJhNtbW3k5eU5E7SmpqYSHR0dsp2w/iHlI0nZcEXqtrW2tkrv67jzQ8fChJ2+pqRK4JuPwqLM+DOepepLnU5He3u729/i4uKoq6sLug4ZGamQlRmZI57+/i2umdv709+G3jV5WDgnElekslX353zBkTiSox6FAsnvW+Fkxz8P9K/LZrM5d2WEVX74dVdGyMCu0+n6nCv4VLS2ttLS0kJLS4vTTEqoRzAjE0zIBGVHMDHz1KZwsGPHDp544gnGjBnDunXrSEtL4+KLO5lz2VJWrFhBUVERt9xyC+np6aLLllLBtVgsTh8jYQdG+Oxaj9DHGo2G5ORksrKy+vizlJaWUlBQ4NxR6+zspLGx0Rm+Wdi1i46O7nNesL5okaDE+ApiIWV5VVVV5OTkiC7Ta31qtUOHGVClEjSR4wgv1b3W6/XU19e7/U2n0wUcalxGJhTIyozMEY/RaAw46kpsbCwtLS0kJCT4NUlEgtAQDLW1tQMCJUQSoVpdDud9s1gsGAwGenp6MBqNWK1WFAoFOp2O6Ohop9LiD8J5qamp9Pb2uhXg+gviXV1dfXxDXMsSHN99/Qt2J2Hnzp2sXr2aoqIi1qxZM0BZmTZtGhs3bmTHjh3ccsstjBkzhptvvjnocOGuwQD6/2+z2Zz/C/0ijDfXKGgajcaZPFWj0YiOMqdUKomOjh4QZctqtToV2vr6eqdC62p+FhUVNaj+esEQqkUedzQ3NzNhwgRp6zvlItiy5lczMwGbDU66QNK6vLZDAusAf96jSqVyQFRC193biNoNlxn2yMqMzBGPzWZzhmEV+wKOioqSLEHYYOcP8Ifq6mqmTJkS9nr9ZaglubPZbHR3d9Pd3Y3RaMRmszl3W4Lxjeg/PoQEr+4QhPD+JlHuyhRM2Fz/CRHAXMMx9xdyBARBRxC4hc/C/z/++CPPPfccOTk53HvvvaSnp2O322lqanKWYTKZaGhoQKFQMGrUKNauXctXX33F1VdfzdixY7n66qtJSEjoE7lMyE8ifPbUV64hml0jlwnRyoS/pVAYPPk2eIqEqFKpBiRrFfrDYDDQ2dlJQ0MDNpvNOX5iYmKGfHhcqd91XV1d6HQ66ZW+OcscpmaHDzh2ZxQKh2Izcx4cd1afQ0P5TpKiXH/7u/8usPC3EOlMRiZSkJUZmSMeYYUpmEkgmFDMgfi7DIYiY7fbvUZbChdiBYFIUmSEZJquuT+ioqKIjY0lPT1d1BiS2izHF0LkrGAQlApXxcJms7Fr1y5Wr15NVlYWDz30EGlpaR7vm7Db5MrJJ5/MrFmz2L59O3fccQdTpkzhuuuuIyUlZUBumUjZHXV3/4QIie4CQHhCCCTg6kvV29tLd3c3jY2NmEwmp0mssOMTqhwzoUDq+1VZWUlubq6kZQIQlwSP/Bc+2Qjf/wd00XDSHDjxfOj3XEfSOylQFApH8kyTyTQgeMhQ3R2UOXIZOm88GZkgCGYVKSYmhu7ubrfhiv1RUoS8EJFOW1ub1zwe4WKoCAJCxvWuri5nxnWtVkt0dDRpaWlBr5iLHTMKhcJtXohw4qpMqFQqdu/ezWOPPUZqairFxcV++TFoNJo+grsrZ599NmeddRaffvopN910EyeccALXX389iYmJUl6GJLi7f4JwKEaZcYcQLMI1aWtPTw/d3d3OSHiCOVxcXJyoMN9DncbGRsaMGSNpmc73fFQMnHON498QIdCdL7vd7gwn7m6RY6i8p2WGB7IyI3PEI6zYBooQU9+dMiOVH00kRBqqra0lIyPD53GR0NbBwmAw0NHRQU9PD3a73bkSnpqaGjIlwt/+FgQPTxnPw8mePXsoLi4mMTGRBx54oE9SzGBRKBTMnj2bU089lY8//pgrr7yS6dOnc/3110eEMu4NrVYrmdmqKwqFYoCJmslkorOzk9raWmcOIiGK2lDauRFDd3f3gMAWUhCO913/51yq92wwZajV6j75qaQqV0ZGao7MN5qMjAtKpdJp+hLICzg6OtpjVBepiISJobGxkdGjR7v9LRwZwCMRk8lER0cH3d3dWCyWPskLw2Vq4W9/R4Iys3fvXoqLi4mJieH+++8nLy8vZHUpFAp+85vfcPrpp/PRRx9x+eWXM3PmTK677rqAk772R2rFXafT0dPTI1l53tBqtaSkpJCSkgLgjJ5WXV2NxWJBp9M5d24GYzcvFIsioTAxG8o5enyZ7Pr6Xa1WYzQaB3w/nBe0ZCITWZmROeIRfGYEpcYT3l7swShDYhmMiULwbxgMcxQprzfYsqxWKx0dHXR1dWEymZyr2Tk5ORG3mt3/WnU6Hd3d3YPSlv3791NcXIxer+eee+5xm3nd9fmS8p4rFArOPPNMzjjjDP75z39y6aWXcuqpp3LNNdcQGxsbVF1SP4dardbjSneoEUzThIhwQi6cw4cPY7VaiY2NJT4+3megCKkItG+93c+GhgZmzpwp+jxvDJbQLkW9vkzBfP3uKbBIJAddkRmeRNbsLCMTAgTn4GBe7NHR0fT09ITFOX4wJs/Gxka32bKlSKToCynLDqQsk8lEe3s7nZ2dKJVKYmJiRIVHHiz6X6ter6elpUVUGcEqFQcPHqS4uBilUsndd9/tVolxrUsgVKvQ5557LmeffTYffPABl1xyCaeffjrXXHONX7tVoTLzcSXcUaC8Jc0UctoIwRi6urpoaWnBaDSi1WqJj48nLi4u4py9Pd2Tnp4eryZmns6Tdxk8IySN7k9vb2/YlF4ZGX+QlRmZIx6lUonFYglqNSk2NpbOzs5Bj/QVKurq6sjMzBzw/ZE6yff09Dh3YATBLT8/36e5TSQLPp4ED3cEq6SWlJRQXFyM3W5n5cqVHs0TAyHYFV+lUsn555/Pueeey9///ncuvvhizjzzTK666iqvAlj/vjgShF/Xdvpqs+BPAw5htb293akcx8bGkpCQEHC0u3D0WXl5eUC+WVLtgIT6+gZjN0SlUrl9p3R3dwcdxEJGRkpkZUZmWCB2dbG/j0hMTEyfXBihJtwCU2trK5MnT3ZOllLWHQnCn91up7Ozk/b2dkwmE1FRUcTHx5ORkdFn5doXg30drrgTbvwVdgIV1MvLy1m1ahVms5kVK1ZIHjXKW9vEolQqmTNnDhdccAFbtmxh0aJFnHPOOSxdujQoQSzY9gUSqj3U9G+LTqdzJjIVTC/r6uowm83ExMSQlJQkaufS0+6QlNTV1TF27NiQlO2LcNxLqaJiirkHKpXKrYl1V1eXZH5pMjJSICszMsMCIVldIMnCIPggAmIJp6AjrLyFqs5gyg1GuRJMZ4RQtTExMaSlpXkUZCNJuHTF05hzN54FM6ZAHbo99UFlZSWPPvooBoOBlStXMm7cuIDKHwyUSiXz589nzpw5bN68mYULF3LBBRdw+eWXh9WUULiParUak8kU8WaMAiqViqSkJJKSkpyLAvX19ZjNZmJjY0lKSvJ7xyZUz1h7ezsxMTGSmsR5M9EbDKRSZPwxue5/Tv+6e3p63O7ky8gMFrIyIzMsiImJobOz02voVl8Tll6vx2AwREToW3cEaobQ2NjodAqONAKZwLu7u2lpacFkMhEbG0tGRkZECI5SOyC7+17qiGaHDx+muLiYjo4OVqxYwcSJEyUpdzBQqVQsXLiQuXPnsmnTJhYsWMDcuXO59NJLg04W6g/C/RISZ7qOyUgQlv1BoVAQHx9PfHw8drvduWNjsVicio3YICJSXHtFRYXkkfPEmOhFGp76NJA5wp0fmcFgIDY2Nuh2yshIhazMyAwL4uPjaW9v96rM+DL/SEhIoL29PWKVGbGTlHCtjY2NfuWX8VVOsARTjtFopLW1le7ubqKiokhNTY04B9Vw+GAIeUyCHaPV1dUUFxfT0tLCihUrmDx5svO3oSJ4e0KtVnPxxRezYMEC3n77bebPn8+CBQu45JJLwhLNT1BmXBGzYxwpUaQUCgUJCQkkJCQ4FZuamhqsVitxcXEkJSX5FQFQirHU1NTEpEmTgi4nGCLhPSgg1btGsGjoX67RaJSVGZmIQlZmZIYFCQkJ1NbW9vnOnWDgbQs+JiaGurq6Ad8PVeFOaHNLS4uoFff+/SZliF0xWCwWmpubnU78SUlJZGVlSdKWcCLl2NHpdHR1dQV8fm1tLY8//jh1dXUsX76co48+esAxQ3Gsu0OtVnPJJZewcOFC3nzzTebNm8eiRYtYtGhRH6VG6udbq9XS2dkZ0LmRoshAX9NdV8XGZrPR3t7O4cOHUSqVJCUlSZ7M1PUd1NTUREJCgtt7NBTD6YtVNnyFOw/GVM5ut7s1XTWZTHIAAJmIQlZmZIYFCQkJlJSUOF/o3vLJeEOj0dDb29vHRGQoC3dCmFgxtuZSOaIGSkdHB62trdjtdpKSkkhPT4+oezCYym0g4ZkB6uvrefzxx6mqquLWW2/luOOOk7xtUu0qSN2/Go2Gyy67jEWLFrFx40bmzZvH4sWLueiii1Cr1ZLfS2H3bKjjyadEUGCSkpIwm800NzfT0NBAbGwsycnJAZn09R87rp/LysoYOXKkx/MGnQPfwIYHYM8XoIuG2Yvg4t9DXFLQRfuzqORtrvOnfzQaDRaLZVASq8rI+IuszMgMC+Li4uju7nbuvAS6+pWQkEBbW1tAZllihLlwmZM0NTWRlCRuUh0MUwqz2UxLSwudnZ3ExsaSnZ0tiUmQ1Cuqg6XIuDqXi0nKWF9fz5o1aygvL+eWW25hMb00TQAAtydJREFU2rRpIW2jFIjpXzH3Q6vVsnTpUhYvXszrr7/OvHnzWLJkCQsWLJBUkNNoNCHLNSPWaV2q8eqpDI1G43QU7+zspLa2FpvNRmJiIomJiX7X7Sn4is1mo6ury22OrFDhrh0er+Pgt/D7s8BmA5sdejrhw/XYf/wCxapPQTt4vnz+9r3wThEW8Nra2khISAhl02RkRBNZ2bBkZEKEsMLqav/rz+6MMIkKxMfHO7Osh1LZCJc5SWNjozMEazjxdyLt6OigvLyc6upq9Ho9I0eOJDMzUzLfBqlDUA8WYp2VGxsbuffee7n55ps599xz2bBhQ0gVmWAJtG8Dub9arZarr76at99+m9bWVubMmcM777wT1mSXgSJ2HIRT8Y6LiyM/P5+8vDwsFgulpaVUV1f7vUvlrq1VVVVhj6rVvx1ex+abfwOb1aHICMdb7Sgq98P2LT7rigSzQpVK1WfebGhoGJQ5Q0bGG7IyIzMsUCqVxMfH09jY6PwukMleoVA4E4kFYn8cabS2tkZcJDOr1Up9fT2HDh2ip6eHnJwcCgoKPNrFDzu+2AzLZsD8FLhmImxZAy6CtqdEdwDNzc3cf//9/O53v+PMM8/k7bff5qSTTpKsaaEa4/7cd3d1B9IeoS69Xs/111/P22+/TUNDA3PnzmXz5s1OwS4Sn+ehgEqlIi0tjZEjR5KUlER9fT3l5eUB+RFVVlZSUFAgfSNF4HVs7vkcbH2/UigAlcJhdhZM2WHEdaw3NzcHFTBGRiYUyMqMzLAhKyuLmpoan8f5mkDi4uJob2+Xqlk+CeWEZrVaA9rlCEWbTCYTVVVVVFRUhGQX5ojg3y/Dqquhci9YbdBYDS//CZ5e7jxECCHuSktLCw888ADXXXcds2fP5q233mLmzJmSNy/QceHJHyLYuqUYp1FRUfzud7/jzTffpLq6mjlz5vDee+8Fpcyo1WqPCmc4iBRFLDo6mry8PHJycujq6qKkpITm5ma/2mc0GrHb7REXtbAPUV4SS0ZHTtJJMeZ+BoOBmJiYELdIRkYcsjIjM2zIzMykra1N1DnuJtWEhISAoxF5K1eKY8XQ2dkZcEQaKdvU09NDRUUFtbW1JCUlUVRUJO/CuMNsgtfvc3x27X4F8J/XoLYMcCgzRqMRcNi3P/TQQ1xzzTXMmDGDd955h5NPPjni+nYo5PSIjo7m5ptv5o033qCsrIy5c+fyj3/8I6BnQaxvk9REQh+7tkGj0ZCVlUVhYSF2u53S0lJn/hpPlJWVkZ+fH46mOhHdb6ddAkqXc4ShYrXDyRdJ1q5g8TdIgJBnTQ4GIBNpyMqMzLBB8JvxZ0XUW+Z5lUqF3W7vY0csFjErYaGiubmZtLS0kJXvi/b2dkpLS2lpaSEzM5P8/PwjasVP8ntXfQA63ewICtXs3Q44lJmmpiYefvhhrrrqKo4//ng2bdrE7NmzI0KIHQp4u3cxMTHceuutvP766/z888/MnTuXDz/8UNT91mg0A3LNhJtw7870r89d/UqlktTUVEaOHEl0dDSVlZVUVlY6lXNXamtrycnJCVl73SG6zxbcBqOOcTyjKgWof3n+ltwDowaGPY8k+ifLBKirq4s4s2QZGZCVGZlhhEqlIj09fUC+GXd4E/rsdjsxMTF0dHSEXCAIpfDZ1NRESkqKJGX52w92u52mpiZKSkowGo3k5+eTm5vbJ9T1kYLk9y7KQ64OoZqoWDo7O1mzZg0rVqxg6tSpvPvuu/zmN78ZtkpMKAMHxMXFsXLlSl599VX27NnDvHnz+Oijj/yqU6PRDOrODIR/d0ZsffHx8RQVFZGenk5DQwMVFRVO80kht0zE7xBEx8FD/4I7XoYzlsKFN8Pj/4OFt3k9LRKeV3dR2+rr60lPTxcVyl9GJhzII1Jm2KBQKMjKyqKuri6oyUKhUJCYmEhHR0dETDqBtqGzszOoEJuukd78CQHb3NxMSUkJAEVFRWRkZIRMGIkUnwBJyciDo47ta7YC2BVgj4phzfb9XHrppUyYMIF169Zx5plnRsT4HEzCcf3x8fHcfvvtvPTSS3z33XfMnz+fjz/+2OsY1Gq1kigzw+H+6vV68vLyyMzMpLGxkYqKCvbt2+cxt0zEoVLDjAvhusfg8vuhcJLPUyLp/SWMMZvNhsFgID4+fliMO5mhhazMyAwb1Go1CQkJopz3PU0qgjASikknHFHSrFYrSqUyoEnJVYHxR4lpaWmhpKQEm83GyJEjw2KmIFUunHCe5xc3PwVxv+TUUCmxK8EKPNBTSOGY8WzdupVzzjlnQDjVcNI/nLkr4RaCwikUJiYmctddd7F+/Xq++uorFixYwGeffea2DVKZmUkROCHUSLU7ptPpyMvLIzU1lZqaGtrb2wcEupAJDXa7naqqKrKyslAoFPLOjEzEIY9ImWGDIHynp6dTXV3t9zmeiI2N9TsQQCQ4/LvS2tpKfLwHsyUf+CuQtra2UlJSgsVioaioiLS0NOc9CJVQ60/fiUlcGkj9IU14OuIo7E9+g2npA/yYeSwbLHn8Z0Ex92z5jPPPP9/ZZp1O59bPwBtSJrUUm408VAxG+PSkpCR+//vf89xzz/HZZ59x0UUX8fnnn/cpX61WSx7iOVJXy6WIcOdKbW0txx13HJmZmQPMzyIVMfc4Uu9jRUUFhYWFg90MGRm3yMqMzLBBWE0qLCyktLQ06PJSUlJobm72+LvrBBZpE1Rra6tk/jLQ91rb2tooKSnBZDI5bd5dV/JCKdAOdqJAoexQ1WE0Gnn29TdZ8OK/OXDadVyy9XvOWnLVgJVSf5WZSB6jg4GUfZCSksIf//hHnn76aT7++GMWLVrEjh07nPX4a6Ip05eqqiry8vLQ6XTk5+eTlZXlND8LV1AFse8wMfc4EnfYhMSmer1e3pWRiUjkUSkzbBC2x+Pi4rDZbKJXrvujVqsBPEZHiyQhpf8E2dLSQlJSUkDnukOhUDjzRPT29lJQUEBGRoZz4ouECToS2hAovb29PP/881x00UWkpKSwZcsW5s+f71Gw0Ov1fmVWj6QxOtTwdzylpqZy3333sXbtWv75z3+yePFivvrqqxC3zjvhehakrqe1tZXo6Gg0Go2zbK1WS15eHhkZGdTU1FBTU4PVJYmsNwId/1LvNgVKOO6jQqGgsrLSGQY74oMuyAxLZGVGZlghTEJS7c4kJyd73Z2JBNxFpTEajcTF+Ze0zdfEbTKZqKiooLW1lfz8fLeO/ZEgNAfjHzRYmEwmXnzxRRYuXEhcXBybN29m4cKFPgUKf5WZ4UCoxp7YctPT03nggQdYvXo17733HitWrGDnzp2DMsbC9TwK9XjzoxLDwYMHGTVqVJ/vhHL1ej0FBQXExsZSXl5OY2Ojzzoj3ewx3OV5oqamhtzc3LDUJSMTCLIyIzOsEITAnJwcv0I0+yI+Pp6urq6gywkl/Sc8qQQLm81GbW0tVVVVpKenM2LECOdulb8MtrLgi8FSwsxmM6+88goLFixAp9OxefNmLr74Yr/7V6lUhjQAQKTfN1cira0ZGRk8+OCD3Hvvvbz11ltcdtllfPfdd4PdrJDizY/K32fMbDZjMBhITk72ep4Q0lmhUFBSUkJHR0dgjQ4zkTJO+/drU1MTOp3OuQssm5nJRCLyqJQZVggvaqVSSVpaWtAKjUKhICoqiu7u7j7fR8rE5I62tja/d2U80draSmlpKVFRURQVFREVFRVQOZGwYxNJ90pQYgQTsnfffZclS5aIVhKhr1+G1ETCfRvq5Obmcv/99/PII4+wceNGrrjiCr7//vvBblbY8XeMlpaWOk2dXHE3FhUKBampqRQWFtLd3U1ZWVnEBwkI9pny1o9iA9C4Hn/o0CGKioqcf8tmZjKRiKzMyAwrlEql80VdVFQkmalZS0tLn++kMmkKRBj1dU5LS4tzdVMsBoOB0tJSent7KSoqIjExMaByIonBFsztdjsWi4WNGzcyf/58bDYbmzZt4rLLLkOj0QRcrlarlU3NIhghPHN2djarVq3igQce4NVXX+XKK6/kxx9/HOzmOYkUZb+6upq8vDxR56hUKrKyssjJyaGhoYGampo+O5aRcm2eEPNu8nas2AAEwvEdHR1YrVays7Od5Qz2+1JGxh3il/tkZIYwrrlVYmNjUSqVAQv3wsq3Xq/HbDZjs9kk3YJ35+vib7u80dbW1melzR8EkzKz2Uxubi5arVZ0uwabQPszlFitVjZt2sSGDRu48MILeeedd9DpdJKUrdfrMRgM6PV6r8cF0i+R2JdDDY1GQ09Pj/PvESNG8Pjjj1NZWcmqVavo7u5mxYoVTJgwYRBbOfjKPkBdXR3Jyclu36/+7EBqtVry8/Npb2+ntLSUjIwM4uLiIuLavGGz2QJWRALF9fy9e/cycuTIPrsx8s6MTCQiKzMywwrXF7XdbmfSpEns2rWLmTNnii7LdQKNj4+nra0t4B2P/m1z97dUdHZ2isox09XVRV1dHWlpaSQkJPg8PlKF40gSXKxWK5s3b+a1117jvPPO4+233/apdIglKirKrwSxwSrMkazYRHLbtFqtW3+OvLw81qxZQ3l5OcXFxRiNRlauXMnYsWMHoZW+CUcfl5SUMGXKFI/1+0tCQgKxsbHU1tbS2tpKdnY2KpVK8vEcVBmHD8B3/w+UKhQnnA0Zv5rW+VLchJ0TT8eICQcu7MrEx8c7zVwj+XmSGd7IyozMsMI1VLBCoSA2NhadTkddXR2ZmZkBl5uUlERFRUVQyoxAqCcMhUKBSqXyWY/NZnOaZRQWFvq9IheK3SQxRPKEa7PZ2Lp1Ky+//DJnn302b731VsD+Rr7Q6/U0NDRIUpa3Po3UvobIbJvQl2q1GrPZ7PG4goIC1q5dS2lpKatWrcJqtbJy5UqOOuqoMLbWPa5CsRR97G18CQFWYmNjJalDpVKRm5tLd3c35eXlpKSk9AlT764dYt8pAfWJ3Q4v3gPvPw3C6S/eDZfcAwtvc7bDdzHelR1/2bt3L+PGjaOjo8Op8Mm7MjKRiuwzIzOsEJQZ15f6pEmT2LdvX1DlqtVqVCqVJEnbxJiqibX5NplMbvugP52dnZSUlBAfH09eXt6QmsS8Xddg5Xmw2Wy89957zJkzh5qaGt58801uuOGGkCkyIG1Es0hUCnwh1b0W6zztC6EvVSqVX/enqKiIp556ittvv53HH3+c6667jpKSEsnbJQapfSe8lXXgwAFGjhwpWR1CX8TExDBy5Eh6e3spKyvz+u4OS9LLLzY5FBkAu8u/DX+F3Z8FVqYIXNvd0dGBxWIhOTkZm83mXPySI5nJRCryzozMsEMQIlzzE6SkpHD48GFGjBgRUJl2u92ZcyYrKyuo9omZDAWTAn8n29bWVq+mYlarlZqaGhQKBUVFRRGvxIRlxdRLXb7Ks9vt/OMf/+CFF17gtNNO44033iAmJibgNohto0KhkNyXa6gglbAtxgQplELvqFGjePrpp9m/fz+PPPIIKpWK22+/ncLCQp/nDkVlFBwJidvb2znmmGPc/h7ILqxrEBiFQkFmZiZGo5HDhw+TlJTkdXfdn/oC7ut/v+LYkek/LJTA/3sVppwSWLl+4jqX7N27l/Hjxw84JtLnA5nhi6zMyAw7VCoVFoulz6QzduxYPv/8c3JycjwKfr4msri4OOrr68Nu5iSmrvb2do8RyATfGME5tn8dYp1Rw4FYZU4M7hQDMef+61//4tlnn2XWrFls2LAhaDMZf+jfRp1OR29vb0h3gCC0pn2RZDYYrt0Ib4wdO5Znn32WvXv38uCDD6LX67ntttvchi2OJAK5jyUlJRQUFHj8XaqokXq9nqKiIurq6qisrCQ3N3eA0uOuPknDn7fUDlRkAGy//OYHwT4rCoWClpYWrFYrycnJA65NVmZkIpXht1wnM+zp7/AJDmfc7OxsysrKPJ7nzySRmJhIc3Oz6DaFK0Roe3u7252Z+vp6mpubKSwsdJuDJhhFRsprc1dWqATdQAWljz76iHnz5vHTTz/x6quvsnLlyoAUmf5mMYEgRDQLNf72VSDXEimKTKgI9P6OHz+e559/nuuuu47777+fZcuWUVlZKXHrpMPTffR2/dXV1ZIpab76WaFQkJWVRVJSEqWlpfT09Pg0p5PU1O+oE0DlRiRTgn30sX7VIcWzsnv3bo4++ugB5clmZjKRjDwyZYYdnlaXxowZQ3l5udN2OpCIXCkpKbS2topuU7gEtq6urj7KisVioaysDJVKRX5+vse+CXa1TyoiVbC12+18/PHHzJ8/n++//56XX36Z2267TVTUOHdlQnDXHBUVhdFoDPh8qYnU+xcMwSibarUai8USVP0TJ07kxRdf5Oqrr+aPf/wjy5cvp6qqKqgyw5l/xdOYqKqqIi0tTTIB2t+xFxcXR0FBAQ0NDdTX10tSt1/1z70JFMpfnf8BlArsGh2Kc68NvnwXPN3fn3/+mezsbKKjo92WLyszMpGKPDJlhh2u5gPw6ySgVCqZNGkS3333HSB+QhdW8eLj450hcSMtKZtSqXROSF1dXZSXl5OZmUlqampI6ou063dFirbZ7XY+/fRTFi5cyM6dO3nxxRe58847/QphHQ70en1EJc6M5PEQKMEoaBqNJmhlRmDy5Mm8/PLLXH755dx9993cfvvt1NTUBFSWFLuCwVJaWsro0aPd/haKdrmWqVaryc/PR6lUUlZW5jXqnGRtyZ8A978HBRN//W7UsSj++iGk+/blFOtr2Z+uri6qq6sZM2aM8zur1eqcL4TwzDIykYg8OmWGHYJAL7z8XSeB9PR0Dh8+TGVlpc9s057spVNTU6moqCAhISGiVqJdIyfV19djMBhEhVwOhEi6/v4E27YvvviCJ554gilTpvDcc89JEpZbaiS16ReBJ9v9UObviCTfGn9RqVSYzWZJfZqOPvpoXnvtNb755hvuuOMOcnJyWL58eUCh5werP5uamtDr9R5zLwWyay7WcV+hUJCWlkZsbCwVFRVkZma6NRd1VfyC7q8JJ8Hjn0NrPShVkBCaRSZXhHZ///33AwItCMqMHJZZJtKRlRmZYYkQBMAdU6ZM4dNPPyU9Pd1rIkNPQqJKpUKr1dLT0+N2u36w6OjoQK/XU1ZWRlxcHPn5+UNO+IsEtm3bxpo1axg/fjxPP/20112tSBCwhRDN3kxE3LbTbIJPNsKO98BmhePOht9cjl0fHbqITj4QG0ksEvrfGxqNxuuqfzAcd9xxvP766+zcuZOVK1eSn5/PsmXLyMjICEl9UnLgwAEmTZokWXlix4DrIkBUVBSFhYUcPnyY3t5eUlJSgq7DpwlpUvjukUKhcC6+9Q8OY7FY0Gg02O12WZmRiWhkZUZmWCKsiLqbTNRqNZMnT+a7777jpJNOCqj89PR0amtrwxphyJfg1tLSQmdnJ5MmTQqrkhWIQBmJQuiXX37JE088wejRo1m7di3p6enO30K1EyEFQhAAbyGhB0SFM5vg/nmwZ9uv4WJ/+Bw+3oDiwQ8hemCQiEgkEvq/P679rFar6enpCWl9J5xwAhs2bODLL7/k1ltvZdSoUdxyyy2kpaVJVoeUz2tnZyd2u91tIJJw4S6KV35+PrW1tVRXV5OdnR0xfoTBYLfbMZvNHDp0iNmzZw/4vbe3F61Wi0KhkM3MZCIa2WdGZlgiJAHzRHp6OjqdjvLycre/+zLd0Wq1AGH1V/A2QXZ1dXHw4EFGjx7dR5Gx2+0BmSEFa5/tqxypI6cFIzzs3LmTJUuW8P7777N69Wr+/Oc/91Fkgi0/UPytU6/XOwVmv7ODf/qWQ5GBX8PF2oGKn+CDZwNorYyAaz/76zMjxTN64okn8sYbb3DWWWdx0003cd9999HU1CS6XHf0j3oVDPv37+eoo44Ktkmi8OdZUigUZGdno9frKS8vx2q1hqFloefbb79l4sSJbndeTCYTOp1Odv6XiXjk0SkzLHEXnrk/Rx99NCUlJW6jQfkz+aWlpdHY2Ojxd1+TvlS+Di0tLTQ1NREfHz/ARMJX6FFPBLLT4u6zP+VIoTgF0pfffvstl156Ke+++y7FxcX89a9/jSgTHXc+X+6Ijo52hmf2+759+V7fqErOSoEvtoho5fAhkDGm0Wj8EoqlfEZnzJjBW2+9xemnn84NN9zAX/7yF1paWkSXL7ZefzAajfT09LjdNQql75eYslNSUkhPT6esrEyyxarBCrRw6NAhoqKiyMjIcGv6ZjQa0el0somZTMQjKzMywxKVSuXzBa1UKpk8eTLffPNNQHVER0djMpk8rrz6ErylWO2vra2lp6eH/Px8ent7Q5p93huBJp/0dnyoBIBdu3Zx+eWX8+abb/LII4/w8MMPB+Q8HQrcKYW++lOr1YqPmGW1uE/gB2CTJvrWUMTvnS0/y/DmuxdqZs2axdtvv83MmTO55pprePDBBwMKKx8InvrxwIEDjBw50u1vgxXMwh0xMTHk5eVx+PBhOjs7gy5vMK6tqamJ2tpapk6d6mwD9A0UI/jMyMqMTKQjKzMywxZ/XtBpaWlkZGSwa9eugOpISUkRnURTCiXGbrdTWVmJSqUiNzfXuQMzmLbaUk/WUl/LDz/8wNKlS3n11Vd58MEHefTRR8nOzpa0jmAJRikUxfHnuP9eCZx4fsDF+jMGIkVgdYcUfd6/jHDt0Hpqy+zZs3n33XeZNm0aV111FX/729+coeV9Eaj5m7t+NJvNNDY2kpub67W9oUKsya1Wq6WoqIimpiba2tpE1SXWv07qMWA0Gtm1axcnnHDCgDrcvWNkfxmZSEdWZmSGLf6YmikUCkaPHo3ZbKaioqLP9/6QkJBAZ2dnn9Uub0gxadlsNsrLy0lISOjj2+FvG0LRJgifX4nY9v70009ceeWVrF+/nj//+c889thjbgWqSBayfaHVan2axPS5vtMvhaLJAxL4kZEP598QcDv89U0YTgxWZLj+nH766WzevJmjjz6aK664gkcffZSOjg7J6/F0PQcPHmTUqFGS1+cvgSz2KJVKCgoKaG9vF2WqF0gOs2DLEM6x2Wx89dVXTJ061Wu0TlfzR1mZkYl05BEqM2xRq9UYjUafuSsAjj32WD7//HNiYmJITU0VNZEkJyfT1NQ0wGncHf4Ke57qFxSZtLS0PtGABNvnQBhs4VJspCR/j923bx+rVq0iOjqa++67z2fkucHuh2CIioqip6fH6xjoc336aPjrB/DBc7BtK1jNjh2Z866H+MjLpyMjDQqFgjPPPJMzzjiDf/3rX1x22WXMmjWL66+/3muOlWCxWCzU1tZy2mmnBXR+sNHUAjnfNQKgYHJms9mCTkDsri39vwv0WhUKBbt37yYnJ8dnO3t7e9Hr9bIiIzMkkEepzLBFrVb7PYkplUqmTZvGtm3bmD59uqjQxklJSZSUlJCSkhK07bFgCuGuzYIik56ePkDw6OrqCpu/jNRhlQMpy1sbfv75Z4qLi9FoNNxzzz0UFRUF28SIJyoqym/ToV9PioUFKxz/AsAfoczTeWLP8afuSEWlUmG1WgN6N4TK10KhUHD22Wdz1lln8cEHH3DJJZcwe/Zsrr32WsnfI3a7nUOHDlFYWBiUkB4MrkmU/aV/IBNBoWloaPBr4coT/pig2Wy2gK65srISk8nk1w5Yb28vOp1OVmZkhgSymZnMsEZICOYPer2eo48+mq+++kqUyZZCofAZ2czficmTKYTVavWoyAD09PSETJnp339ihdVQtMNdGw4ePMj111/PE088wR133MGTTz45LBQZcCgz7qLyuRIOn6ZAzMzCEW1vMBGUGX9wp+h5+k0KFAoF5513Hlu3bqWoqIjFixezZs0aenp6JOtjm81GdXU1BQUFkpQXCFL13YgRIzCbzdTX10tSnlu6O1B88Bw8fi28cLcjXLoftLW1UVJSwnHHHefX8UajEb1eLzv/ywwJZJVbZlijVqtFRRNKTk5m1KhR7Ny5kxNPPBHwvQqsUChISEigubkZi8XidqUrmMnUarVSUVHhUZEBx85MUlJSwHV4w9e1i1V2pGqHUHdJSQnFxcVYrVZWrlwZ9hwW/QnXroFrPf3vg7s2DCUF4EhCiGgm5Kbyhq9nzRUpx5lSqeTCCy/k/PPPZ+vWrVx88cWcddZZXHnllURFRQVVdllZGfn5+ZLlMRnsXbmcnBxqa2upra0lKytL2sLrK+H3Z0JLncOfTaGAfzwD1xfDWVd5PK2rq4tvv/2W6dOn+93PZrMZrVaLRqORqPEyMqFD3pmRGdao1WpRuyLgWH2LjY1l7969fb53h2AWZrfbSU9Pl3zFTtiRycjI8KjIABgMBq/OnuHYLQk3ZWVl3HTTTTz44IPcdNNNPPvssz4VmaHs5N+f/uPSNQxwuMNdy/TFVbkMVXjmUAj0SqWSefPmsWXLFtLS0li4cCHPPfecz10/T9hsNioqKigsLJSsjcFct1R9Jigxnt73AT9nL9wOrXWOsOk2wPpLOc/dBk01bk8xGo189dVXHH/88X4rngqFAovFErSiKiMTLmRlRmZYI8Ye2HUCmjhxIgaDgZ9//tnrOa4r47GxsZhMJkwmk191+NOeiooKMjMzfZqQGY1Gr8ccSavylZWVLFu2jL/85S9cf/31rF+/nvHjx/t1bjj6YbD6Wq/XO5NneiJcO0ZHMv6Gn3YNeztYuWYCRaVSsXDhQt577z0SEhJYuHAh69evF51EsqSkhLy8vIgxZZIyTHZWVha9vb1uc/cE9JwZuuCbjxxKzMCGwY73BnxtMpnYsWMHRx99NPHx8X7XK5hRR8p9kZHxhazMyAx7/FVo+k8Exx57LO3t7Rw8eNDvujIyMqirq/O7Dm9UVlaSkpLily+MYDJwJFNVVcXy5cv505/+xNVXX8369euZOHHiYDdLMsT6R/Q/RohoNtgE4swfaUiRPFPAkzITidfdH5VKxaJFi9iyZQtRUVEsWLCAl19+2euCjYDNZqOystJjkkypkaI/xd7bESNG0N7e7jWxpt9lmns9J7JVAMbuPl9ZLBa2b9/OhAkTSE5OFlWX2WxGpVLJzv8yQwZZmZEZ9gg2wb6S2bmbDI8//niam5spKSnxq67o6GjsdnvAZhkCdXV1REVFkZCQEFQ5RwI1NTXcfvvt3HPPPVxxxRW89NJLTJ48OagyI3GnSmxo1v7HREdHi145jwTE3At3z2go7qWUZarVarcBACJxDHpCrVZzySWXsHnzZtRqNfPnz+e1117DbDZ7VCIOHTokqa+MLwajP4UoZw0NDR53Rf1WsuKSYcSYvrmfBGzAlFN//dNmY/v27YwZM8YZWc3fpKAKhcIZMEZWZmSGCrIyIzPsEUI0i01sKZiKnHjiiTQ0NFBWVubX+ZmZmV53Z3whBBIIJvznkUBdXR133nknd955JxdffDGvvPIKU6dODbi8UEeGGmxCYc4Uaf0kVXLBcCImmpk3pLzOQMvSaDRceumlvPvuu9hsNubNm8fGjRsHjDur1crhw4cHLZpgOMeEUqkkPz+f6upqv3asPKJQwNIHfinUZZwrcOSAOsoRpcxms7Fjxw4KCgr6BCDwV5mz2+10dXWRkJAwpBRqmeGNrMzIDHuUSiUqlcrv6E7uvp82bRo1NTWUl5f7PF8IdxmIyU9nZycdHR1kZ2f7fY7VanWufgY6iQeabToU1NfX8/vf/56VK1c6V4CPPfbYoMsN18Q9mMK1UqkUFVbcF7KwEzyedmbEMti5nVzRarVcccUVbNq0id7eXubOncubb77pvM4DBw5QUFAQtl2Z/oR73KrVavLy8qisrAzuXh/7G/jLP2DyLIiOgcw8uPReuG2985BvvvmGzMxM8vLyAq7GZDKFLS+ZjIwUyHuIMjI4JhtfjvneJkClUsn06dPZsWMHSqWSvLw8j0Kr3W4nMzOTqqoqUVF8jEYjDQ0NFBYWihICDAaDM/N7OJPSuWbIloLGxkbWrFnDwYMHufXWW52hsYcag6kA6PV6enp6vEa+kwkPwrMh1c5MJKLT6bjqqqu45JJLeOWVV5g7dy5LliwhOTmZ008/XZL3Q/+w46FKJBosWq2WrKwsDh8+HFxOnYkzYOJAZ3+bzca2bdvIzs4Oyg9J6DvZxExmKCHvzMjIgM9Y+u52bfp/Jyg05eXlVFRU+KxPp9N5dQx1xWazUVVVRV5enujVzN7e3rDmCvCVvFIsTU1N3Hfffdx8882cffbZvPnmm0NWkQmWYIW06Ohov3cEI1EgDBfhuHaplNpwK8eB9I1er+e6667jrbfeYt++fTz66KNs2bJFkn72x7dRbBmhIiYmhujoaBoaGiQt12Kx8MUXX5Cfn++3IuNp3BgMBqKiomRlRmZIISszMjL4Vmb642nyUyqVzJw5k9raWmceGk9kZGRQX1/v10RaVVVFRkaG13Z6KsdkMnnNMSM1UglXLS0t/OUvf+GGG27g9NNP58033+Skk06SpGx/iTSBPtAdMoHo6Gif4ZmDqetIYTCvXeyYk0KYF4Nr34itS6VSccopp7B161Zqa2uZM2cOW7duxWazDeqzJja4hkAgbU5PT6e7u5vu7m7fB/uB0Wjk888/Z8yYMR5Ny9y1U/iu//V2dHSQkJAwaCaAMjKBII9WGZlfkGolSqlUcuKJJ2KxWPj66689HqdSqUhOTva5Stfa2oparSYuLs7rcZ4mYZPJ5DQzi2SEybW1tZUHH3yQa6+9lpNPPpm3336bWbNmBVResALSkSDQu/aBVP4ZMu6RwidNCrMrKdoUSF2+2Lt3L0cddRTR0dHcdNNNvPHGG1RUVDB37lz+8Y9/RMTigZg2BHqv8vLyqKmpCTogR1dXF9u2bWPKlClkZGR4PM5XYmfX44xGoxwlU2bIISszMjK/4E2ZCWSSnTx5MsnJyWzbts3jpJWcnExXV5dHfx2TyURLS0ufqDRiCcbMLJzCfEdHB3/729+4+uqrOfHEE3nnnXc45ZRTgvLzORKUEXcEI/RJHQRgOOGr3wMdb0qlMmSCvNCmcAb/cIfBYKC9vZ2cnBzndzExMSxbtozXX3+dgwcPMnfuXP75z38OulIT7A6oL1QqFTk5ORw+fFh0PQItLS18+eWXTJs2zZlHpj+B7PJZLJYhsfglI+OKrMzIyPyCt6SSgQopI0eOpKCggC+++MJjbpns7GxqamoGfG+326mqqiI3NzeoRIPB7MwEkpxRLB0dHTz66KMsXbqUY489lnfffZfTTjvtiFVEpCCYvtHpdIOaPNPrePlpO7eZvoWrx8Edp8Onbzmym0cIoRqTKpUq5ApmoDs2Ul3znj17GDdunNvf4uLiWLFiBa+++ip79+5l3rx5/Otf/wr63RJOpUhsXTExMcTGxlJfXy+6rvr6enbv3s3MmTO9BvMQE44ZHHOFVquV/WVkhhyyMiMj8wtKpVJSO2FhIsnJyWHy5Mls27aNjo6OAcfp9XrUavWA3+rr60lISECn04kWKFyPl9LMTMqkhF1dXRQXF3P55ZczadIkNm/ezG9/+9uQKzGDveo72MTExAyqMuPx/u54H/5wLkfbmqC5Dg5+B6uvh9f+HN4GDgJKpTLs5n/u7kOonr2Ojg56e3t95saKj4/ntttu45VXXmH37t3Mnz+f//znPwE/s4FeTzh2sex2O2lpafT09PRJZuurjIqKCn7++WdmzpwpmS+k0E/d3d0kJSVJUqaMTDiRlRkZGRekXJFynZSSk5OZNm0aX3/9tVsfmezsbBoaGpyrs8IEl5KSAhDUqq2w2uZPO30hhelWd3c3q1evZsmSJYwdO5YtW7Zw1llnhc3WPxjFMFSEU8GKjo72uEs4aFitsP4usIHql6/sVsAOis2roSFwcxypCcW9ipTwzKEahz/++CMTJ070+/j4+HjuvPNOXnzxRb7++msWLFjAf//734hbiOjfnkDeFTk5OX125j2VYbPZ+Pbbb2loaGDmzJleTYeDWWCS/WVkhiKyMiMj40IotteFCS82NpZZs2axf/9+Dh486PxdoVCgVCpJTU11Kjp1dXV9EmMGY2ZmsVi8Xle4zLl6enpYu3YtixcvpqioiC1btnDuueeKSk4aKrwJSUMpTK8n+gcBCNbxOBjcXmtNCTTVOLKZCygBBdgBfvjMa5necjpJTSju1WDszPhCql2N+vp6NBoNCQkJou9HYmIid999N88//zzbt29n4cKF/O9//wuoXaFAirGg1WqJjo6mpaXF4zFCxLLk5GSOP/54n0mQAxn3CoWC3t5en4FmZGQiEVmZkZFxQRD6vSVeEztRuE54Wq2WmTNnYjAY+PLLL51Cpd1uJzExkZ6eHmpra4mJifG48uZP/a51WiyWAWUFI+SJPddgMLB27VouvvhicnNz2bp1KxdccIFXk75gw9OKRUoBNdJWj2Hg9Q1mEAC3/aMZuHPYp8Vq//JAiV0pFyLeDfY9i0RlRirTrv379zNp0qSgdnWTk5P5wx/+wDPPPMMnn3zCwoUL+eKLLwIqCyLvGU1PT6elpcXtGKivr+eLL75g0qRJA5Is9+nP7/4L982Bq8bBH86Frz7wu3673Y7RaCQ2Nlb2VZQZksjKjIyMC0qlEo1G4zUzdbC25kqlksmTJ5Ofn89nn31GW1ub8/zMzEz279/v1bZcikg74ZiwjEYjzzzzDIsWLSIrK4stW7Ywd+5cv/ySpDIFGwyhJRJ2mnwRFRU1qH4zA8jIh/zxoHTTR2o1HHuGX8UEMm4iIepdpJiZ+ULs81RRUUFycjJRUVGS1J+amsqf/vQnnnrqKT766CMuvvhitm/fLrqcwb7f/VEoFGRmZg4IBHPw4EEOHDjAySef7DFiGQAfb4A/z3fsYLbUwd4d8NClsHWd3/W3tbV5r0NGJoKRlRkZmX4EEsY4EKE5Kyvr/7d353GOlHX+wD+V++pOujudvu85YGZggGFAYLhcXTwQ8UbXe0XRdUXQdVdYf7q6i6vLoai4Xgiyy+LBpajIuorcAwwwMAzDMNP3fXfuu35/tFUm6RxVSaWT9Hzer1e/ZjqpVD2pJJ3nW8/z/T4444wz8Nxzz2FoaAjA6horXV1dWFlZUb2/ahGJRPDDH/4Q73jHO+ByuXD33Xfj7W9/O/R6feEHa0zrTouS6WjrOeWpWFarVbNF+zQhCMAnbwTMVshdev2fX7uPfwOo29hJyaUGM+v13lLzeUokEjhy5EjOCmalaG5uxpe//GV885vfxH333Yf3vOc9ePLJJzU/TqnUVIOUqpL5/X7E43E88cQTCIVCOPvss/PmPCIaBm7+/Or/pcHWpLg6P/O/vwIEVhS1w+/3M5ihmsVghihD6lQzidJFx9Sy2Ww455xzsLS0hEceeQShUAj9/f2Yn5+v+Fogap9XNBrFLbfcgre//e2w2Wy4++67cckll1QkiFGqlCmDue6rtqu+2djt9rxFACoSeG3eBdz4JO7R9wGnXQC85oPA9Q8Cf/U369+WdVZqMFON77nDhw+jr69vTb6elu+tlpYWXHPNNbj++utx55134r3vfW/ehYqzKSUfUYt9p27T3t6OwcFBPPzww3IVzIKOPAsEfH9OLkvdMYBYFHjx0YLtSCQSMBqNLMlMNYvBDFEGnU6n6gu41I6ETqfDKaecAr1ej8HBQfj9fng8HkxNTRV8rNL8mWITQpWIxWK47bbb8La3vQ0GgwF33XUX3vOe99TEF2M1dgKVKLVDWKjzXLHz0tyBnxu3AFfdAXz8eqB/Z2XakUU5A7xS15mp5KhftnylcDiM6enpNTkeqdurle85tra24mtf+xq+/vWv46c//Sne97734dlnny15v9mUughp5n5SDQ8P4+WXX8aWLVvQ1dWlrI0GI/Ke0QL5ZgCwsrICt9tdcDuiasVghigLKW8mm3J0HILBILq6unDmmWfi6aefxvz8PBKJBHw+X97HKekYJBKJsnRO4/E4br/9drz1rW+FKIq466678N73vreoaXpAdU3DyqXcbVzPhQwNBgNisVjJ+zlWlOMzJOXm1fLITLb37PPPP49t27Zp2i4l+2pvb8e1116Lr371q7jtttvwgQ98APv379esDWrbk09m8CeNzF988cVp684UNHAyxMaW7L05qwPYcXbBXTCYoVrHYIYoi3LU8M+3v7m5OXg8HjgcDpx33nnw+/0YGhrC0NBQWiennCMsmXIdKx6P43/+53/wlre8BeFwGHfeeSfe//73Fx3ESKp1lCT1PJS7jet5Dqoub+YYJI2a1koBgHyk9+7i4iLi8ThaWloq1pbOzk5cf/31+MpXvoIf//jH+NCHPoQDBw4oeux657yNjo7i0UcfxXHHHYcdO3bAaDTCYrGkXcjKO7qu1wOf+u7qv1JxFb1udZrZ338bMOVfWFMUReh0uvx5OURVrvrngRBVgE6ng16vRzwez1spS4vOp5S7IH2ZCIKAE088EYuLi3j88cfh9XqxZ88e+T61xy62jZmPSyQSuOuuu/CTn/wEF110EX7xi1/AbDYXtW9Au/NXbrXQxmLY7XYsLy/D5XJVtB253ge5OnC18r5RQ6fT1cTIpBIvvPACTj311Eo3AwDQ3d2Nb3zjGxgZGcG1116LUCiEK6+8Etu2bcv5mPWqRhiNRrFv3z6YzWacf/75aVUePR4PRkdH09Z8yZu3ufM8CN98EnjgR8D4y0BrH3DB30LoOb7g+8rn88mLMxPVKgYzRDmYzea8iwtq9eU2OzuL5ubmNfttbGzE61//ejz44IO4//77cc4558Bms5V07GI6gslkEnfffTduvfVWvOENb8DPf/5zWCz5r/YpaUMtd0hL7VBXQ4fcarVieno65/3r1Ua1ZbW1alOxuWTlUE1tUSrb+2N0dBQNDQ2w2+1pt1fi+aUes6enB9/61rcwNDSEa6+9FtFoFJ/97GexdetWTY6l9rMyMTGBgwcP4sQTT8w6gmUwGGCxWOD3++UqZ/kIggB09AMf+rc17SpkZWUFmzdvVtx2omrEYIYoB6PRmHV9llIXnMxc0DIej8tBSiadTofzzz8fzz77LB599FH09fVh06ZNRR9fzShTMpnEL3/5S9x888244IIL8NOf/lST9SJqPQgAilvPZD2nqykhtSnfyMhGpqTMthR011qgsR6yjdy+8sorOO+889Zsq+X5U/o3INsx+/r68J3vfAdHjhzB9ddfj2Qyic985jMld+al90ihdsXjcTz77LNIJpM4//zz8xZJ8Xg8GBsbyxnMFPO3MNtnPplMlnRxiqgaMJghykEQBBiNxrQkaa0r2MzPz8tD/Pk6lccffzwmJycRiUTw0EMP4ZRTTlF0xa6YhHJRFHHffffhBz/4AV7zmtfgf/7nf9ZcadVKtQQn5SY9z2rrFJvNZoTDYc0WNdwoMj8P633MYh5b6ffWgQMHsHnz5jWl2DM/46V+5rU4T5s2bcJNN92Ew4cP47rrroNOp8NnP/tZ9Pf3l61dY2NjOHz4MI4//ni0t7cX3JfBYIBOp0M0Gs2az6L0PKSe79QgXRRFBIPBik8zJdICgxmiPEwmU9kqPomiiEAggNbWVgD5v5ysViscDgdcLhfa29vx1FNPob29HZs3b06ba53tGGq+9H7729/ie9/7Hs477zz893//d9qc7XIo5spirVqPSmiZ56fQ62+32xEIBHIGM8dKsKmVUs5XqSO+qdY7uFlZWcHKygp27lxbSjvb6HalZJ6TLVu24D//8z9x6NAhXHPNNTCbzfiHf/gH9Pb2anZMr9eL559/Hg6HA+eee66ikvVSOxsaGrC0tFRSMYVcswsEQcDKykrW8tlEtYbBDFEeRqMROp0ubQ0IrTp4fr8/5/SybDweD4aGhtDZ2Ylzzz0Xr7zyCv70pz/huOOOQ1tbW9a2KenUiKKIBx54AN/97nexZ88e/Nd//Rfq6uo06xCxQ1w+qee2mKlidrs9b96MmteNr3PpUyi1Iu2rXK9J5n7379+Pk046SfPjqG1HsY477jj88Ic/xIsvvoivfOUrsNls+OxnP4uenp6i9xmPx3HgwAF4vV6cdNJJqK+vV72Puro6zM7OFgxmlP6tTt0mmUxCFEWOytKGwGCGqACTyZS2Wnq2L89ivlSXl5fTEv8LEQQB7e3tGB8fR39/P7Zu3Yq+vj7s378fg4OD2Llz55qpZ3kr4Igifv/73+Omm27CGWecgVtvvRVOpzPtfi0ond9+rHeECynHOTKZTHmLXKixUV8/NTkaas7BeuRRFVP9UM1+AWBkZAROp7OoznrmPotdwLIY2c7J9u3b8aMf/QgvvPACvvSlL8HpdOIzn/lM2gKWSoyOjuKVV17B5s2bSwryBEGA1WpFMBjMe+FLafCaet/y8nJFy2cTaYnBDFEBJpNJXsQsX4WlfF8kmV/UoigiGo2qTry0WCyoq6vDzMwMWlpaYDKZsHv3biwvL2Pfvn1wOp3YsWNH3qkMoijiwQcfxLe//W3s3r0bP/7xjxXPmy5X0LFRO8JaUjryona6mU6nQyKRWJPrQKuUvjfVvodzTQ2rpc9XLBbDkSNHsib9q1WJame5nHDCCfjxj3+M5557Dv/8z/8Mt9uNK6+8Eh0dHXn36fV68dxzz6Gurk7xlLJU2V7/xsZGLCwsKBrFV/M6+/3+kkaeiKoJgxmiAnQ6naLV0guNgqTy+/1FJ9U3NzdjcHAQoVBIniLgcrlw7rnnYmxsDH/605/Q39+fdS70Qw89hG9961s46aST8IMf/ACNjY2qjs2go/qpCXp0Op185bfc+VFKrXtuUTIJ/P6/gAduBpbngC2nAW/9FLDp5LK2I5M0nVWv19fMSOWBAwewZcuWDRsIn3TSSbj11luxb98+/NM//RPa2tpw+eWXrwlq4vE4XnjhBQQCgaKnlAHZP6dWqxWRSETde2JwP7D3t6v/P/0NQP+J8v5FUUQkEoHD4diwrxsdewQVXxzVVYaHaB3F43EEAgHNOlpjY2Nobm6WR2bUdl7i8TiGh4fR19e35gspmUzi0KFDmJ2dxY4dO3DgwAEYDAbceOON2LFjB/7u7/5uzSJpagsF1EJHSwvrlXNQSYFAAD6fTy5EkUltWwttX+j+d73rXfjpT3+q+Hglu+ly4IGfrK6YLgLQCYAgAF+6Fzhhz7o1Y3R0FG1tbTAajet2zFIsLi7i4MGD8oK+kkIlv5XSouqZ1oHxU089hRtuuAHd3d244oor0NzcjFdeeQXj4+PYvHkzuru7NT2edA6mp6fhcDgKV7AUReD7nwF++2NA9+eRPhHAGz8CfOTrq+9rANPT0+jq6ipblUoijRX8Q8CRGSIFpDKZ8Xhck05o5hQztfvU6/Voa2vD2NjYmso7Op0O27ZtQ29vL/77v/8b3/72t/H6178e3/72t+HxeLLuT+1cf61UU6d+PVXTiu82mw0zMzNptxUqLJBPoe1LvV9TIy+uBjLAaiAjAkiKgCACN/8TcMMj69aUzEIj1UwURTz//PPYvXt31vuA0l/HUh9fjs/X7t27cfvtt+Oxxx7DpZdeCpfLhU9+8pM4//zzs1aVVPL3LV/QJT3W4XDA5/MVDmYeuXM1kAGApAghCUAH4Nc/BI4/C9hzMURRRDweZyBDG0rumq5ElMZsNuctg6xUOByG2WwuaR+CIMBut2ftiALAk08+iY985CMYGRnBFVdcgTe+8Y0YHh6G3+/Pu9/17GBrceVWq3bkUq6OdbUEMkB6knjmbZVW9vO07/fp34LS0xYBDL24Ou1snZQazKzne+rw4cNobW2t6g6xlqWuU42OjiIUCuGrX/0qPvrRj+L666/Hv/zLv2B+fn7NtkpGhwq95tLf+tQiNDn9/r/S38PSe1snAH+4DcBqXk+ui1pEtYojM0QKmUwmhEKhkqcvBAIBVSWZ8/F4PBgdHYXP50NdXR2efvppfOMb30BXVxduuOEGtLS04MEHH8TZZ5+N+fl5PPfcczCZTNixY0fWNqxnJ7ZSV24zF5ErtJ9jYfTIYrEgFApp9r7UStnPu9GUfwK1XtlXpBZTmkoNZtbrPRoIBDA5OalJ0r8axVaLK+a8ZHvM1NQUXnrpJbjd7rTk/j179uCRRx7Bxz/+cZxwwglrpvGWOhKZuuBuweezsvCX93PqZkkR4soCBAA+n69gIQOiWsNghkgFacX0bJR+cQaDQUVXxpR2kDo7O3HffffhZz/7Gdrb2/Ef//Ef8rozqftxu93Ys2cPZmdn8fTTT8NqtWL79u05O7DrvfDeeslch0fN9huV3W7Pue7Rhg7mTr8QuPmqtbfrBIjbz4JQ16BoN1p8TgRB0GyaWTlfs+eeew47d+5UVTGvVFoGJWrNzs7i0KFDcDgcOPPMM7NWoNyzZw/OOussPPTQQ/jYxz6Gk08+GZ/4xCfQ0JD7/aP276tUqCPvaNiOs4DRA4D0NhKxGtQIgLD9TESjUVitVtVV1oiqHd/RRCpkrjmTSukXZywWWzPNLNsXm5Ivuv379+OGG26Ay+XCJz7xCZxxxhlr2pFMJtNu83g88Hg8clBjt9uxffv2tC9pNV+yG7qzW0DqVdNyremxHux2O5aXl7PeV2vPJZ81r42nC3j/vwC3fhHQ64BEcnVqjr0ewqX/sa5t0zJnplyv2ejoKKxWa9YqiNUSyGj1+Zufn8ehQ4dgMpmwa9euglPqBEHAueeei3POOQd//OMf8ZGPfAS7d+/GZZddlrX0vdoA2OFwpFXBzBoMXXgZ8If/AsLB1dwvYPX9bK0DLrwMKysrOQt9ENUyBjNEKuh0OphMJkSj0aIenxlYSNQGDwcOHMANN9yA+vp6fOUrX0FXVxeWl5cxMTGBzs7ONW3ORgpqZmZmsHfvXtTV1WHbtm2wWCwVKwiQTTVUWsu132xJ8uU6H6lBk9YjZgaDQZPFM6s9kMvatrd8CjjuNOD3twErs8DALuCCDwGN5VtQMNt5qvYCAJFIBIcPH8b555+/LscrdppYqe+/iYkJHD16FFarFSeddFLhpPssx3/1q1+N888/H7///e/xoQ99CGeccQYuu+yykhYWtdvtWFhYAJDn+6K1F7jmd8CtXwCe++PqqMyJ5wMf/Dck3Z2ITE5WTQl2Ii0xmCFSyWw2IxqNFlW1JxQKrRkBUfP4gwcP4rrrroPdbscXv/jFtEXPXC4XAoEAFhcX11w5zXeclpYWtLS0YGpqCk8++SQsFgu2bNmieCHNcislsNKqcy0IQtmm3eVqY+btqat8F7PPQufCaDQiGo3CZDIpbfoaWpzrfM8vX1BZ0mtz/KtWf9ZJtudQTDBTjuAx17l87rnncMIJJ6SVgi/31LL1kkwmMTIyguHhYTQ1NeG0005TvaBxJkEQ8NrXvhavec1r8Lvf/Q7vf//7sWfPHnzsYx8rKqCQFreV9p2NKIoQercDX7wLiIYhCDqIxtXP8+L8PNrb24t/QkRVjMEMkUp6vb7oK9nBYFDOS1DTETh06BCuv/56mEwmXH311ejv78+6XXt7O4aGhmC1WuUFNaUvwULzpNva2tDW1obFxUUcOnQIsVgMAwMD6/4FqGXQoHUZaTXbKj12ru3K0UnNR8qbyTWFKNvzzxZwlbOwQ75OXK2TSr+rsV6jYBMTE9DpdGhpSR+tKufx12OULx6P45VXXsHk5CQ6Oztx9tlna55PIggCXve61+GCCy7Ar3/9a/zN3/wNzj//fFx66aVFjfoovfgBk2U1ZebPuVjBYBADAwMlPhui6sRghqgIZrO5qGAmtb6/ki/qV155Bddddx10Oh0+97nPYdOmTXm3FwQBXV1dGBkZkRfUlK64K/2SbmxsxKte9SoEg0EcPnwYhw4dQnd3N/r7+zUpTV1INXVMK5l4XIpiju9wODA7O5s1mCm0Dka+bTL3k69t6/3aV7ocdeZ6PpV+72c7fiwWw6FDh3Duueeua1vK+XqEw2EcOnQIS0tL6O/vz7lOjJYEQcCFF16IN7zhDbjvvvvwnve8B695zWvwkY98RHEVQb1en/PCVOb7KPX9tLi4iNbW1or/XSIqFwYzREUwGo3yF4sasVhM0Qrfg4ODuPbaayGKIq688kps2bIFgLLOtdFoRGtrq7ygptFoRCQSUV1212az4aSTTkI8HsfRo0fxxz/+ES0tLdi0aVPJUzCqWSkLRqrdfzWRpk/mUqjdWlSGW+/zouR45SzukJlrVelgJptnn30W27Zt2xAVsJaWlvDKK68gHA5j8+bNOOmkk9ZsU+7XQafT4aKLLsKFF16Ie++9F5dccgkuuOACfPjDH5ZH03O1RfqMGgyGnO2U8jKl+xKJBHw+X87RfKKNoPb/OhFViNlsRjAYVPXlF4/H83YKhoaGcN111yEajeLKK6/Ecccdl3a/0o6Uw+FAJBLBxMREwU5qPqIowmAwYOvWrdi6dSvGxsaqMq8ml2KKB6jt4Kq1Xh32YjplUoCemheRur9jUa7iDuUMbColsw3T09MQRTGt1DtQ/oC82P1ne1wymcTY2BiGhobkv1vZRh9T96G2TWo/a6IoQqfT4S1veQsuuugi3H333XjnO9+JN7zhDfjQhz4kXyzK3GfqhSklo6UAsLy8zFEZ2vAYzBAVSVpEU22FqWxfKiMjI7juuusQCATwmc98Btu2bSu5fU1NTZicnITP54PT6VT9+Gxf3l1dXejq6pLzaqLRKHp6etDV1bUmEKiGEYhyVWWr9PNSopiryzabDX6/v6j3y7FmvRLvKyUWi+HAgQNZp5eV+/2vxYUCr9eLI0eOYGVlBW1tbTjzzDOzFrdQ+neq2DZl23/q73q9Hm9729vwlre8BXfeeSfe+c534qKLLsL73//+Ne01mUwIBoOF255MAn+eNreysoLe3t6i2k5UKxjMEJVAWkRTaSckc7uxsTFcd9118Hq9uPLKK7F9+3bFX6yFjimKolwQYHFxEV1dXXm3zfeFm0nKq4lGoxgaGsKDDz6Iuro6DAwMyFc9y93hqXSwVI7jV/o51dXVYXFxcUMGM5U6t0qDlGoLZp555hns2LFD0bTYXNa7VLo0CjM8PAyTyYSBgQGccsopefelRZCS+rplVrlU+vdcr9fjne98J9761rfi5z//Od761rfibW97G/7mb/5GDmqMRmP+XM29vwF+eg0w+CLgcCJ89jvheefn1iXXkaiSGMwQlcBkMiESieRcPyaXiYkJXH/99VhYWMAVV1yBnTt3qjqukuNJ9/f29uLgwYNpldRybauWyWSSp6DNz8/jyJEjCAQC6OzsRE9PT94yv4qr8uS4T6tpKMUqRyet0iM+VqsVkUikom0ol0qd20KlpnW+RYjhIARHk6bBTCnv9bGxMRgMhpIXWCzXSG3mfvx+Pw4fPiwvCnnGGWeUVGK8mDYUul0pg8GAd7/73XjHO96BO+64A29729vwjne8A+9+97vXBLxpx3rsXuBrH1xdJBMA/Cuw3/8DOJaGga/+DqiB0WSiYjGYISqBTqeDwWBALBYDsPaqnPR/6fbZ2Vl873vfw+TkJK644grs2rWrqOOq+cK02WxwuVyYmJgoOsBQwu12w+12Ix6PY2xsDI8//jjMZjP6+/vh8XgUPwelSeaVWFAvVaVHUcpFKuWdLW9GK/lGIappdKJUed8jE0eA734a4oFHIQAwt3bD9ObPAu3v0+TYxb43pcUxc00vK/b10TqwSSaTGB8fx/DwMIxGI/r7+wuOwhSi5bpUpVb3MxgMeO9734t3vetduP322+WRmvPPP3/t94woArd9CYKw+l+IgCACViMgPPO/wIFHgBPOLvl5EVUrQcUfpo3zDUOkoWQyCZ/Pl/YFk/m5mpqawo033oiXXnoJ//zP/4xTTz113doXiUTw9NNPY/fu3RgdHZVLNq8Had764uIi2tvb0d/fX7AS2kYNEpQSBEH1SF8has7p7OwszGZz1qlm6zEV6pJLLsEdd9xR1mOUquTz4FsC/v40wLsAJFf3k8TqxXPhS/cAO9e3DHKqxx57DJs2bVpzAaIaPpfJZBIzMzMYGRlBJBKBx+NBX1/fhq6uKIlGo7jllltw55134gMf+ADe+c53/qWYzPIcxPdvgfDnURmdCOgEwGECoNMDH/gy8O6rKtZ2ohIV/MPDkRmiEul0OnktFyB9dGZmZgY33ngjBgcHcfnll+PSSy9NK5GpRQeh0D7MZjNisRhMJhPa29vlNWjWo2NSX1+PU045BclkEhMTE9i3bx8SiQTa2trQ1dVV1Z2QSnXeyrWqu1LZ8mbUFrnY6Eo+D//338DKfNolQh0AUQBw53XrEsxke58NDQ3BZrOpGkldD7OzsxgZGYHf74fb7ca2bdtQX1+f9zEb7f1qMpnwgQ98AH/1V3+FP/zhD3jLW96C973vfXjb294GvdkGQY/VERmsvo8s0vUqMQnYN14OHFEqBjNEGrBYLIhGo/IX6Pz8PG688UYcPnwYl19+Oc444wwAwNGjR9Mep9WUBqVsNhsaGxsxNjaG7u7uvNsq7VQr2U6n08mV0OLxOCYmJvD0008jmUyira0tbfpbvn2tZ4BR6avQlZItb6aaz0Uymay6BOeC79Oj+/GXOUF/ISQBHHl2zebl6JjrdLq0ffp8PoyMjOCcc85RtZ9yfSaXl5cxPDyMpaUlOJ3OtOIiStu1EZlMJlx66aV43/veh1tvvRUXX3wxPvjBD+Itr7oIur2/hJgEDAJgkIIZvQE4+x0VbTNRuTGYIdKATqeDyWTC1NQUvvOd7+CFF17A5Zdfji9/+csl71uLzkLq410uF6LRKKanp+UEX7XVzIrZTmIwGNDT04Oenh5Eo1FMTEzgySefRDKZREdHB7q6unLm9VRzp7qaqV34cT3yZrRSbYEMoOB92uj5c0J2eodbBCC41o6KqKmWqPQzkrrPZDKJffv2YdeuXarPZ2pBjmKnR0rt9vv9GB0dxczMDGw2G3p7e7MubFloP+tNbWl+LQIti8WCj33sY3j/+9+PH//4x/jAo9O4ydmMOu8czGbdXxL+/+FWoGHte4poI2EwQ6SBpaUlXHvttXj88cfx6U9/Gl/4whfkL63MYgBqaTFSIQhCWufU4/FgYmICCwsLaGpqqliQYDKZ0NfXh76+PkSjUblwgF6vR0dHBzo6OspelWg9aHllvdTCB0oea7PZEAgECk7lob9Q9br81XuBX96U/b7X/W3RbSj2c/ziiy+iq6sLDoej6GNnPn+l52N5eRnj4+OYn5+H2WxGd3c3jjvuuKKC1ELHU/vZUTM6reTxmX8H1LYnmUyuucBgtVrx8Y9/HB/4wAfwg+/ehMj//Q/+dtfx6N91BnSveR/Q0qN4/0S1isEMUQmWl5fxjW98A0888QQ+85nP4KqrrpIrmwHqF2LUYgHObLIthtjW1oaxsTHo9Xq4XC7F7SwXaV2IgYEBhMNhjI2N4YknnoAgCPB4POjo6Mjb2VI7+pDv8WruU9oeraxH4OlwOLC8vKxJMCOKIhKJBJLJpPyvKIpZf4DVxRqXl5fXlODW6XTQ6XTQ6/Vp/68Wql6X7uOBv/sW8N1PA4nEnxMdAN9pF6L+jR8rVxOzmp2dhc/nwwknnFDU43N9NnKdDymJf3JyEl6vFw6HA52dndi2bVvZR9myXWAqtH2px0uV+XdA7f4jkUjWizuCIMBut+Mt73gnWv/+U7jlllvw+1t+j086TsBFF3VzRJs2PFYzIyqC1+vFN7/5TTzyyCO44oorcMEFF8jTLLxeb9q2qV+eQ0ND6O3tLfrqYLHTKF566SXU19ejo6Njzb6Hh4fR2NhYtQslRqNRTE5OYmpqCuFwGE6nEx0dHWhubq7KKUYbxeDgYFqxCkkymUQ0GkUsFkMsFkM8Hkc8HkcsFksLVFKDkdQARKfTpd0nCELabR/5yEfw/e9/HwDSghxRFJFMJuWgSPo98ztMCnIMBoP8r9lshslkyrkAZMUqdS3PAXt/DUQCwInnYzBp0bxASD6xWAwPPfQQ9uzZA7PZXLbjRKNRjI+PY2pqCvF4HE1NTWhvb1eVA0OrgafFYkm7yCAFaIFAAIFAAFu2bAGwmgP1rW99Cw8++CA+9alP4Y1vfCODGqpVBd+4DGaIVEj9grj88svxhje8Yc0XRCgUQjQazTqdYGxsDB6PB2azWfORgHzGxsYQCoXkL7rMYw0PD8PtdqOurk6zY5bL/Pw8Jicnsbi4CKPRiPb2drS1tVW0MprWI0Fa7L8U0lojzc3NSCQScqACrHaeTCYTDAYDjEaj/K/RaIRery95PZFSSzMnk0k5wJKCLCn4koIgANDr9TCZTDCbzTCbzbBYLOs20pOraMHQ0BD6+vrWpQ0A8Pjjj6Ovr6/kxTGz8Xq9mJiYwMzMDAwGAzweDzo7O3Mu3Juq2Pd7NZSPLqfx8XG43e41f+uSySSOHj2KnTt3rhm5Sb3w9ulPfxqve93rNvQ5og2JpZmJtOD3+/Gd73wHv//97/H3f//3+PznP5/zC8FqtcrBTOZUGYvFgnA4DLPZnPcLResvG7vdjrm5uZzH6unpwfDwMARBKGnefDHUdkCkxTkBIBwOyyWf4/E4Ghoa0N7eLt9fznak0joXKlW5OmiiKCISiSAUCiESiSASiSAej8vBitFoRDweh9vthslkKksOQzlIxTiyTcdJLZueSCTk5+3z+TA/P49EIgEA8miOzWaD1Wr9y3oeGhBFMe1clvL6FnpsvvuPHDkCu92uOJApdCypqMjMzAz8fj8sFgs6OzuxefNm1eev2M/GRu+kx+Pxv7yvjz4H/O5WYHkKIc8AOv76g1nf8/X19fjCF74gT4n+5je/iSuvvBKvfe1rN/z5omMHR2aI8ggGg7jppptw//334+/+7u/w5je/WVGnLhKJIBgMrvmy8Hq9CIVCaGlpKbltanJrYrEYnnjiCZx9du5VoJPJJIaHh9HS0gK73V5y+8ol1/NOJpOYm5vDxMQElpeXYTab0dzcDI/HUxU5QZUkiiLC4TCCwSCCwaC8JpLFYkn7SR2ZCIfDWFhYWDM1sdwqsWhmZqc4FoshFArJP1KQY7VaYbPZYLfbc05ZK0WuqX1aW1xcxAsvvIBzzjmn6Cmv8XgcMzMzmJmZgc/ng16vR3NzM1paWrJ+3pQEXkDpAUk1j3iWeuyjR49iYGAAeOAnwE2XA3pAjAN6HVDnrIdw7YPAppPz7mNpaQnXX389nn76aXz2s5/Fq1/9agY1VO04MkNUjFAohP/8z//Er3/9a1x22WV44IEHVF2ZNpvNiEQiaVNzRFGExWLBysqKJm1Uk1RuNBrlDlnq41O/xHQ6Hbq7uzEyMoK2tjbYbLaqnLaR63nrdDq0tLTIgWI4HMbs7CxeeeUVBAIBGI1GuN3unJ2tStCyylmqRCIBv9+PQCCAcDgMYDVwsVqt8jTHQqRRxFyKrV5VjTLbLU2bk3ITpNwdKSCcmppCLBaDwWCA1WqFw+GA1WotuZrWepy/eDyOZ555BmeeeabqSlpzc3OYmZnB4uIidDod3G43uru7FY2EFjqWVs9dzXuyXOdbyWeh6GOvzAPf+/Tq/+OrFZitOkAIB4AbLgW+83Tehzc0NOArX/kKFhYWcN111+GGG27AP/zDP+Dcc8u/UCtRuTCYIUoRDofx/e9/H/feey8++tGPqg5iUlksFvj9/rTF6Uwmk3xVvBKyTX1LZTAY0Nvbi+HhYbS3t8Nqta53EzVjsVjQ3d0tLw6aGtwEg0EYDAbNgptS5vhrsf94PA6fzwe/349oNAq9Xg+bzQaXy7Wmk602CI7FYllHITLbU6uBjBJSoQKbzZaW8xGPxxEIBLCysoKpqSl5m7q6Othstuo7R74lzH37szj/4B+h/3EMOPmvgXf9I9C1NpcumUxifn5e/hFFEQ0NDWhtbcWOHTs0Lb5RrkC4Uue7HMeNRqOrn8OnfwckRIji6uVqgwAY9QCSCeCVfcDsKODJvyAyADQ1NeGaa67B3Nwcrr32Wlx77bX43Oc+l3f0nqhaMZghwuq0sB/96Ee488478bd/+7d44IEHSk4Glubtx2IxRZ1JNVfppS9/6TFKOgMmkwnBYLDgFDK9Xo+enh4MDQ2hu7tbsypHWk0jybf/fPvOFdwcPXoUfr9fDm4aGhrgdrtVddbKPa0lW4nXQCAAn8+HUCgEvV4Pu92uaNRFzfHtdjt8Pl9Zqk6tx0hOuY9hMBjgdDrlSoDS6+L1ejEzMwOdTge73Y66urqCeXIA5JHcsggHEfncX6F1egjCn//MiI/dBd2++yFe+yf4na1YWFjA/Pw8/H4/BEFAfX09WlpasGXLFk3zhjLVwrSw9ZTtefr9/tV8xnhMnnMjjcqkiUVUHau5uRlf+9rXMDs7i69//eu49tpr8Y//+I8488wzi38CROuMOTN0TItGo/jxj3+Mn/3sZ/jgBz+Id7/73Zp+aaeWapa+oMbHx9HU1LRm1KPcX9QHDx5EfX09Ojs7FW0fi8UwPDxcMKApZ7tL6fyrnb4VjUYxMzODhYUFrKysQBRFWK1WuN1uNDU1ob6+vuir0VpMJ0skElheXobP50Mymcw5AqDl6xGLxTA1NSUHgOuhEjkz5ZJIJODz+eDz+RAOh2Gz2eB0OmG327O+RnJORBkE7r4JtluvXjP5PCkAs8edi+E3/xOam5vR1NS0btMwayk4UTJlrRxTRiXS9F/T4iTwsZMBATAKgF0eNBVWF8i89ShQwqjZ9PQ0vva1r2F4eBj/9E//hNNPP12T9hOVgDkzRNnEYjHceuutuP322/H+978fv/vd78py5VGn08FqtSIUCslfhPX19fB6vWuCGS2+1PN94TqdzjVr4ORjNBrR29uLkZERdHd3Z62UA5R3KkcpVZ4yf1cyctXV1YWuri75tpWVFSwvL8ujN8DqgpJSgKO08luxnRxpAUnpSnldXR26urrS1mXJpOXrIU0zo+JIC9JKwUEwGJRHbaScnNQguRyfJWm6WPD/foEeAemXJUVAB6B16kW0vupViveZ7fNUTGBSyeBALSX5UOUkVzJr7UX0jZfC/OsfwCoFMjo9IIrAJ75ZUiADAK2trbjhhhswOTmJf//3f8fXv/51fP7zn8epp55a+pMgKhMGM3RMicfjuO2223Dbbbfhb/7mb/C73/2uLFWJUqUWA5BKHy8sLCh6rNoOQurUs0xOpxPj4+OK9wWsdma7urowOjqKzs5OzdZyWe8rssUeS5pC1NPTA2C1Y7i8vIyFhQUcPHgQoVAIwGpSrdRpdTgc8utQjHg8jqWlJfh8Puh0Ovn4lVog1Gw2IxwOq37tC3V4q62zuh5Sc26i0SiWl5cxNDQEo9GIhoaGks9HOBzG0tISlpeXsbKygkhkdcrRkSNH8KYmNzCpA8SUqWzSy2NWlxuX7b1dKyMstSg1by2RSGD0/Euxbesu6P73R8D8OLB512ru0449mh2zvb0dN954I8bHx/HVr34VX/va13DVVVfh5JPzV0sjqgQGM3RMiMfjuP3223HLLbfgkksuwf33359zpKEcrFYrAoFA2hoTuRbOS6VlUrndbkcwGFT0+NTjms1m9PT0YGRkBO3t7XkXvVMapJRa9alSdDodGhsb03JI4vE4FhcXsby8jJdfflk+xyaTCXV1dXA6nWhoaMg7iiOKIlZWVrC0tARBEOB0OtHb21uxACZVXV0dvF7vmmCmmEpRxRYiqFX5zpHJZILH44HH40EkEsHS0hLGxsZgsVjQ0NCQ93MmBdXSe8bv90MURRgMBjmo7unpgc1mw8GDB1dLlJ/cB+z/35S2reZcQAfgvHfnbHulPouF3h/VOL21XMfy+/3ydNKJiQm0tbfDtns38OaPlb19nZ2d+M53voPR0VF89atfxeLiIq666irs3Lmz7McmUorBDG1oiUQCd9xxB26++Wa8/e1vx29/+1vNEtrVkEq9SlN2bDYb/H6/XPp1PaSO2qjthBqNRvT19WF4eBgejwd1dXWKH5tLviv3pXQktOyIKBk9kFY393g8abeHw2F5mtrk5CTC4bBcnru+vh5OpxMWi0VetFKaQlbOROt8cpVadjgcWFpaWrN9rQakWtAqaJeYzWa0trYiEAigoaEBS0tLmJqagsPhgE6nQzAYlHNvotGo/Lo0NDSgt7cXLpcra+A7MzODpaUlnHXWWYB4PPD6D0P8zc0QDAIEUQCSSWBgF3Dxp3K2vVpfQ7XtUvN+1Oo5F1Wi+ehzwH//K7D/QcBsAc59J4Lnfgjuvi1YWlqCTqdDc3OzJu1To7u7G9/97ncxPDyMa665Bj6fD1dffTV27Nix7m0hysQCAFRz4vE4rr/+elxxxRU5p4glEgn8/Oc/xw9+8ANcfPHFuPTSSzWbIlUsURTh9XohiiJCoRAWFhYUJ+OXcszUL8unnnoKW7ZskasvZdsmH2lhzaamprR9bHRarqkSCAQwMjKCiYkJhEIhWCwWmEwmGAwGOanf4XDAbrfLndlKO3r0KPr7+9elY6u0AIDazmm1jgTF43F4vV74fD48/fTT6OjokNf3CQaDSCQScLlc6O7uRktLS86/Y5nnIxAIYO/evTj77LP/8ndSFIEXHgEevQuIhoFTXg286s2A0ZR3X7luqyVK26/181S1v6EXgH94NZCMA3+eDSjqgKi7B7rr/oTh6Vls3bp1XS+C5TI4OIhrrrkGoVAIV199NbZt25Zz20cffRShUAivec1r1rGFtIGwAABtLAsLC/jwhz+M97znPVkDmWQyiTvvvBPf+973cOGFF+K+++6rmrVSBEGQ8w+sVqs8n10Lub4wM29raGjA8vJyWiCi5otbp9Ohr68Po6OjSCQSZSnZW42yrReittMTi8WwsLAAn88Ht9uNrVu3ppX/ljq1fr8fS0tLGB8fRygUkjvh0urzdXV1sNvtqK+vX7epkna7HYFAQHHBg/WgdhSwUpLJJILBoLyAqbQeUCQSgSiKclnturo6uN1unHjiiWummIXDYczPz2NyclLOz8q3hk0ikcCTTz6JXbt2yX8n5ffriWev/uShWU5M0Ac8/ktgeQbYtAs48Zw/z20rXTH5hFpup/VxAQA//RqQiKddOhYSgGl2BPO/+gE63/J3BUvrr5f+/n788Ic/xJEjR/Bv//ZviMfjuPrqq3Hcccet2fbkk0/GZZddhgMHDuDyyy+v6aCYqhNHZqhmHDhwAJ/61Kdw3XXXrUlCTCaTuOeee3DTTTfh9a9/PT7+8Y/nnXNeSV6vF8lkEtPT07DZbJpcZVN65XlxcRFDQ0PYtWuX4n3nuko7Pj4Os9m8ZnpVuVXzVfZsIpEIZmZmkEgk4Ha7c07RK0SaauT3++Hz+RAIBBCPx+X7TSYTzGYzrFZr2o/NZit56pq0dkpbW1tJ+1GiVkozi6KIWCyWFqhI/4bDYbnghyAIsFgssNlssFqtcDgcckntzP0NDw+jr68v5zETiQTm5+fh8/ngdDrR1NQkj9ylfk6feOIJdHZ2ln3kN68XHgG++m4g6Ad0ApAUgc2nAP/vF0BdQ+XaVc3e07V6vlKIIgC9gPCpr4frX35RNRfnMr388su45pprIAgCrr76amzevDntflEU8R//8R84fPgwvv3tb1d8pgTVFI7M0MZw991344c//CHuuOOOtM6zKIr45S9/iW9/+9t47Wtfi3vvvbdqrlzlYrfb4ff70dTUhImJCU2CGSWde1EU4XK55BLDSuW6itbV1YXJyUlMTU2tSydXUiuBTCgUwtzcHERRRHNzs+rgOjOIlCphtbS0ZN0+HA4jGAwiFAohHA5jbm5OzsdJJBLydgaDARaLBVarFWazWc7nMpvN8kKvmSM+NpsN09PTqtpfa5LJJKLRKMLhMCKRCKLRKKLRKCKRCMLhMOLxOKLRKBKJhPzaSOcy9bWx2+2w2WyqpwcqGWnQ6/VoaWmBx+ORL0zYbDZ4PB55lO/QoUOw2+2VDWRC/r8EMsBqIAMAR58BfvhPwBXfq1zbyqykiy32+r+cM1HaHyBChK3RU7WBDABs3boVt956K1566SV8+ctfhtFoxNVXXy2vmyQIAj73uc/hN7/5DS6++GLcfPPNaG9vr3CraaNgMENVLZlM4l//9V8xPT2Nu+++W+5kiaKIX//617jxxhtx/vnn46677ir6ivd60+v1aVfKU8tulirfF2lqAYB8HSc1Savt7e2YmZnB+Pj4ms5TtcyxX++RnFAohOnpabnjaTKZijoPah9jsVgUXe2MRqNy0CN11P1+v9x5j8Vicocd+MvrODMzg+npaVgsFjkAMhgM0Ol08vtZ+l2v18u3S79L73udTpe2rkq2NYFSJZPJrL/H43HE43Ekk0n5/4lEQv439f+p96fel0oQBJhMJhiNRphMJjmXyWazwWw2p+U2lYOavCxBENDU1ITGxkZ4vV4MDw/DbrcjmUxiYWFhNeF/HeRs4xO/AgL+tddTkwAe+TnwsWsBW+6/18X87aiWvzdp719RBMZeBiIBiN3bIOQogS23/fz3AL+4FmLiL7PxBACIA/bXf6jsbdfC8ccfj9tuuw0vvvgivvCFL8But+Oqq66SRxzf8IY3YGBgAO973/twzTXXcFFO0gSDGapafr8fH/nIR3Deeefh//2//wdg9Y/+/fffj2984xs4++yz8Ytf/KIqkiHVstls8Pl8aGxsxMLCAlpbWzXZr5JOu8PhwMrKSs5VvtV2CFpaWjA/P4/R0VF0dXVpUgVJy45JoeBNK9FoVB696OjoWNfS32pIIy9qV3mfm5tDPB6H1WqVg55kMolkMikHB+FwGIlEQg4wpPtEUZRvTx3ZyPa6LC0t4aGHHlpTujxzpEMKkFIDpdT/G41GWCwWOZgyGAzyT6GgpBId48xjKjm+tA5RfX09xsfH8ac//QmvfvWr1639OY+xNAPohb+MyKRKiIB/JW8wsx7Bf9kN7gdu+Bgw9jJEAIKjDnjvl4DXfVjeZM1n4K1XAC88DOHgXkAvIJkUoUsCxnf/Aww7z6nI0yjW9u3bcfvtt+P555/H5z//eTidTlx11VXo6enB1q1bcdddd+HDH/4wLrroInzgAx+odHOpxjFnhqrS4OAgPvrRj+KLX/wizj77bIiiiP/93//FDTfcgFe96lX49Kc/XfPVtGKxGAKBAF555ZU184uB8nWoRkdHEQ6HsWXLFk33u7S0hKWlpapYH0X6u1bsOj1qHhePxzEzM4NYLIaWlpaqngqSi5LnHI/HMT4+jp6enrJ2HGslZ0ZrsVgMU1NT6O7uLrht5usVjUbx8MMP47TTTkMsFsPi4uKa9ZCU0mQk84WHgS9clP0+lxv40UsQdfrS30fhIPB//wU8eR8g6IDT3wjx1e/NOQIiKXuwtzwH/N0uIOSTq5KtRjQAPncLcOabcz82EQee/C2WH74XMZ0BLRdfBscp51T8b2qpnnvuOVxzzTVwu9246qqr0NnZiUQigS984QsIhUL4j//4j4qVpaeqx5wZqj1/+MMf8O///u+4+eab0dXVhf/7v//Dddddh1NPPRW33347Gho2RvKoNFVHWpQwc4RJ7Zet0k5IU1MT9u/fr3kw09DQAIPBgKGhIXR1deUcmVDbWSqm41FKR0XpY0VRxNzcHHw+H1paWrJW+qqWqS+5KK3KJi3ImJp7s1Gt92tWzOKUqdslk0ns3bsXO3bskKfaNjQ0YHZ2FoODg2htbc2Zr5WruEex5M/2jj3A1t3AK0+vHZ15xz8AekPh3kkhoQDwzxeurssiYnXxz+f+BOFPPwO+/CvAlHvKZcHzfORZ4Lc3A/OjQPc24PWXAu39ytv2h/8GAr6Mg/75587r8wczegOWjtuDl8Qm7N69Gxans+YDGQA46aST8LOf/Qz79u3Dpz/9abS1teHzn/88rrnmGtxxxx1429vehptvvhlNTU2VbirVIAYzVDVEUcS3v/1t7N27F/fccw+efPJJfOITn8DOnTvxX//1XxuyDLDVaoXb7cbw8HDJ0+WUdkLsdntaWWgtO291dXUwGo0YHR1FW1tb1mIMajtLxbZNzfNSew4CgQCmp6fhdDrlBNdspH1WY1Cj5nWQ2m61WhEMBlUV2ajG557Perc19T0i/a7mtXn22WfR0dGRVhhCEAS0tLTIoz2CIKCtrW3NlW+tn6vcbkEAvvAz4EdXAQ/dsTq1zNUEvONzwBsu1eZg9/8IGHzuz8fDX+aOvPw08L8/Ad740eL2++AdwDc+vjpNLvHndXnu/xHw/+4ETshf0lo2dng1uEpm3C5iNYcmj1AohPHxcXR1dcFms1XtdNVi7dq1C7/4xS/w5JNP4pOf/CS6u7vxj//4j9iyZQve/va341vf+hYX4iTVGMxQVYhEIvjkJz+JgYEBfPSjH8W73vUubN++HbfccgvcbnfatqIo4siRI2htba2ZpP9cdDod6uvrYbPZsLy8rDqPoVgmkwnhcBgWi0XzDo3FYpHXonE6nUUHoaUmAZcjkEkkEpicnIQoiujp6VE8LaISi/UVUsyxnE4nvF6vomBGej61FMhUkiiK0Ol0cknnXNuk3nfkyBEIgoD+/uyjBkajEd3d3fD7/RgZGYHL5VJ85bvk96PDBVx+E/DRr6/myDS2AHoNuxyP3Zt98rsI4PF71wQzip5PwAt89/LV/yf+vPNkEhCTwE2fBG56Ttk6OZ61leRE8c8P9XTlfFg8HsfExARMJhPa29urdnkBtYaGhtZ8F5x22mm466678Pjjj+PjH/84BgYG8K1vfQv/+I//iEsvvRQXX3xx5RpMNYfBDFXc1NQUPvzhD+Ov/uqv8PDDD2NhYQE/+tGP4PF4IIoiRkdH8dRTT+Hpp5/Giy++iGQyiYGBAXzmM5+p+WAGWA0surq6cOjQITidzrJU8cncxuPxYGZmBj09PUW1uRC9Xo/e3l6Mj48jEokUVbo523Mq9FwzE6iVXOFWer5XVlYwNzeH1tbWvItH5mqjmrZrScsgSU2J5mMpiJECkVKmaCkJ/lLvm5qawtTUFPbs2VNw3w6HA3a7HbOzsxgaGlJUoEKz18/qWP3RmphnymMyc0hE4fPZ/0cgEs1yLABTo8DoQaBne95dCIIA8dXvXZ1OJibSSiwDAC78ePquU4LY0dFRuFwuhEKhor4LqtULL7yAn/3sZ1hcXITT6cSpp56KU089FaeccgrOOOMM3HPPPXj00Udx1VVX4bjjjsO9996L559/Hv/8z/+8IabYUfkxmKGKeuqpp/CJT3wCTqcTk5OT+Nd//VeMjIzgpptuwv79+xGNRtHV1YXdu3fjkksuwfbt2zdkkqDdbofL5cLi4qJ85VRtZ7xQKddUbW1tOHDgQNmCGemYXV1dmJubw8jICLq6ukr+YtKywpnSfSWTSYyPj0Ov16O/v7/gc8gVyKyXzPeNlh0iaW2VeDxe1hLF0r/V2pnLVnks32tczAWHfJaWlvDyyy/jrLPOUpVn09LSglAohLGxMTQ0NNT21N3TLwSO7l87OiMAOO2Nxe0z+edy3VKyfqZYrOAuRFEEWrqBf7oduOEjf8mdEQC8+ZPABekllqX3zvj4OBoaGrC4uIiBgYEN9T130UUX4aKLVgtCLC8vY9++fXjiiSdw0003we/3w+12Y/fu3bjqqqvg8/nwzW9+E1NTU3j729+On/zkJ3kvHhEBrGZGFfT5z38e3//+9zEwMICWlhYkEgm0tLRg9+7dOPXUU3HiiSceU6sERyIR7N+/H5s3b4YgCPKVXqWfUbVz7f/4xz/i/PPPL7a5qvh8PszOzqK7u1uzNXUK0aIz7Pf7MT09LSf4V2vnej0tLi5CFEVF05WKeQ2KqWaWOb1wvcpxaykQCMDr9RYcxQwGg3j88cdx5plnFl05TxRFzMzMIBKJoLOzU15ws6YEVoDP/RUwdTQ9N6X7OODfHwBsdeorsy3PAX97HJBY3aE8NQwAXM3Ajw6qmyoXCQH7HwTCfmDbWYC7Pev7cn5+HtFoFC6XC8vLy9i2bZvyY2wAs7OzePrpp/H000/jueeeQzgchk6nw8GDBxGJRHD33XfjtNNOq3QzqXIK/iFnMEMVIYoitm3bhne84x147Wtfi5NPPplXXwCMjY0hFArB4/EAwJq1NrS0d+9eHH/88XkLDyiZGqXkb4goiohGoxgbG8tZGKDazMzMIBwOV11nT5PSuSUcOxaLYXx8HL29vWU5hpalmcs1QlUOfr8fgUAgLZE/UywWwyOPPIKTTz65pPw66XMdCAQwNTVVu/kZ/mXg198HHv/lanfnVW8GLvwYYFdeTGXN5+nOG4Dbvgzo/rxOjg6rvZ/P3gxhz1u1qfaWYmVlBcvLy+ju7sbg4CB27NgBs9lc9DE2AlEUMTExgaeeegq33HILbDYb/ud//qfSzaLKYTBDVEtEUcSzzz6L7u7usi/qNzIygkgkonmJ5lSZ7UwkEvK8cLUlttfrSnsikcDY2Bjsdjuam5vLfjytaH1+8u1vcHAQfX19ZXk9pGBmPUdW8h2rHO3Itk+v14twOCxfyMiUTCbx6KOPYsuWLXLAo0Xb4vE4RkdHUV9fv6bYSi3SZErfE/cBv/k+hJlhiL07gDf/PbDtjLRgpJS1rCTSiHV/fz9mZ2dRV1eH9vb2ovdHtEEV/JAxs4qoigiCgE2bNmF8fLzgdqVqbW3FzMxM3m1KvbKd+RipMIB0RbiUfZVDOBzG4OAg3G43mpubq/5qfiotXh+l99ntdvh8vpz3K5XvYlqlK7tp0VnNd7zM/RYahX366afR1dW1pgRzqfR6Pfr6+uSgptRRv3KMGmbbZ67jKDknBbd51YXAl38J8XvPA5+/Hdh2xppjlnruA4EA5ubm0NfXh2g0ilAoxECGqEgMZoiqTH19PVwuF5aWltJu17pTZTabEY/H8y6EmHpMrTopgiCgs7MTRqMRQ0NDiMfjebdfrylVXq8XExMT6O3tlavkVWo613ooZrqatL3T6cTKyoombahW5S7kkLmvZDKZczrj/v374XA4yjK1TwqsWltb4XQ6MTQ0tOZvQjFrEmkp2z7LWf1P6TbFVJ4EVteSmZ6eRk9PD3Q6HSYnJ3H88cerbywd82699VZcdtllGB4ernRTKorBDFEV6unpgdfrTetUqLk6mSnXl67H41E9QqIVt9uN1tZWDA8Pw+/359yu2A6DGouLi1haWkJfXx+MRmPRnfxaUkybpdfCYrEgGs1SwnaDK2fwlUgkso7MHD58GIlEYl2Swp1OJ1pbWzE0NCS/vpUqpFDJvLB8ij0f0vpBkUhEvmii1+uxtLQEt9t9zOfJ1LLh4WEIgoDzzjsv7fYHH3ww6+1aSiaT+N73voef/vSnZTtGLWAwQ1SFBEHA5s2bMTExoarkci65OgadnZ2YmJgoup2lslqt6O/vx8LCguL1SwpR29GYnZ1FIBBAd3d30cUWSu3slbOzWK59WywWBIPBsuz7WJRtmtno6CgWFxdxyimnqNpXKYGAzWZDV1cXRkdHEQwGKzZ6VurfNrXbKFXs+dDpdHIRlJ6eHuj1eiQSCXi9XnR2rl1kk0iJN73pTdDr9bjnnnsq3ZSKYjBDVKVsNhsaGhrg9XqRTCZL/tLOdp/T6UQwGFT1Za/1FVOdToeenh4YDAYMDg7mnXam9bEnJyeRSCTQ2dlZ0SlPWnTIct2v9TlLnWrm9XrX3KdmBLHY57QRSYsnSiYnJzE0NFRUSdpS38smkwm9vb2Ymppa14C10KKhuR5T6jZafPbzvcelKoDSeltScZeJiQls2rSpqqdbUvFOO+00vPTSS/jJT35StmO43W6cddZZ2Lt3r2YXBGsRgxmiKtbZ2Qm/35+zg5/5BZovDyLXF2Z9fT3m5+cL7rvQfkrV1NSEtra2tGln2Z6fViYnJ6HX69Ha2loTnYn16JCpaYfdbl8zPTBXZ7TYkcVaeF20kjrNbG5uDocPH8ZZZ50l31bsuShmyqS0OGpvby8mJyfXLaBRs65WqlLfJ8lksvBGRbZBEATE43E5kJGmk83NzcHj8dREmXoqjs1mw3HHHYfu7m7FjznvvPMgCIKqHJiLL74Yoiji3nvvLaKVGwODGaIqJggCBgYG5KpjmV+YWiTG9vT0YHR0tOT9lEoQBFitVvT19WFxcREzMzN521DKVXtp3y0tLeu6bosW+Qfr+boUqjZmMplqMncms7xuuSl5zaSRmaWlJbzwwgs444wz5Cv4xXbyU49dTH6dVH1wamoKoVCo4GMrNZJWzHGVViYr9fOWSCQwPDyM9vZ2WCwWiKKIQCAAYLWiJG1c65EzA6wGMwCO6almDGaIqpzFYkFnZyemp6eL6gwX+qJ3u91YXl5WvL/M4yvpSKhps16vR3d3N/R6fd5qZ8UGIXNzc4jH42krra/nqIYWV4HLIdu5LHRe6uvrNalqtt6k57We69hk+3+qZDKJQCCAZ555BmeccYZ8BV+rBPxi92EwGNDT04OJiQmEw+GyHGO9qTmnpRQDicfjGB4eRktLizwCE4/Hsby8jP7+flX7Jcqlr68PJ554Iv7whz9oUjK/FjGYIaoBLpcLTqcTi4uLWb+Ii12vQ3qc2+1WXNWsmKlfxQQdSqqdqe08LS0tIRQKoaOjI+c25b66XGqHr1ztK6Zd9fX1eSvR0Vq5zrPP58O+fftw+umnw2q1Ftx+PRkMBnR3d2N8fDxvKfdKUfqZ0GrtICV/b6PRqDwi43A4IIoikskkJiYmMDAwkLMMN1ExLr74YkSjUfzmN7+pdFMqgsEMUY1ob29HIpFAMBhcc3VfSTnRbKTH9fT0YGxsTJuGKqC0M5E67WxqaqqkJPdQKISlpSV0dXVp0jYlSg08qqEjm0tqwrqWHdxyruVSLfvKFAqFsH//fpx22mlwOByqH78e07tMJhPa2tryLqxZzCiGFm1XekFFq89Tof2Ew2E5R0YKTEVRxNzcHLq7u9OCVSItHOtTzQyVbgARKdff34+XXnoJLS0tMBqNafeVUsLZ5XLB7/cjkUhocsWw0BQwNR0YadrZ0tISBgcH0d7evqYzUOj5JRIJeW0HnU4nr/lQqlznXKvOZaFzWMlgR3qNpalmjY2Nmu1XrVznQsvzU65zHYlE8Nhjj+G4446D0+ksah/ZRmrL0V6bzQaXy4WJiYms5YTLUYlMK+U+lvR5CAQCmJycRH9/v/y3VBAELC8vw2KxaPY5odr27//+7zh06NCa26XbPvvZz2a9sHHttdfC7Xavuf3kk09GT08Pfvvb3yIWi63pH2x0DGaIaoher8emTZtw+PBhdHZ2Qq/XZ506ka8zk+u+trY2jI+Po6enp+R2luNKcUNDAxwOByYmJmCxWOTkfSVGR0fR3t4Og8GwLldo16OTVg2jNoIgwOVyYWxsLK2Ttt6BVjWci2JEIhE8+uijOOmkkzTJPZLOe7nOhyAIaGhoQDAYxNLSEhoaGjTddyULCBRzzlLbLIoiVlZWsLCwgIGBgbQqdCsrKwiHw9i6daum7abadf/99+NPf/pTzvvvvPPOrLd/6UtfyhrMAJDXh1paWoLH49GknbWC08yIaozFYkFvby/Gx8fT1p9J/TLO1qEplPTc19eHkZERRW2oVEUto9GI3t5emEwmDA4OKqqwNDs7C4fDAZvNVs5mlkyLjtx6VmWT6PV6JJPJtKlm1RBc5Avmq0E0GsWjjz6KE088EU1NTZVuTla5zlV7ezsWFhYQi8XKfqxyK3ZEOzP4WlxcxPLyMvr6+tLWC/L5fPB6vdiyZUtVfC6oOjz44IPyNMvUn3PPPRcAMDQ0lPX+3t7erPtbWFjA448/jtNOO+2YC2QABjNENam+vh6dnZ1pwUdmZ6DQ75ksFgsEQZDLhmo1TazUx2brADQ2NqKrqwvT09OYmZnJuc9wOAyfz4fm5mZN2ljODlclK1aVehyn07kuVc20WNx1PaYbZZOaHyIFMieccIJ8lVWr3JFS96OkZLEgCOjs7MT4+HhJx6oG+d4P+SoPSveJoojZ2VkEAgG5CqMkHA5jfn4exx9/fFqAQ6S1X/3qV0gkEnLuzLGGny6iGtXY2IiOjg5VHYpCq7MPDAzg6NGjAIovKlCoM6WkM6lkG5PJhL6+PhgMBgwODq4pGyuKIiYnJwsm/Ks5frVeWdU6yFK7P6fTCa/Xq2kbsinH+V+vcyeNlkajUTz22GPYvn27HGSnFlMotX2lLq6p9PEWiwUOhwOzs7NFHS/zuNVIyfozk5OTSCQS6OrqkvPxACAWi2FychLbt29n5TIqOynxn8EMEdWc5uZmNDU1pS16mS9gKZQk3dbWhoWFhZLWjtEqsV6ppqYmdHV1YXJyMm2UZm5uDvX19TCZTIr3pVW+wXp30LTu5Kvdn5SLVC1le9Wc//UIUKX2SMn+xx9/fNpUkHyFNyo12qZEc3MzfD5fzrWgynXcSkl9XyWTSYyOjspV3lLF43GMjo5i27Ztx1wiNq2/YDCIBx54AFu3bsVxxx1X6eZUBIMZohrX3t4uVxgCsk81UdphEAQBHo8n52jPelTpKobJZJKrBw0NDSEYDMLn8+VMlMzXrmqZ7rNetOpMVtMCmqXky5TjdRMEAeFwGI8++ii2b9+OlpaWtPsTiUTBaUjV+n5qbW3F5ORkpZuhCSWjyoIgIBKJYGhoCA0NDWmja6IoIhaLYXR0FFu2bIHFYlmPZtMx7oEHHkAoFDpmR2UABjNEG0J3dzcsFgump6cB5O9MF+q8btq0SZ5qpvaxSpXraqzb7UZnZyeef/55+RyUOu2mWNU8wpO6X62OoXSqmVYBYzG0muKoVigUwqOPPoqdO3dmzd+Kx+MwGPIXF13vEQylr5HdbocoioqKceRSqc9oMe1YXl7G+Pg4urq6UF9fn/bYWCyG4eFhbN68GXV1dZq2jSiXY32KGcBghmjDGBgYgMFgSBuhAdQXAjCbzbBarVhaWipPQ9eBx+OB0+nE0aNHi87lUNPBKlfnvJwldjOV+hwMBgOSyWTepGnp2LU0tahY0vkMBoN47LHHcMopp+SsWqZkZGa9qXmN2tra5Asp60XtWlFajJZOT09jZWUFfX19MJlMadN3I5EIhoeHsW3bNgYyBAA477zzIIoiHnzwQcWPkaqc5apalimRSOC+++5DW1sbTj/99OIaugFU119PIirJpk2bYLVaMTIyIncqi/kS37p1K15++eWa7HTOzs6itbUVjY2N6Ovrg9frxfDwcM4yslpWEau2qUCF2qOkcpVSgiBU1VSzcr8WSqYk+f1+PP7449i1axcaGhpyPkbJyEw1M5lM0Ol0a4pwKFXMa5Uv+NO6kl0ikcDQ0BAMBgO6u7vXHDsYDGJ0dBTHH3887HZ7UccgKsbDDz+MhYUFXHTRRTX5fa0VBjMbwNVXX43LL7+86jpSVBn9/f1obGzE8PCwfPVSbUDjcrkQjUYRDAYLbqu2XG45/+AmEglEo1HYbDYIggC9Xo+Ojg60tLRgbGwsaxlnNVOutKjUVkgx+yi286blayGKIlwuV9UEM5UqwSxZXl7G3r17cdppp8Hlcq15TOr/8xUAqCQ1n+2WlpaSK5tpJdtrU2jEMNfjQ6EQhoaG4PF4subgBQIBTE1NYdu2bVlXbCcqJ04xW8VgpsyGh4chCALOO++8sh1jfHwcN954I5588smyHYNqS0dHB9rb2zE4OCiPSKjt3G3ZsgUvvfRSwe3We6pHPouLi3LHMZXVakV/fz+MRiOOHj0Kn8+Xs335lLv9xSaoZ07dqtSFjWqralYuhc7v/Pw8nnnmGZxxxhk5pxyl7iORSFTlyIyaz7bFYkEikSipslk5FTNtdGlpCVNTU+jp6ck64uL3+zEzM8MRGaqYb3zjGxBFEa973esq3ZSKYjCzAUgRuRShE+l0Ong8HnR1dWFoaAiRSES+T+lV/NbWVqysrKieOlKJzr50u9frRUNDQ87HS1PPVlZWMDIyUtQK5uW84q8kWFJSqauU0Z1Sn5/T6ayafCutFndVUh1Q2mZ6ehoHDhzAnj17YLPZFC0+W+5pZrkCYK01NjZiYWFB8/2WSu1zFUURExMTCAaD6Ovry1peeXFxEbOzs9i6dSusVqtWTSWiIjCY2QAuuOACWK1WBjOURqfTobm5Gf39/RgdHZWnjKkpW7tlyxYcOnRI1XHL3dnPdXswGITFYil4fL1ej87OTng8npxTz45FWuX9uFyudVlAUwnpORXTmU0NLJVWQRsdHcXhw4exZ88emEymgsUOpPvi8bgm65FI7c2sGFeOgg/Z1NfXIxAIlLSPcox+qtlfOBzG4OAgbDYbOjo61pw7URQxPj6OYDCIrVu3ckSG4HK58MUvfhEf/OAHK92UYxaDmSokCILiShYAYLPZ8NrXvhaHDh3C4cOHy9cwqjk6nQ4NDQ3YvHkzpqenMT8/n3Z/oc5WR0cHlpaWEI1Gy91URfK11ev1wul0Kt6XNPXMYDDknXpWbqV23KotENPpdDAYDKreM4U628Wum5Tr8UrbkyvHJZsjR45gfHwcZ511ljzKovS4yWRSTipX29bU7aV9lFoxrtj3lCAIql77XK/7eicySwHUzMwMpqam0NXVlXWENxaLYWhoCHa7Hf39/QxkCMBqMPOlL32JwUwFMZjZIKSpZnfffXdlG0JVR6fTwel0YtOmTYjFYmmVzkRRLJgYOzAwoHp0plzydbKCwaDqzoUoimhqapKrnkkLbpZLOab7lLPjV2zH2uVyqZpqVui8ZLs6vt7yFY7Yv38/VlZWcMYZZ0Cv15fUPrWvp5JcKbVr+5QyklNfX4/l5WVF2xZznkp9Htn2Ew6HMTQ0BL1eL5ddzhQKhTA6OorW1lY0NzfDZrOpazgRlQ2DmQ3iTW96E/R6PaeaUVaCIMBut6OjowMulwtHjx6Vr54W6jx1d3djYWGhpEXxstGyQxqPx6HX6xV3BDOnD0lVz9rb2zE3N4eRkZG0PCOtKGlfNY20KG1v5vl0OBzw+/1p26ih5Tkox/mURg+SyST27t0Lo9GIXbt2KZrWVonXV4u1fZRO/6qvr0977bWmNpE/VxAq7Wdubg4TExPo6OjIWq0MWC0EMD09jZ6eHtTX17NqGVGVYTCzQbjdbpx11lnYu3fvui9eRrVBr9fDbrfD5XKhu7sbY2NjinMbtm3bhgMHDqTdVmqnTMsRBb/fr2hUplAOhNlsRk9PD1paWjA5OYnR0dGiigSUohLTg0qRraOs0+lgNpvlALiU0QagtOeV7dhadOxjsRgeeeQRtLS0YNu2bUW3J3WKWSatChhota2S81bti39Kv0ejUQwODkIURfT398NisWR9/NTUFPx+P3p6emA2mxnIEFWh6vqrQyW5+OKLIYoi7r333ko3haqUXq9HXV0drFYr+vr65CuOmfkJmZ2blpYWhEKhtLwSLa4+a9X5DofDiioKKe3EWiwW9PX1oampCWNjY5iamspZbrjWRlKK2Wcx+21oaFA81SzbOdRyQU8lx1MjGAzikUcewZYtW9Db21vS/mKxWM5KZqUEYmpGKdWOaBZiMBg0uQhQrs/WwsICxsbG0NHRAY/Hs+ZYgiDIwY7RaERnZyeMRiMDGaIqVX2F7Y8h+ZLF5ufns97vdrtx7bXXZn3MxRdfjCuvvBL33HMPPvaxj2nUStpodDodbDYb/H4/ent7MTc3h6GhIXR1dckVlbJ1bk444QQ8//zzOOusswDk7wRp3eEqJBwOo7m5WZN9pZISfb1eL4aHh+FwONDc3Jx29VlNR1Cn063LyvRqp+KUY1qU3W5XPEqcbSRmvZLA1R5rYWEBzz77LE499dSsi2GqFY1GVVUyU7oWUSmfwVyPV7pPq9WKQCCQdc0nNQodT+1rF4vFMDExIRf/yPXYhYUFLC0toaOjAxaLBTqdDna7fd0LExCRMgxmKujWW2/NeV8gEMh6f09PT85gprW1FSaTCWNjY5q1kTYmg8EAh8OBQCAAt9sNu92OkZERNDY2orGxMetjGhoaYDKZMD09jdbW1op9sWfrwCSTyYIrqJfSQa6vr0d9fT0WFxcxODiIhoYGNDY2qr76vR6jOMVM6SqmbUrOp91uh8/ny7lwZL42qTlOKaTnruQYo6OjGBoawp49e3JOS5JyaZS2uRxrzJQazJZ6vi0WS1kLaUjUfP7m5ubg8/nQ3t4Oq9Wa9f2eSCQwMTEBg8GA/v5+6HQ6eXouAxmi6sVpZhUkTefJ/AFWg5Zs9w0PD+fc3+9+9ztEo1FceOGF6/QMqJYZDAY5z8RqtWJgYACRSATDw8NrVvGW3pcnnngiXnzxxYIV0Mqp2E6FFp2RxsZGDAwMIJFI4MiRI1haWio4RaqYY5c78MlXmUvp45Q8p4aGhpIXUcyXP6PVOcpWESxz3wcPHsT4+DjOPvvsnIGM9Hda7WhBvpEZLZ6jkrVutGQ0GnNOyyxWsVPhvF4vjh49Cr1ej4GBAfm1y1xXyefzYXBwEE1NTWhvb5cDGYfDwUCGqMoxmNlApEpmUplmokIMBgPq6+vlq/NtbW3weDwYGhpKK68qfZmbzWZ0d3cXXM8oXwes1I6+mmOVgyAI8Hg8GBgYQCwWw9GjRzE/P190jkeuYKiceSLlCggzn4vZbIYoiqo7tvleU6Vrv5SyVkrqv4lEAk8++SQSiQTOPPPMvAnuxZzXQgtmavE+WM/PiLTWTOYFEaXylZfOd8zM/0sXZnw+n5z/lrmtZHJyEgsLC2lrx0ij10RU/RjMbBCJRAL33Xcf2tracPrpp1e6OVRDdDodHA6H3Emz2WzYtGkTAoEAhoeH13REN23ahImJibRSzWoCFK3XDJGqQa13UKPT6eSgRhAEHD16FDMzM2vOV6HOaKE1Pcox+pDrWOU4hsvlwuLiYsn7KaUtxe4vFArh4YcfRmtrK0444YSS25RNNBrNuq5JsSpdkEIURRgMhpwBbDGfByXHlCSTSUxOTmJychKtra3o6OjIOQU1FAphcHAQdrsdvb29cnl3k8nEBTGJagiDmQ3i4YcfxsLCAi666CIOiZNq0nQKKSgQBEFed2FwcFAu4Szdt3PnTjzzzDPy40sdiShFIpFQtcZMqbLlFzQ1NWHTpk0wm80YHh7G1NSUfGW6mOerpCNe7FSxfMcqB6fTqbgEeLnkmjqWb9v5+Xk89thj2LlzJ7q6usrWtnylmYtRLSOdufZTaIpqoePne99LOW1ScJJrOmAikcD4+Djm5ubQ3d0Np9Mp32cymbggJlGNYTCzQXCKGZVKGqGRVjAXRREOhwObNm2Sq3lJ5VbdbjdsNhtGR0dVH0frzvN6B+/5OlsulwsDAwNwOBwYHR3F+Pi4vDiplrKVSy5HQKnFuc1cc6aQco4sZOZJ5NpmcHAQL774Is466yw0NDRoMpqYLyitpgtQWgVWxVY6LCa/LBgM4ujRo4jFYhgYGJCnzmYSRRFLS0sYHByE0+lcU8HRarUqKvFORNWF1cw2iHvvvRf19fV49atfXemmUA2TAppgMIh4PC53tDo7OxEOhzE+Pg6bzQaPx4MTTjgBDz74IFpaWmA2mwvuO7XTpmUHTq/XK8rJ0DqpPt9zqKurQ11dHfx+P6ampuQ8m1xXios5dimUnns1VbnyaWpqwsLCAjo7O1U9rlyFEHI9p2QyiWeffRYAcPbZZ+fs2BfzPs72PJRU4VtvWpzvchYIST3fkUgEMzMzEEUR3d3dOXOPBEFAOBzGxMSEPI02MzfKZrOpKpFNRNWDwUwVUvtl8txzz2F4eBjvete7NJ17Tcem1IAmdVTBYrGgv78fS0tLOHr0qBzQPPPMMzjjjDNy7k/q8GmRw5CrvVpXTlJCyXNwOBxwOBwIh8Nyp6upqUl1qWJAuwBQyX6yvWalsNlsGB8fV1yEIFsp69Tfpf8Xc05yPSYYDGLv3r3o7+9HT0+Pon0VW9ZakrnGTLWN0hRLWlOpVLnOrRTEJBIJtLa25h1NSSQSmJ2dRTgcRkdHh1yUIrWtdrudgQxRDWMwswFwihmVg81mg06nQzgcTutUNDQ0wOl0Ynp6GpFIBMDq+hvd3d1pjy+mQ5yr86JFJ6+SidEWiwU9PT2IRqNYWFjA9PQ0nE4nmpqa1v3KvJLzWI5Kak6nE8vLy2hoaCh4bKVFEYpZjybbNlNTUzh48CB27dqleqHHUt5XkUgk7QJUruddzQFOttciGo1mXTsn27ZK9i0Jh8OYnZ2FKIryiHC+fXm9XszMzMDtdqOtrU2+XcoN1Ov1sNlsVTc6RkTqMJjZAO655x6YTCa84Q1vqHRTaIOxWCzQ6/UIhUJpU450Oh3a29sRiUQQj8fx2GOPob6+Pq0jWGpVolTlqIBUTrk6oCaTCW1tbRBFEcvLyxgZGYHBYJBzkHLtpxo6tIXaUGiEoqmpCaOjo2nBjJbPK3PkT2my/8GDB7GysoJzzz03ZwdcyUhWMRX1lFQyK9frrtWFg2zbhsPhrFMqi30u4XAY09PTEAQBLS0tsFgseV/jQCCAmZkZeTQ5M1iRXi+73a5p8QUiqgwGMxvAc889V+km0AZmNBqh0+kQCATSAhpRFGE2m7F582aIoog777wTb3rTm9Dc3KzZ1B+l2xoMhoKLD66nQgGIIAhoaGiAy+VCJBLB/Pw8pqam4HK50NDQIHewtJzqlY2aTnihUYNC+9Dr9dDr9YhEInKOVbmeW7aKV5nHCofDeOqpp+DxeHDmmWfm3JeS/Jhip5pFo9GiphxqIbXCm9ZTQKPRqKrSxrneh6FQCNPT09DpdGhra0ubIpYtn0sKevR6fVpyfypBEOSptJW+QEBE2mAwQ0QF6fV61NfXY2VlJWunbcuWLRAEAS+//DK8Xi8aGhrQ2NiouLNQ6pVgi8WCUCikSTCj1WiBkpwQQRBgsVjQ2dmJZDKJxcVFDA0NwWKxwO12r5nfr3WbS8k9kR6vRlNTE+bn59HR0aH6WKXI7KxPTU3hxRdfxM6dO+F2uws+ttRgOxe1a8wo3beaNpSjQx8Oh+VFKpW2IfV9HgqFMDMzI48ApxYYyUzcB4BYLIbp6Wkkk0k5hyZbEQJBWF3Qk2vIEG0sDGbKzOVy4Ytf/CJ6e3sr3RSikjmdTvj9/qyre2/evBlzc3MwmUxIJpM4evQompqaCuZIaBE8WK1WBINB1NfXK35MruOux9XabMfQ6XRwu91oampCMBjE9PQ04vE4mpqa4HQ6C07x0ro95WC32+VOZ6HcmNTXR6uqZslkEi+88AKCwSDOOeccRcGv2opuaraVqplpXSq70iMO8XhcnrKnJgBbWVnB0tISjEajPBKTbTtpf1JyfzAYRGtrqxykZDumdOFASeVFIqotgooviMouK0xEVSO10llqxyEej+Ohhx7C7t27YbfbMTc3B7/fD7fbLS9Ml21ai5q5+9luTyaTGB4exsDAQEUT/QFtywknEgnMz8/D7/fDbDajoaEh61VlLa/YZyZpF3qMkn2mnpOFhQWIophzROSSSy7BHXfckXd/So+buo3f78dTTz2Fnp4e9Pf3a/o6Fdu+wcFB9Pf3l60NlSBVGsssCJLrfMdiMczPzyMQCKCurg5ut7tgQn4ikcDCwgJ8Pl/a3xYgdyBjtVpZ7ZOoNhX8cuPIDBGpJlUACoVCaR0HvV6P008/HU888QTOOecctLS0wO12Y3Z2FgsLC2hubs6aI5CrA5JNrlENnU6HeDxedGWizM6W2spLmY/Tgl6vR0tLC1paWhAKhbC0tISpqSnY7XY0NDTISdZaXrHPHA0ppvhCrnMJrFbDGxoakoOZzGMUM0pRaJRtaGgIw8PDOOWUU+TRu8wyz4X2leu5KWlfNpFIpGpyvADtAmKv15t1hDTznPn9fszPz8vlylOrjeWSTCYxMzODQCCAxsbGrIFgZtv0ej0T/Yk2OAYzRFQUs9kMvV6fVhhAEATYbDZs27YNTz75JM4880zo9Xq0tbUhHo9jdnYWMzMzaGpqgsvlKrpSV7bHOBwOOV+nGJmdLa2n6pRamSx1dXK/34+5uTlEo1E4HA40NDSUdNVZaUChZmQnF51OB6vVCr/fr1kSduY+pHZGIhHs27cPdrsd5557btYOrdrXXatgNVfFr1KUMmVTq4A4EAigq6sr633JZBILCwvwer2w2Wxob2/P+b5NfS6xWAxzc3MIh8NobGzMGvhkBplSfozVamUgQ7TBMZghoqIZDAbU1dUhEAjIC1cKgoDW1lZ4vV7s378fJ510krxte3u7PEXk6NGj8lor+VZaz9Z5zNZ5dTqdmJycXJccnVxtK1TxKvXfUkiLcYqiCK/Xi6mpKSQSCbk8drYSw/mUMioGrM1vKcTtdmN6ehoOh0PxMdSanJzESy+9hBNOOAEej0fRY3IFdUqnO6oRDoezluMu5RjVkCsjrd+SKhwOY25uDrFYDC6XS57ml48UjM7OziIej6O5uRltbW0FRwKlymhms1nzYJGIqhODGSIqiU6nQ11dXVoejSAI2Lp1K/bt24eXX34ZW7dulbfX6/XweDxobm7G0tIShoaGYLPZ0NzcvKYTrrTSliAIMBqNSCaTBUs0a9Xhq3RuDrD6XJxOJ5xOJ5LJJJaXlzE6Opp2u16vL3t+iJIgJ5XJZEIikZBfKy3Xm4nFYnjuuecgiiLOO+88VdMOlQR1qZXolO4z27mPRCJpFb+ybZetPdXwvstlYWEBjY2NAFYrtS0tLcHv98NkMsHtdssji4WEQiHMzs4CADweD6xWa97cutT3j7QQptqAnohqFz/tRKQJqQMRDoflsqi7du3Co48+CpvNtmbqiSAIaGxsRGNjI7xeL0ZHR2E0GuHxeLKWYlXC7XZjYWEBra2tANZ/9fRSE+WVyrYvnU4nn894PC4vygmsjuQ4nc68lZzKca7y7a+pqUl+rVK3Sy2pq7ZN0mjM8ccfj/b29qL2k3mVP7MQQq4pbbnkCj5isVhah1tpCW4lx6yUpaUlNDQ0YGFhAQaDAU6nEx6PR3Eujs/nw/z8PAwGA1pbW9Per1LQAqzNl5JGdpkfQ3RsYjBDRJoxmUzQ6/UIBoPytLNXvepVePjhh2EymdDS0pL1cfX19aivr5dLEouiiMbGRlWllgGgrq4OMzMzqq+ea0UQhJylfLVsS6F9GQwGuN1uuN1ueSra7OwsotEoLBYLnE4n7HZ72n7yja5I92fmJJSivr4ec3NzSCQSaaMnqR1RpdO7otEonnnmGej1+qwll9W0NddzVDv1Lte+S51uqEVxArXyBU9S4Dw5OYlwOIzW1lY0NzcrDiji8bhcsa+urg7d3d1ZR1VSc85Sb5OOY7FYOK2M6BjFYIaINKXX69Omnen1epx55pl45JFHoNPp0NzcnPOxNpsN3d3diMfjWFxcxOzsLOrq6tDY2Jh36lhqZ6u+vh5LS0vydBe1snXcyrFYYTlldpqlKWfA6hSelZUVzMzMyDlP9fX1OaflpHYg1eaO5AvugNV1uJaWlgouXJm5z9RjT0xM4PDhw9i+fXvOYFnaNtsq85nblPP1k/YdjUazBlxqRmfU3leKzHOSSCSwvLwMr9crv7+kwh9Kp3dJRSyA1VG6lpaWgoFaZlsEQYBOp+O0MqJjHD/9RFQWNpsNJpMJgUAAZrMZe/bswSOPPIKdO3euWR08s/NtNBrlksRerxcTExNIJpNwu91ZR2tSOzhutxuDg4NoaGjI2/kuVM630G3rSc2aO0D+9qZWRYvH41hZWcH4+DgSiQQcDgfq6+vX5DZkTrXKdfzUcysFDvna0tjYKC+umnoMJQFlIBDAc889B6vVinPOOadgZ1Zql5IiDeUWCoXWjCKUK8jSKkALh8Pwer0IBAIAVhfQ7e7uhl6vh9frhd1uL/gaSNXMVlZW5GpmuaY+5mu39P6S8mM4rYzo2MZghojKxmAwwOFwIBgMwmQyySM0J598MhobG9dcZc223oc0BS0Wi2FxcREzMzOor6/POVoj5Y7Mzc1lrWKVa5pPpUZVlBY4yLZdqVOO9Ho9mpqa0NTUBFEU4ff7sbi4iHA4LF/xrqurk4ObXEFNZnuyHTtX/kldXR1WVlbgcrnyPi+dTodkMglRFPHSSy9hdnYWO3fulEfglJaNLnZaWKHnokYoFMq63lKu/akZFcx8fLHv6Xg8Dp/PB6/Xi3g8DrPZLC9qmRmozs3Nobe3N+e+AoEAFhcX5WpmAwMDBdtWaNojq5URkURQMSxdvSVUiKjqhcNh+efRRx/Fjh071kwLyjedKZXX68XCwgIEQYDL5YLT6VzzmKNHj6K3t1fOx6iWKWBKVENbk8kk/H4//H6/vDiqzWaDw+HIezU8tZOfelu+SlSDg4PYtGkTAOCd73wnfv7zn69JdhdFEfPz89i/fz+6u7uxZcuWrPur9HlT0o6hoSH09PSs64hCoeBWCma9Xi/C4bB8IaKurg5msznnYxcXFxGNRuWiG5JIJCJXM7PZbGhoaFBczSy1TZlBI6eVER1zCv5R518DIloXFosFRqNRTtJ+6KGHEIvF0NnZKW+jtCOaOlqztLSEwcFBGI1GuFwu1NXVQRAEeDweTE5OylXU8k2PUqtcidaZ+y+ljWoen6s6mnSepW0CgQD8fj9mZ2chiiJsNhvsdjvsdnta0Jj5PHIFMtIVfpvNBr/fL1eiSt1ep9MhGAxi//79AIA9e/bIV+RLGYVQMyKmVraRlVyJ62r2qbYt+Z5jMplEOByWA1YAsNvtaGhoWLP+Ta7XL5FIYHFxUR5picfjWFpagtfrhdFoRENDw5ogp5BcOVqCsLoIJqeVEVEmBjNEtG6k4gB6vR7nnXceHn30UcTjcfT09BTVcZdKOXs8HoTDYaysrGB2dhYWi0VePNPr9aquiqbEeiWL57qvUMdWTduUbCsIgrxYJ7D6/MPhMHw+HxYWFpBMJuUcBovFkhbg5CoEIJ3D5uZmjI2Noa+vTy7NLAgC4vG4PKVsx44dcLvd0Ov1BUfwMitfFZsHpVXAmrqfbMn/SqfIqZW6z3A4jEAggEAggFgsBgDy69TU1JRzPZ58UwonJibQ2tqK5eVlrKysAFjNpenr61sTcGTmxWV7PvlymSwWS97S4kR07GIwQ0TrTpomsmfPHjz55JPw+/3YsWOHfH+2zm+hDp9UmrWlpQWhUAjLy8sIhUIYGxvDiSeemLbafKlBSKWnM2nVyU7tVCqd4pf6WKmYgHQ+YrEYgsEgQqEQFhcX5bLL0mtjt9vljnzqqI3JZILBYEA0GpWPPzIygpdffhl9fX149atfvaa9mb9nC17yPZdChSDKJRAIrBn50Pr4sVgMgUAAwWBQXvfJYrHIi9OqyTXJlTM0Pj6OmZkZJBIJ1NXVobOzM+/ULylHKtdInbRf6V9pW5PJBKvVytEYIsqJOTNEVDHJZFKeQuT1enHaaacpXrE919X+TDMzMxgeHkZjY6Ncrctutys6Rjk6ulrts9xT3UolPc9kMolQKCT/RKNRAJCvtNtsNpjNZsRiMczNzeGTn/wkrrjiCtTX12P79u0wm815CwpkBmSVCFCytSuXiYkJNDY25s0fUdr+RCKBSCSCcDgs/yuKIgwGA6xWK+x2O6xWa1HnIvOcJxIJrKyswOv1IhQKwefz4cQTTywYGKmtxCfR6XQwm80cjSEi5swQUfXS6XRwOBzYvXs3XnrpJTz00EM4/fTT11y5zkZpx7W1tRXJZFKeb+/1ejE1NQWTySTnhBRKZteSVvssdyCTeV4LlcrNVUlLp9PBbrfD4XCklUYOh8MIBoPwer0IBoPw+XzYt28fVlZW0NLSgqamJsRiMXlUQapmljnqkrpP6bZC68kUej6p7U/dvxKFtotEIgUDgNR9JJNJRCKRtB9pmpher5c7/PX19WhpaSlqBCPb8xNFEdFoFMvLy/D7/dDpdKirq0NHRwdGRkawc+fONYGGmkpsuaYcAquL70qvORFRIRyZIaKqIIqrCyDu3bsX27dvR2tra0lX2DMfOzIygqamJnm6WTQaxcrKCvx+P5LJJOrr6+F0OmEymTR5PtUuW+CRK9Fby0T51MR/URQRiUTw4osvIhAIYOvWrfjgBz+Iu+66C/F4HKFQKK3znkwmYTKZYDabYTAYYDQaYTAY5J9sa9usZ7GHXEFBauA1NDSE/v5+AKujHbFYDPF4HPF4HLFYTL5Nes6CsLrukjRVz2w2F5Vzo7S90hTNYDAIo9G4JuAfGxuTPytqZTuXmdMDbTZb3gVyieiYw5EZIqoNgiCgs7MTjY2NePDBBzE/P4/t27eXtL9UXV1dGBwcRHd3N0wmE0wmE5qbm9Hc3IxEIgGfz4fp6WnEYjFYrVZ5VXOtO8LS70pGD0qVryOerdOtZLtsslXqyvW8pTZJQczy8jKOO+44tLe3yxWrRFFEfX29vBZL6vOIRqOIxWLytCopEIjH43LxAKkNOp0uLdgxGAzQ6/XQ6XTySI70k+u2zOchHSOZTMrr3mT+P/U2KThJJBLw+/1yojywOrKi1+vltkm5Q0ajEUajUfG5zzf6ke89JuU5SYthxmIxmM1muFwutLa2rtnvwsICDAaD6kAmM1cm2xRBk8mkaESWiCgTR2aIqCrt27cPExMT2L17d1qSeSmi0ShGRkbQ39+ft3qTNP0pdX0VafFILaeeKelsKskLqiXRaBQHDx7E4uKiHMQAfwma3vGOd+DrX/86+vr61kwhU/J9lbpdMplMG/mIx+NIJBJp90uBB/CXcsPSfdK/mSNYer1+TRCUGgxJgRSAtBGk+fl5ee2WcsoVUAKQgyqfz4dIJAKj0Si3Kd+IyPLyMrxeL7q7u+XbCo20FPrMSufSarUqzpUjomMOR2aIqDbt2rULXV1deOyxx9Db25t3hXGlTCYTOjo6MDw8nLagZipBEOS1UwRBkDt/y8vLmJ6elhftk4KbQgrlmhR6bCHF5HUUQ0lgla8NoVAIL7/8MpaWlrB582acdNJJaY9JHbkRBAHBYBAWiwV6vV4OOgodJ/N85UoiL1fxhEKvQTgcTlsottTXLNfjU18rUVxdH8jn88nBud1uh9vtXrNeT679+Xw+LC8vo6enZ83x8/2eOr0u25RGllsmIi1wZIaIqloymcRTTz2FhYUF7Nq1S16NvJROYCAQwPT0dNb1MPKRruJLCw1KK6XbbDY4HI6Sg5tiabHPclVZCwQCOHjwIAKBALZs2YL29va0+zM7vO9617tw2223YWpqSl5/qFCwtl7Vy9QWAsgMwFLzZdQ+Xql4PC4vbhqJRABADr6LmTYZCAQwMzOD3t5eTRLyU4tCMMGfiBTgyAwR1TadTofTTz8ds7OzePzxx9He3o6tW7fK04DUkDqjdrsdLS0t8giNkk6V9Fi9Xg+n0ynnDcTjcfj9fiwuLiIcDkMQBJjNZnl0J3Pqjhad7mxXukulZh+FOvWiKGJ5eRmHDh1CIpHAli1b4PF40rbJnAaVuj+TyQSdTodAICCX0c6XY6S07cUERJmjRkplttXv9ysuCZ7t8bmEQiF5TZlYLCYvXNrQ0FDStEhRFBEKhTA1NZU36Fca4EmfHSlfjYhIKxyZIaKakUgk8OKLL2JkZAQ7duxAQ0NDznKwSv62+Xw+zM7O5pxypkS26llSBzMUCiEej0On08nrfthstopekS52hENJp1UURYyNjWFwcBBWqxVbt26Fy+VS1bZ3v/vduOOOOxCPxzEyMoKBgQHFbcn2WgDaLpJa7CjQ1NSUXFSiWPF4HMFgUP6RpmrlCpxL4fV6sbCwgO7ublVrP2X73Ol0OrncMhGRShyZIaKNQ6/X48QTT8TAwAAef/xxCIKAbdu2rZnelW0uf7YOaF1dHfR6PYaGhuQqZ2plC6RsNltapzWRSMhTf2ZnZyGKolxu12q1wmq15l09PVOu8sNKyygXui9XYncu0WgUR44cwdTUFFpaWnDGGWcoWoMkX9sMBgMcDgeWlpbSgtZC1bsyf1eaT5RZbS3XyJeS55CtQx8IBNDa2pr3saltiUQiCAaD8oKYoihCr9fDYrGgrq4OLS0tJQdpqQFaqsXFRXi9Xnman1LZ3jPS+5xTyoioXBjMEFHNsdvteM1rXoPp6Wns27cPLpcLW7ZsyXllWkoqz5bAbrPZ0NXVhZGREXR2dubMe8mWA6G0o6fX6+X1OiTRaBShUAjBYBBLS0uIx+Ny508KcHJ1ArN12rWkdMR+bm4OR44cQSQSQV9fH84///ys7c12rpQES83NzTh69CicTqe8X7XPVcn2mdW/Sh2dypRIJGAwGLI+NpFIIBQKyT/xeBzA6lQ7q9WKhoYGWCyWgtP6crVbbQGK2dlZhEKhnIFMrtdSen2kfRoMBlYpI6J1wWlmRFTzhoaG8MILL6C5uRmbN2/OOcqRr2MnTWtyu92K19HQOvFcuiIfCoUQDocRDofljqLFYpEXjJQWjVzPtkkikQiGhoYwOTkJp9OJgYEBOJ1OzY51ySWX4I477pB/X1paQjQaTasCpoTSqYbZttPy3ImiiIWFBUSjUdjtdoTDYUSjUUSjUQCQq+NJeVbZAnIlAUm2AENNLpEoihgfH4fZbFZ9riVSXozFYlE10khElEfBP2QMZohoQ0gmkxgcHMSBAwfkoMZkMqlap0Tq0BkMhqyLBhaj0LQoJW2S8nAikQii0SjC4TASiYT8vMxmc1qgU2i6nNIRBmn/iUQCY2NjGB8fRywWQ29vL7q6utZcdVdzrnPJDGYA4MiRI+jt7VXVQS5X+eVcRFFELBaTp4VFIhHEYjH5PdXb2yuPtil5jYqR+pyVTusTRRHRaBSjo6PweDxpo4e59pNtGp4gCLBarZrm7RARgcEMER2LhoeH8eKLL8JsNmPLli1rOmiZMju+CwsLWFlZQVdXV1rnTKuEci0lEglEo1G5Ax2JRBCPx+URndRFG6WV5aUfIH8y/ezsLEZGRhAMBuHxeNDb21v2VdqzBTOBQEBORi+m4EOpIy1SoCKNqMRisbTFOKXOvNFolANKaSQtmUxibGxMk3WStJJ6Pnw+H2ZmZtDV1aV6zRcpjyfbWj5ERBphAQAiOvZIi2xOT0/jhRdeQDAYRF9fHzo7O9fkdGTLhWlqaoLNZsPIyAhaW1vhcDjkbaVtUh9fToU64lKltGy5PlInXPqJRqNyCV8p4JH2bTQaodfrsbS0hKmpKUQiEbjdbvT19aGpqQl6vb7kkY5ic07sdjsWFhYQCATkYCpzFCLfMbKNLCQSCTkYicfj8u+p/6bu12g0wmQywWg0wmazyf/PldgutW9paQl1dXWKz0cpgZeaMsmiKGJqagqxWAz9/f0FPxfZ9mG1WhnEEFHFcWSGiDa8UCiEF154AWNjY3A6nejp6UFzc7N8f66OWyKRwMTEBHQ6Hdrb2xVVZFIzvUntFLhiOrmFHheJRDA5OYnR0VEEAgE0NjaitbUVVqsVyWRS7thnrusjjfzo9XoYDAbodDr5uQiCIP+u0+nS/p/6b7bn/d73vhe33XbbmmNJOU19fX0QxdXFSzN/Um+XghHp9tRRNakNBoMBBoNBfg7Sv9KPFoHq8PBw1il5lRQOhzE+Po6mpiY0NDTIt+d6H6ZWeBMEARaLBUajsapGKIlow+LIDBGR1WrFaaedhl27dmFiYgKHDx/G/v370dzcjK6uLjQ2Nq55jJTM3N3djZWVFQwODqKtra3gwodqRi9ylcZNvV/p1LZcQUu2K//z8/OYmprC4uKinB+0a9cueQQq89i5SEGDNMqTGlAkEgkASLtPekzq75mi0SgWFhaytl8QBBw9elQuSywFSlIwle8n3zmS7st2vtScj0xSEJgvkNGi2ICafczNzcHn86Gnp2dNfkuuMtZS4Mq1YoioGnFkhoiOOclkEqFQCKOjo5icnITX64XNZkNbWxva2tqyJjHH43FMTEzAaDSitbVV7qCuR5J5KR3eZDKJubk5zM/PY25uDoIgwOl0orW1FR6PR9P1P7RIun/Xu96Fn/70pznvP3LkSFH5HdmUu0jA/Pw8dDpd1mC53DKfWygUwuTkJOrr69Hc3Ky4MEVqJT0iogrgyAwRUSadTge73Y6tW7eit7cXsVgMy8vLGBsbw/DwMOLxOJxOJ5qbm9Ha2gqTyQSDwYCenh4sLy9jcHAQbrd7zer2Ugcx89/M+7M9JpvUqT1KiKIor9y+sLAAv98PnU4Hl8uFlpYWbN26tawlc9WOSinZPvP8dHV1YXx8HAMDA0UFI6n7UzK1T2qrGlK7VlZW0NfXp+qxWpHankwm5dyY7u5uOVCXnlOuc2gwGFhimYhqAv9KEdExKzV53mw2w+VyydOgFhcXMTs7i7179yKZTEKn08HpdKKxsREejwd+vx8LCwtob2+Xk+9TO4ip/0qUTANTcp8oiggGg1heXobX68XKygrC4TAAwOFwoLGxUa7ipnVeQ7aCCUqOkS2wy7XPzOOlMpvNcDgcWFhYQFNTk9rmpwUySkoXF0MURfj9flitVk1HvtRaXl7GzMwM2traUF9fv2YaWWrALS0oK1VkYxBDRLWCf62IiAC5vGw8Hkc4HEZjY6PcWZaqgi0uLmJ5eRnj4+MIh8OIxWLYt28fBEHA1q1b4XA4YLFYYLFY5DU31HQKpfwTacFMaV2ZYDAIv98vL7QoiiKsVivq6+vhcrnQ3d2dN5dHynkoNBKR2qnNto9sQUehUaVC20nbKtlO4vF4MDg4CIfDUfR0My0qhuULiObn59He3l7U/ktpH7Baynp6eho2mw2bN2+WA6rM1yO1GpzVaoXJZKpo8EVEVAwGM0REKQwGAxwOBxKJhBywCIIAk8mE1tZWtLa2pm2fSCQwOjqK6elphEIh1NXVyau8x2IxeXHLVKkd1tQr43q9Xl4DRlqrxGw2o66uDgMDA7DZbIpHQVIVO6Ur9Ta1oy+lBAuFCIKArq4ujI2Nob+/X5PRJ6VTAPMFaNJ5lhbLLCbPpJTnEgqFMD09DaPRiJ6enpyBtNROKamfQQwR1TIGM0REWej1etjtdrlzGg6H0wKP1O36+vrQ19eHpaUlLCwswO12o7m5uegKZKXScp9qcny0KB2dr6JW6m0mkwlNTU2YnJxER0eH6uNmUjsFMBspECtmClwp74VoNIrp6WmIooj29nZ5tCpXEKvX65kPQ0QbBv+SERHlIY3KmEwmJBIJRCIR+cp7ZunkhoYGOJ1OLC8v48iRI3C5XGhqasp61btcgUwhpR63mA6+mrwgaQ2aXNul7s/lcsHn88Hr9aK+vl5Vu/K1p5QKZ4lEAoFAYM0InpLjplIynS0cDmN6ehrJZBKtra3ygqKp+5AYDAZ54U+uD0NEGwmDGSIihfR6PWw2mzxaE4lEEI/H15SybWxsRENDA5aWlnD06FHY7Xa0tLSkrTeiZj0TrUoIaxVA5crrSA3wpBwdNSM7SmQ+tqOjA4ODg3KOUqlKPc8zMzPweDx5918ofyhzWl/m9sFgENPT0/IaQdLaL5n71ul08pRFTiMjoo2KwQwRkUqZozXRaBTRaHRNR7ixsRGNjY3wer0YHR2FXq9HS0tL3qT1bJ1ppR1sJQs/Sv8qKQagtMKYmv1rEUxlBo9dXV0YHR1FX1+f6k670uBKOma+7aUAN1vif2aQkusc5RqVSiaTWFlZweLiIkwmEzo7O+WcnNTXXRBWF3s1m82aBHdERNWOwQwRUQn0er1c3jkejyMajaatei8IAurr61FfXy9fUY/H42hqaoLT6ZQ7oLmCmFxJ5tkoDRSUFgPItv/1WCS0kMw2mM1meDwejI6OoqenR1XApLagQq6KYAAwNTWFlpYWRcfJFxil3i5V0ZOm0vX09ECv16dVIgNW34dM5ieiYxGDGSIijRgMBjmpWhqtSSaT8to1DocDVqsViUQCi4uLOHz4MOrq6tDU1JQ2WpNtqlGu0sip9+WjRcnfciyKWUpbUp9LXV0dYrHYmoIAWrQjX/lpSTAYRDKZXJO3Usx+BUGA3+/H/Pw8kskk3G73miBJGoGRqt+lTmEkIjqWMJghIioD6So5AMTjccRiMXmdGKPRCI/HIy++OTMzg3g8DpfLBafTmbVjmpkMnll8QLov13oyWid9K8n9yDx+sUGF0qlgjY2NmJqawuzsrJy3UuiYanN4sm2fTCYxMTGB3t5exfvJJhwOY3FxEaFQCFarFe3t7WnlnQVBkMspGwwGBjBERGAwQ0RUdtKIjTQVLRaLyRXRHA6HvK7N8vIyRkZGoNPp4HQ64XK5cq5zkjnNKN90NS1kSy5Xcyy1eT+p1JRNbm1txdjYGObn5+F2uwseq1DFMCWLf05OTsLj8RSVoxKPx+VpZGazGQ0NDWhra0vLrZES+TkCQ0S0FoMZIqJ1lBrYJJNJObABgKamJrjdbjlP4ujRozCZTHLOTWYuhNrRFqWJ/1KuT75j5StUUOpIRykEYXVBzfHxcczMzOTMYZG2Tf1/tudeqOqc1+uFKIpwOp0F2yY912g0iuXlZfh8Puj1erhcLgwMDKQFpFIpZaPRyBwYIqI8GMwQEVWITqeD2WyG2WyWyz1LpZ6laWhSx3doaEguJuB0OmE0GtOCh8wk9WKroikZrchFSd5OoSBJzWPztaOrqwtTU1OYmppCW1vbmvuV5B7lO6YoiohEIpiZmZEDkdTRsmzllFdWVuD3+2EymeByueB2u+V1daTRl9S8KyIiKox/MYmIqkBquWdgdfHFRCIhrxPS3NyMZDIJr9eL8fFxJBIJ2Gw21NfXw263p12912qqmdKgRk1541LbokZbWxtmZmYwOjqKzs5O+RwpzefJd8xIJCJXT8uccicIAmKxGPx+P1ZWVhCPx2G1WuF0OtHa2ioHL1LgYjQaNc9pIiI6VjCYISKqQnq9Xi63C6wmmUejUVgsFjQ1NSGRSCAYDMLn82F2dhYAYLPZUFdXB5vNpmiURGnei9TZL7S+jBJqCgdky1fJ195s97e0tGB5eRmDg4Po7OyUF5hMJVWbUzqdKzWQkfJkEokE/H4//H4/QqEQjEYjHA4HOjo6YDKZIAiCHLwYDAZOHSMi0giDGSKiGqDT6dI64vF4HHa7HQ0NDUgkEojH4/JIwPT0NADAarXCbrfDbrdDr9crygWR7ss2epGpmBGbQoFPaidfSZ6OkvtdLhdsNhvGxsZQX1+P5ubmNW3MNWqTuf9AIIDp6Wm0tLTA5/MhGAwiHA7DYDDAbrejqakJVqs1beTFYDBw5IWIqEwYzBAR1SApryK1dG9dXR08Hg/i8bgc3AQCASwsLCCRSMgdbpvNBqvVKgc4mbk3SqepFeqgF9OBTyaTWW/PV21MOla+4MpkMmFgYAAzMzM4cuQI3G53WrW4bNXhJJFIBH6/H8PDw4hEImhqasLKygocDgc8Hg+sVqtcaUz6ISKi9cFghohog5BGAaQFOJ1OJ+LxOBKJBJLJJMLhsDwVam5uTq7cZTKZ5ADHbDbnnAKVbY2bzPtKlevYSqa4KTl+S0sL3G43FhYW8Morr6ChoQF1dXUwm82IxWIIh8MIh8MIhUKIxWIIhUIIh8NIJBLYtGkTWltbodPpoNfrOV2MiKgKMJghItrAUqtjWa1WNDQ0QBRFucCAlHvj9/uxtLSEcDgMYDU4MRqNMJlMsFgsMJlM8u/S6I3aQELaLt/Ij5S/orSqmJr9S6WwpWlhVqsVY2NjCAQCiEajcmU5s9kMm80Gs9mMxsZGuN1u1NXVKTo+ERGtLwYzRETHmNRkdGC1cIC0wGQymZRHcqLRKEKhEEKhELxerzxCIY3opC7mKE2zklaml+6TRnIk2QIhJe1Nlfp4KSCTRqCk8tbS4qTxeFwOblJLYZvNZrS2tqK/v18eYUnNn+GICxFRbWAwQ0REstSOvNlsXjMiIeW0SKMc8XgckUhEXvxTmpoViUTkIENajFKSmZeSGqyEw2EcPXp0TS5L5u8SaW0Ws9ksV3+z2+0wmUzy7dJzYoBCRLTxMJghIiLFpIBAqtYFQPEUrFzJ/am319XV4eSTT5Z/zxyVYUBCRESpGMwQEdG6yBWIpN7OamBERKQGL3EREREREVFNYjBDREREREQ1icEMERERERHVJAYzRERERERUkxjMEBERERFRTWIwQ0RERERENYnBDBERERER1SQGM0REREREVJMYzBARERERUU1iMENERERERDWJwQwREREREdUkBjNERERERFSTGMwQEREREVFNYjBDREREREQ1icEMERERERHVJAYzRERERERUkxjMEBERERFRTWIwQ0RERERENYnBDBERERER1SQGM0REREREVJMYzBARERERUU1iMENERERERDWJwQwREREREdUkBjNERERERFSTGMwQEREREVFNYjBDREREREQ1icEMERERERHVJAYzRERERERUkxjMEBERERFRTWIwQ0RERERENYnBDBERERER1SQGM0REREREVJMYzBARERERUU1iMENERERERDWJwQwREREREdUkBjNERERERFSTGMwQEREREVFNYjBDREREREQ1icEMERERERHVJAYzRERERERUkxjMEBERERFRTWIwQ0RERERENYnBDBERERER1SQGM0REREREVJMYzBARERERUU1iMENERERERDWJwQwREREREdUkBjNERERERFSTGMwQEREREVFNYjBDREREREQ1icEMERERERHVJAYzRERERERUkxjMEBFR1Xj3u99d6SYQEVENEURRVLqt4g2JiIiIiIhKJBTagCMzRERERERUkxjMEBERERFRTWIwQ0RERERENYnBDBERERER1SQGM0REREREVJMYzBARERERUU1iMENERERERDWJwQwREREREdUkBjNERERERFSTGMwQEREREVFNYjBDREREREQ1icEMERERERHVJAYzRERERERUkxjMEBERERFRTWIwQ0RERERENYnBDBERERER1SQGM0REREREVJMYzBARERERUU1iMENERERERDWJwQwREREREdUkBjNERERERFSTGMwQEREREVFNYjBDREREREQ1icEMERERERHVJAYzRERERERUkxjMEBERERFRTWIwQ0RERERENYnBDBERERER1SQGM0REREREVJMYzBARERERUU1iMENERERERDWJwQwREREREdUkBjNERERERFSTGMwQEREREVFNYjBDREREREQ1icEMERERERHVJAYzRERERERUkxjMEBERERFRTWIwQ0RERERENYnBDBERERER1SQGM0REREREVJMYzBARERERUU1iMENERERERDWJwQwREREREdUkBjNERERERFSTGMwQEREREVFNYjBDREREREQ1icEMERERERHVJAYzRERERERUkxjMEBERERFRTWIwQ0RERERENYnBDBERERER1SQGM0REREREVJMYzBARERERUU1iMENERMeExx9/HJdddhkeeOCBSjeFiIg0wmCGiIiq0vDwMARBwHnnnbfmvt/85jf40pe+hDe96U1ob2+HIAgQBAHj4+M599fa2orvfe97uOGGG8rYaiIiWk+GSjeAiIhIrfe85z1YWVlR9Zi+vj6ceOKJ+MMf/gCfz4e6uroytY6IiNYLR2aIiKjmvPWtb8U111yD+++/H7Ozs4ofd/HFFyMajeI3v/lNGVtHRETrhcEMERHVnJtvvhmf//znccEFF6C5uVnx4y6++GIAwD333FOehhER0bpiMENERMeMk08+GT09Pfjtb3+LWCxW6eYQEVGJGMwQEdEx5c1vfjNWVlbwhz/8odJNISKiEjGYISKiYwqnmhERbRwMZoiI6JhyzjnnoLGxEb/85S8himKlm0NERCVgMENERMcUvV6PCy+8EJOTk3jyyScr3RwiIioBgxkiIjrmdHd3AwDGxsYq3BIiIioFgxkiIjrm/OpXv4LJZMJf//VfV7opRERUAgYzRER0TBkeHsb+/ftx/vnno76+vtLNISKiEjCYISKiY4pUxUyqakZERLWLwQwRER1T7rnnHgiCgDe/+c2VbgoREZXIUOkGEBERqfWVr3wFv/71r9fcftFFF8FkMgEATjnlFNx0001p9y8sLOCRRx7Baaedhra2tnVpKxERlQ+DGSIiqjlHjx7F3r1719z+7LPPyv+3WCxr7v/Vr36FRCLBKWZERBsEp5kREVHNueWWWyCKYt6fBx98cM3jmC9DRLSxMJghIqJjQjAYxAMPPICtW7fiuOOOq3RziIhIAwxmiIjomPDAAw8gFApxVIaIaANhzgwRER0TLr74YoiiWOlmEBGRhjgyQ0RERERENYkjM0REVJVcLhe++MUvore3t9JNISKiKiWoGHLn2DwREREREa0XodAGnGZGREREREQ1icEMERERERHVJAYzRERERERUkxjMEBERERFRTWIwQ0RERERENYnBDBERERER1SQGM0REREREVJMYzBARERERUU1iMENERERERDWJwQwREREREdUkBjNERERERFSTGMwQEREREVFNYjBDREREREQ1icEMERERERHVJAYzRERERERUkxjMEBERERFRTTKo2FYoWyuIiIiIiIhU4sgMERERERHVJAYzRERERERUkxjMEBERERFRTWIwQ0RERERENYnBDBERERER1SQGM0REREREVJMYzBARERERUU1iMENERERERDWJwQwREREREdWk/w+8FjPpZfhNOQAAAABJRU5ErkJggg==\n", + "image/png": 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\n", 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    " ] @@ -447,7 +447,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:20:08.888161Z", @@ -562,7 +562,9 @@ "source": [ "# Quantum Neural Network\n", "\n", - "After the preparations above, we now have the necessary knowledge to have a taste on quantum machine learning (QML). QML uses quantum circuits to replace classical neural networks to complete machine learning tasks. So we need to prepare a parameterized quantum circuit (PQC), which is also called Quantum neural network (QNN) or Ansatz. The quantum circuit parameters are adjustable (usually these parameters are the angles $\\theta$ of rotation gates). As we have seen in the last section, using angle $\\pi$ to create a $X$ gate is probably the simplest QNN. If we design an appropriate loss function, then certain computational tasks can be transformed into optimization problems. Keep adjusting the parameters in PQC until the loss function convergences. " + "After the preparations from the last section, we now have the necessary knowledge to have a taste on quantum machine learning (QML). In Paddle Quantum, we provide a bunch of QML algorithms, which use quantum circuits to replace classical neural networks to complete machine learning tasks. \n", + "\n", + "In this section, we introduce how to construct a parameterized quantum circuit (PQC), which is also called Quantum neural network (QNN) or Ansatz. The quantum circuit parameters are adjustable (usually these parameters are the angles $\\theta$ of rotation gates). As we have seen in the last section, using angle $\\pi$ to create a $X$ gate is probably the simplest QNN." ] }, { @@ -580,7 +582,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:20:13.355621Z", @@ -653,7 +655,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:20:15.796777Z", @@ -699,7 +701,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:20:18.642677Z", @@ -713,9 +715,9 @@ "text": [ "--Ry(3.142)----*----Ry(3.142)---------------\n", " | \n", - "--Ry(3.142)----X--------*--------Ry(3.142)--\n", + "--Ry(3.142)----x--------*--------Ry(3.142)--\n", " | \n", - "--Ry(3.142)-------------X--------Ry(3.142)--\n", + "--Ry(3.142)-------------x--------Ry(3.142)--\n", " \n" ] } @@ -735,7 +737,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:55:20.402902Z", @@ -746,7 +748,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
    " ] @@ -776,7 +778,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:55:21.071722Z", @@ -786,7 +788,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
    " ] @@ -857,7 +859,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:55:24.555510Z", @@ -867,7 +869,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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XtPs6j6mq64BfAXdo2/ZO8vUkX0rysK4vSHJUktVJVq9bt27Lppekbdy0DkT/CNizqh4AvBT4YJKNZk1V1clVtbyqli9ZsmTBQ0rS1qzPAnElsMfI9u7tvs5jktwCuB3w86q6tqp+DlBV5wLfA+7RY1ZJ0pg+C8QqYFmSvZNsB6wAxleIXQkc0b4/FDi7qirJknaQmyR3BZYBl/SYVZI0prdZTFV1Xbtu0+eAxcApVXVhkuOB1VW1EngP8IEka4GraIoIwMOB45P8EbgB+OuquqqvrJKkjfVWIACq6gyapTpG97165P3vgad1nPcx4GN9ZpMkzW5aB6klSQOzQEiSOlkgJEmdLBCSpE4WCElSJwuEJKmTBUKS1MkCIUnqZIGQJHWyQEiSOlkgJEmdel2LSRrS0mM/M9h3X3bC4wf7bmlL8QpCktTJAiFJ6mSBkCR1skBIkjpZICRJnSwQkqROFghJUicLhCSpkwVCktTJO6klbcA70LWeVxCSpE4WCElSJwuEJKmTBUKS1MkCIUnqZIGQJHWyQEiSOlkgJEmdLBCSpE4WCElSJwuEJKmTBUKS1MkCIUnqZIGQJHWyQEiSOlkgJEmdLBCSpE69FogkByVZk2RtkmM72rdP8qG2/atJlo60HdfuX5PkcX3mlCRtrLcCkWQxcCJwMLAP8Mwk+4wddiTwi6q6O/A/gDe05+4DrADuAxwEnNR+niRpgfR5BbE/sLaqLqmqPwCnA4eMHXMIcGr7/qPAo5Ok3X96VV1bVZcCa9vPkyQtkFv0+Nm7AT8Y2b4CeMhMx1TVdUl+Bdyh3f+VsXN3G/+CJEcBR7Wbv0myZstEn7c7Aj/b1JPzhi2YZGNm2zRm2zRm2zRDZttrpoY+C0Tvqupk4OShcyRZXVXLh87RxWybxmybxmybZlqz9dnFdCWwx8j27u2+zmOS3AK4HfDzCc+VJPWozwKxCliWZO8k29EMOq8cO2YlcET7/lDg7Kqqdv+KdpbT3sAy4Gs9ZpUkjemti6kdUzga+BywGDilqi5McjywuqpWAu8BPpBkLXAVTRGhPe7DwEXAdcCLqur6vrJuAYN3c83CbJvGbJvGbJtmKrOl+YNdkqQNeSe1JKmTBUKS1MkCIUnqZIHYDEl2SbLL0DkkqQ8WiHlKsmeS05OsA74KfC3JT9t9SweON/WS7Jrkge1r16HzzCXJjkNnkIbiLKZ5SvKfwFuBj66fetsuJPg04JiqOmDAeDNKckFV3W/A798PeCfNzZDrb3rcHfgl8MKqOm+YZLNL8v2q2nMKcuzKTcvNXFlVPxkyzySS7FhVvxk4Q2jWcbvxZwd8rab4F1+Se1XVd4bOARaIeUtycVUtm2/bQkjyFzM1Ae+sqiULmWeDAMn5wAuq6qtj+w8A3lVV+w4SrMnw0pmagFdW1WDdiDfXwgrDF9ckBwInARez4c/u7jQ/u88PlW02Q//cRt2s12IayLlJTqJZhXb9YoR70NwR/vXBUjU+BPwvoKvq77DAWcbdZrw4AFTVV5LcZohAI/4ReBPNTZnjhu6GfR8zF9b3AoMV1jbHbMV16O65fwEeU1WXje5sV2c4A7j3EKHaDG+bqQm4/QJGmZUFYv6eQ/Mci9ey4WXr+jvDh/RN4J+r6lvjDUkeM0CeUZ9N8hng/WxYWJ8DnDlYqsZ5wCer6tzxhiTPHyDPqGkurDDdxfUWNCtBj7sSuOUCZxn3POBlwLUdbc9c4CwzsotpK5LkYcDlVfX9jrblVbV6gFijGQ6medbHBoW1qs4YLhUkuSfw86raaLnlJLsO2d/f/qV5N7oL66VVdfRQ2QCSfBn4mxmK6w+qao+O0xZEkuOAp9M8i2b0Z7cC+HBV/dOA2c4GXlVVX+5ou7Sq9h4g1kYsEPPUrjp7JPBkNvxF9yngPVX1x4GiaSs1rYUVbiyuV1XVuo62QYtrm+HedP/sLhouVTNFHvh9VV0zZI65WCDmKclpNAOEp3LT5evuNGMQu1TVMwaKNlq8ngL8Sbt76otXkpOr6qi5j1x405xN6psFYp6SfLeq7jHftoUw5cVrpplAAb5RVbsvZJ4NAkx3ttsBx9H8FbwrzQSEn9IU/ROq6pdDZYMN8j0ZuBNTlm8mST5bVQcPnaPLNGVzkHr+rkryNOBjVXUDQJJFNPdB/GLQZPCgjgJ1BfCVJN8dItCIdcDlNL9016t2+06DJLrJNGf7MHA28Miq+jFAkjsDz23bDhwuGnBTvkeM5TuCgfMleeBMTcB+Cxhl4wBTnG2UVxDz1N4t/QbgkTR/rUMzLe2LwLFVdekgwYAkXwHeTHfxemlVjT8TfCGzXQw8eoYB9KEHM6c525qquud82xbKNOdLcj3wJTYs/OsdUFW3WuBIN5rmbKO8gpinqrosyT/Q3POwwSD1kMWhtYKmeJ2Y5JftvtvTFK8VA2Va763AzsBGv4SBNy5slI28lenNdnmSvwVOXT/g295V/VxumpkzpGnO922ae0guHm9IYrYJeAUxT0n+juaX7elseHfmCuD0qjphqGww46yNT1XVt4dL1UhyL7pnlJhtBkl2Bo6lyba+u+snNPfdnFBVg3ZrTnO+JIcCF1TVmo62J1fVJxc+1Y3fP7XZRlkg5qnty7/P+Iyg9rnbFw681MbUFq/2r8zD2myjA+hm20RJnldV7x06x0ymOZ/ZJmOBmKck3wEeV1WXj+3fC/j8wH2u01y8zLaFTdOaPV2mOZ/ZJuMYxPwdA3yhHdhc31e4J80CYIPe1QrcQHP/w+Vj++/Stg3JbJsgyTdnaqKZ9jqoac5nts1ngZinqjozyT3YeAnhVeuX/x7QMUxv8ToGs22KXYHHsfEU6gAbLdMwgGnOZ7bNZIHYBO0U0q8MnWPcNBcvs22yTwM7VtX54w1JzlnwNBub5nxm20yOQUiSOg29HK8kaUpZICRJnSwQ2mYl2T3Jp5JcnOSSJG9Psv0E53U+ZznJ8esfzJTkmCS3nuG4JyT5epJvJLkoyQva/U9Oss8E3z/RcdLmskBom5QkwMdpniS3DFgG3IrNWFqjql5dVf+n3TwG2KhAJLklcDLwxPY53A8AzmmbnwxM8ot/0uOkzeIgtbZJSR4NvKaqHj6y77Y090LsARwKLF//xLYkn6Z5nOs57RXEu2lWKv0xsKKq1iV5H83slD8B/hlYA/ysqh458h27AN8B9qqq343s/9P23F+1r6cCjwKOArYD1gLPplnpc/w4gBOBJcA1wF9V1Xe2yA9K2zSvILStug+wwWMyq+rXwGU09z/M5jbA6qq6D82KnK8Z+5y3AT+kWaL7kWNtV9GsU3R5ktOSHJ5kUfvoyZXAK6pqv6r6HvDxqnpwe6XxbeDIGY47meaxnw8CXg6cNO+fhtTB+yCk+bsB+FD7/t9ouqomVlXPT3I/4DE0v9AfS7P66bj7Jnk9zYq8OwKfGz8gyY7AnwIfaXrNAJhzHEWahAVC26qLaLqRbtR2Md2Zpmvovmx4hb3DLJ81737aqroAuCDJB4BL6S4Q7wOeXFXfSPJc4BEdxywCfllV+803gzQXu5i0rfoCcOskzwFIspjmYUtvb8cGLgP2S7IoyR40d1mvt4ibisthwL93fP7VwE7jO5PsmOQRI7v246Y1oMbP2Qn4UTuwfXjXZ7fdYpe2TzkkjX1n+49Lk7JAaJtUzeyMpwCHtmsw/Ry4oar+e3vIf9D8ZX8R8DbgvJHTfwvsn+RbNAPJx3d8xcnAmUm+OLY/wN8mWZPkfOC13HT1cDrwinYK7N2Avwe+2mYZHXQeP+5w4Mgk3wAupHk2g7TZnMUkceMsotOAp1TVeXMdL20LLBCSpE52MUmSOlkgJEmdLBCSpE4WCElSJwuEJKmTBUKS1On/A8Ejm9q06/CHAAAAAElFTkSuQmCC\n", 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    " ] @@ -900,6 +902,464 @@ "res = cir.measure(shots = 2048, which_qubits = [0, 1, 2], plot = True)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "---\n", + "\n", + "# An Introduction to Variational Quantum Algorithm" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Overview" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Many classical problems, such as travelling salesman problem, classification, finding the ground state of a molecular, can all be regarded as optimization problems. Limited to the classical computer capabilities, such problems are extremely difficult to be solved. \n", + "\n", + "The development of the quantum computers provides another approach to deal with these problems. It is quite believed that in the next few years, Noisy Intermediate-Scale Quantum (NISQ) devices with tens or hundreds of qubits will be developed and used for real-world experiments.\n", + "\n", + "Paddle Quantum provides a bunch of high-level quantum algorithms. We believe from these tutorials you will learn more about quantum information and feel the potential of the quantum computers.\n", + "\n", + "**To make it easy to understand, we provide one simple example here, preparing pure quantum state. With this example, we introduce the basic idea and the program structure how to realize Variational Quantum Algorithms (VQA), i.e. using quantum neural networks (QNN) to solve optimization problems., which will help you understand tutorials easier.**\n", + "\n", + "Note: The different operating modes of Paddle Quantum for the pure states and the mixed states and the more detailed introduction to PaddlePaddle will be given in the next two sections." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Use Quantum Neural Networks to Solve Optimization Problems" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "QNN is a quantum algorithm used for solving optimization problems. It generalizes the idea of the classical neural networks (CNN) to the quantum region.\n", + "\n", + "To help you understand QNN, here we first introduce the basic concept in optimization problem and CNN.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### CNN and the optimization problems" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "CNN is a classical algorithm, which use neural networks to optimize some loss function.The neural network can be characterized by its structure, the weights $\\vec{w}$ and the bias $\\vec{b}$ in it.\n", + "\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Mathematically, use CNN to solve an optimization problem can be regarded as follows: Modify the variables $\\vec{w}$, $\\vec{b}$ in the neural network, to get the best output vector $\\hat{y}(\\vec{w},\\vec{b})$, which minimize a loss function $L(\\hat{y}(\\vec{w},\\vec{b}))$**\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the salesman problem, the loss function can be the distance salesman travels. In classification, the loss function can be how real output labels different from the target ones.\n", + "\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Use QNN to solve the optimization problems" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The difference between QNN and CNN is that **QNN use quantum states and quantum gates to build the neural networks (a quantum circuit)**. \n", + "\n", + "A QNN can also be characterized by its structure, how you connect your gates, and a set of parameters $\\vec{\\theta}$, which describes which gate you put in the circuit.\n", + "\n", + " \n", + "\n", + "Here is a very simple example of a quantum neural network, with 3 qubits and 1 layer. $R_x(\\theta_1)$ means performing a rotation around $x$-axis with angle $\\theta_1$. Here $\\{\\theta_1,\\cdots,\\theta_6\\}$ are variables.\n", + "\n", + "- Note 1: arbitrary gate can be decomposed into one-qubit gates and two-qubit gates (e.g., CNOT).\n", + "- Note 2: one-qubit gates can be characterized by its rotating axis and its rotating angles $\\theta$.\n", + "\n", + "With these ideas in mind, you can see that by modifying the parameter $\\theta$ in this circuit, and when the depth (the number of layers) of the circuit is large, we can generate arbitrary unitary gate with this circuit.\n", + "\n", + "**Mathematically, VQA (use QNN to solve optimization problem) can be regarded as follows:\n", + "Modify the variables $\\theta$ in a (given structure) quantum circuit to get the best output state $\\rho(\\vec{\\theta})$, which minimize a loss function $L(\\rho(\\vec{\\theta}))$. The input state is usually chosen to be $|00\\cdots0\\rangle$.**\n", + "\n", + "In the following, we will use a very simple example to see how to do this optimization with Paddle Quantum." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Use Paddle Quantum to Realize QNN: A Simple Example" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The task we consider here is very simple: **use VQA to prepare a pure state**. This task is simple but still important as when the pure state is large and highly entangled, how to get the unitary gate to create this state will be difficult. QNN provides a method to use single-qubit gates and two-qubit gates to realize this task.\n", + "\n", + "For simplicity, here the target state we want to create is $|01\\rangle\\otimes|+\\rangle$. \n", + "Readers could modify the following code to try to create entangled state with larger qubits number." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Structure of Using QNN" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Use QNN to solve an optimization problem usually contains three steps" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Step 1: Create your own quantum circuit as a function\n", + "- step 1.1: Create an N qubit circuit\n", + "- step 1.2: Add gates to each layer" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "# import packages\n", + "import paddle\n", + "import numpy as np\n", + "from paddle import matmul\n", + "from paddle_quantum.circuit import UAnsatz\n", + "from paddle_quantum.utils import dagger\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "def circuit(N, DEPTH, theta):\n", + " \"\"\"\n", + " Input data:\n", + " N, qubits number\n", + " DEPTH, layers number\n", + " theta, [N, DEPTH, 2], 3D matrix in paddle.tensor form\n", + " Return:\n", + " cir, the final circuit\n", + " \"\"\"\n", + " # step 1.1: Create an N qubit circuit\n", + " cir = UAnsatz(N)\n", + " # step 1.2: Add gates to each layer\n", + " for dep in range(DEPTH):\n", + " for n in range(N):\n", + " cir.rx(theta[n][dep][0], n) # add an Rx gate to the n-th qubit\n", + " cir.rz(theta[n][dep][1], n) # add an Rz gate to the n-th qubit\n", + " for n in range(N-1):\n", + " cir.cnot([n, n+1]) # add CNOT gate to every neighbor pair\n", + " return cir" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is the figure of the circuit we use, which has 3 qubits, and 2 layers, $\\theta$ is randomly generated:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--Rx(0.273)----Rz(0.650)----*----Rx(-0.96)----Rz(0.150)-----------------*-------\n", + " | | \n", + "--Rx(-1.70)----Rz(-2.27)----x--------*--------Rx(0.141)----Rz(1.101)----x----*--\n", + " | | \n", + "--Rx(0.253)----Rz(-0.06)-------------x--------Rx(-0.18)----Rz(-0.94)---------x--\n", + " \n" + ] + } + ], + "source": [ + "N = 3\n", + "DEPTH = 2\n", + "theta = paddle.to_tensor(np.random.randn(N, DEPTH, 2))\n", + "cir = circuit(N, DEPTH, theta)\n", + "print(cir)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Step 2: Define and calculate your loss function" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we use “-fidelity” between the real output state and the target state to be the loss function. When the real output state is the target state, “-fidelity” will be “-1”, which is the minimum number.\n", + "\n", + "- Note: To update the parameters in QNN, we usually design the following class to calculate loss function with a given QNN. We will then use an optimizer to minimize the loss function and update the parameters." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "class StatePrepNet(paddle.nn.Layer):\n", + " # Step 2.1: Give the initial input of the QNN: def __init__(…)\n", + " # Here you need to give the parameters for creating your quantum circuit and loss\n", + " def __init__(self, N, DEPTH, psi, dtype='float64'):\n", + " # N, DEPTH: circuit parameter\n", + " # psi: target output pure state, np.row_vector form\n", + " super(StatePrepNet, self).__init__()\n", + " self.N = N\n", + " self.DEPTH = DEPTH\n", + " # The initial circuit parameter theta is generated randomly\n", + " self.theta = self.create_parameter(shape=[self.N, self.DEPTH, 2],\n", + " default_initializer=paddle.nn.initializer.Uniform(low=0., high=2*np.pi), \n", + " dtype=dtype, is_bias=False)\n", + " # Target output state, used for loss function\n", + " self.psi = paddle.to_tensor(psi)\n", + " # Step 2.2: Calculate the loss function: L = - \n", + " # note: here we want to minimize the loss function, so we use “-fidelity”\n", + " def forward(self):\n", + " # Create the quantum circuit\n", + " cir = circuit(self.N, self.DEPTH, self.theta)\n", + " # Get the final state\n", + " psi_out = cir.run_state_vector()\n", + " psi_out = paddle.reshape(psi_out, [2**self.N,1]) # change to paddle.ket\n", + " # Calculate the loss function: L = - \n", + " inner = matmul(self.psi, psi_out)\n", + " loss = - paddle.real(matmul(inner, dagger(inner)))[0] # change to shape tensor([1])\n", + " return loss, cir" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Step 3: backward part, optimize the loss function over iterations" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The optimizer we usually use is Adam." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "iter: 0 loss: -0.0006\n", + "iter: 10 loss: -0.8561\n", + "iter: 20 loss: -0.9270\n", + "iter: 30 loss: -0.9783\n", + "iter: 40 loss: -0.9932\n", + "iter: 50 loss: -0.9977\n", + "iter: 60 loss: -0.9996\n", + "iter: 70 loss: -0.9997\n", + "iter: 80 loss: -0.9999\n", + "iter: 90 loss: -1.0000\n", + "iter: 100 loss: -1.0000\n", + "iter: 110 loss: -1.0000\n" + ] + } + ], + "source": [ + "# First, we give the parameters for the QNN circuit, and the parameters used for learning\n", + "N = 3 # qubits number\n", + "DEPTH = 2 # layers number\n", + "ITR = 115 # iteration number\n", + "LR = 0.2 # learning rate\n", + "\n", + "# The target state we want: as a row vector here\n", + "psi_target = np.kron(np.kron(np.array([[1,0]]), np.array([[0,1]])), np.array([[1/np.sqrt(2), 1/np.sqrt(2)]])) # <01+|\n", + "# Record the iteration:\n", + "loss_list = []\n", + "parameter_list = []\n", + "# Use Class defined in step 2\n", + "myLayer = StatePrepNet(N, DEPTH, psi_target)\n", + "# Choose the optimizer, usually we use Adam\n", + "opt = paddle.optimizer.Adam(learning_rate = LR, parameters = myLayer.parameters())\n", + "# Optimize during iteration\n", + "for itr in range(ITR):\n", + " # Use forward part to calculate the loss function\n", + " loss = myLayer()[0]\n", + " # Backward optimize via Gradient descent algorithm\n", + " loss.backward()\n", + " opt.minimize(loss)\n", + " opt.clear_grad()\n", + " # Record the learning curve\n", + " loss_list.append(loss.numpy()[0])\n", + " parameter_list.append(myLayer.parameters()[0].numpy())\n", + " if itr % 10 == 0:\n", + " print('iter:', itr, ' loss: %.4f' % loss.numpy())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Step 4: Now we have finished our calculation, let’s see the results" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The minimum of the loss function: -0.9999968501679325\n", + "Parameters after optimizationL theta:\n", + " [[[3.14315954e+00 4.69366501e+00]\n", + " [3.14114250e+00 3.76582580e+00]]\n", + "\n", + " [[3.13958514e+00 3.05953797e+00]\n", + " [3.14269637e+00 3.94608975e-01]]\n", + "\n", + " [[4.71171514e+00 9.01298259e-01]\n", + " [1.31037031e-03 3.81143977e+00]]]\n", + "--Rx(3.143)----Rz(4.694)----*----Rx(3.141)----Rz(3.766)-----------------*-------\n", + " | | \n", + "--Rx(3.140)----Rz(3.060)----x--------*--------Rx(3.143)----Rz(0.395)----x----*--\n", + " | | \n", + "--Rx(4.712)----Rz(0.901)-------------x--------Rx(0.001)----Rz(3.811)---------x--\n", + " \n" + ] + } + ], + "source": [ + "# Print the output\n", + "print('The minimum of the loss function: ', loss_list[-1])\n", + "# The parameters after optimization\n", + "theta_final = parameter_list[-1] # Get self.theta\n", + "print(\"Parameters after optimizationL theta:\\n\", theta_final)\n", + "# Draw the circuit picture and the output state\n", + "# To create the circuit, “theta_final” should be changed to paddle.tensor form\n", + "theta_final = paddle.to_tensor(theta_final)\n", + "# Print the circuit\n", + "cir_final = circuit(N, DEPTH, theta_final)\n", + "print(cir_final)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "state_final:\n", + " [ 1.60015226e-04-4.11355044e-04j 1.76011799e-04+4.69345541e-04j\n", + " 2.05362221e-01-6.76576746e-01j 2.05154372e-01-6.76742815e-01j\n", + " -9.66090886e-05-1.26102052e-04j -9.62457101e-05-1.26342776e-04j\n", + " 5.18950813e-04-1.94232290e-04j -7.01086260e-05-5.49575311e-04j]\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Print the final state\n", + "#state_final = cir_final.run_density_matrix()\n", + "state_final = cir_final.run_state_vector()\n", + "print(\"state_final:\\n\", state_final.numpy())\n", + "\n", + "# Print the loss function during iteration\n", + "plt.figure(1)\n", + "ITR_list = []\n", + "for i in range(ITR):\n", + " ITR_list.append(i)\n", + "func = plt.plot(ITR_list, loss_list, alpha=0.7, marker='', linestyle='-', color='r')\n", + "plt.xlabel('iterations')\n", + "plt.ylabel('loss')\n", + "plt.legend(labels=[\"loss function during iteration\"], loc='best')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As the “-Fidelity” becomes “-1”, this circuit learns to prepare the target state “$|01\\rangle\\otimes|+\\rangle$\"." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Practice\n", + "- Try to prepare entangled states.\n", + "- Try to prepare larger quantum states with larger qubits number 'N'.\n", + "- Change circuit layer number, ‘DEPTH’, and see how the performance change\n", + "- Change the learning rate 'LR'.\n" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -922,7 +1382,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 17, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:55:44.714297Z", @@ -934,8 +1394,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "[[ 1.08337247e-03+0.j 1.00193659e-04+0.j 1.16958435e-03+0.j ...\n", - " -6.02439155e-04+0.j 7.83088243e-05+0.j 6.42545561e-05+0.j]]\n" + "[[ 5.21890277e-05+0.j -2.92638723e-04+0.j 5.14596730e-04+0.j ...\n", + " 2.02212900e-03+0.j -1.17159500e-03+0.j -5.82856577e-04+0.j]]\n" ] } ], @@ -984,7 +1444,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 18, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:55:45.027724Z", @@ -996,10 +1456,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "[[ 0.86516792+0.j 0.08806816+0.j -0.21659148+0.j 0.2489669 +0.j]\n", - " [ 0.08806816+0.j 0.00896474+0.j -0.02204753+0.j 0.02534312+0.j]\n", - " [-0.21659148+0.j -0.02204753+0.j 0.05422285+0.j -0.06232791+0.j]\n", - " [ 0.2489669 +0.j 0.02534312+0.j -0.06232791+0.j 0.0716445 +0.j]]\n" + "[[ 6.96262776e-01+0.j -3.29640355e-01+0.j 2.06852686e-02+0.j\n", + " -3.19984811e-01+0.j]\n", + " [-3.29640355e-01+0.j 1.56065737e-01+0.j -9.79328424e-03+0.j\n", + " 1.51494393e-01+0.j]\n", + " [ 2.06852686e-02+0.j -9.79328424e-03+0.j 6.14538578e-04+0.j\n", + " -9.50642772e-03+0.j]\n", + " [-3.19984811e-01+0.j 1.51494393e-01+0.j -9.50642772e-03+0.j\n", + " 1.47056948e-01+0.j]]\n" ] } ], @@ -1058,7 +1522,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 19, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:55:49.403917Z", @@ -1068,7 +1532,7 @@ "outputs": [ { "data": { - "image/png": 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    " ] @@ -1133,7 +1597,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 20, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:56:01.481603Z", @@ -1145,7 +1609,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "The minimum value of the loss function is: 10.000000010745854\n" + "The minimum value of the loss function is: 10.000000010746223\n" ] } ], @@ -1258,7 +1722,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 21, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:56:04.176637Z", @@ -1271,8 +1735,8 @@ "output_type": "stream", "text": [ "The randomly generated matrix H according to the spectral decomposition is:\n", - "[[ 0.26680964+0.j -0.06472222-0.17729436j]\n", - " [-0.06472222+0.17729436j 0.73319036+0.j ]] \n", + "[[ 0.4148327 -6.93889390e-18j -0.28540716-3.59066212e-02j]\n", + " [-0.28540716+3.59066212e-02j 0.5851673 +0.00000000e+00j]] \n", "\n", "The eigenvalues of H are:\n", "[0.2 0.8]\n" @@ -1302,7 +1766,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 22, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:56:04.205868Z", @@ -1324,9 +1788,9 @@ " \n", " # Initialize the circuit and add the quantum gates\n", " cir = UAnsatz(num_qubits)\n", - " cir.rz(theta[0], 0)\n", - " cir.ry(theta[1], 0)\n", " cir.rz(theta[2], 0)\n", + " cir.ry(theta[1], 0)\n", + " cir.rz(theta[0], 0)\n", " \n", " # Return parameterized matrix\n", " return cir.U" @@ -1334,7 +1798,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 23, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:56:04.793520Z", @@ -1372,7 +1836,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 24, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:56:11.561432Z", @@ -1384,17 +1848,17 @@ "name": "stdout", "output_type": "stream", "text": [ - "iter: 0 loss: 0.6071\n", - "iter: 5 loss: 0.4024\n", - "iter: 10 loss: 0.2953\n", - "iter: 15 loss: 0.2710\n", - "iter: 20 loss: 0.2666\n", - "iter: 25 loss: 0.2654\n", - "iter: 30 loss: 0.2643\n", - "iter: 35 loss: 0.2627\n", - "iter: 40 loss: 0.2601\n", - "iter: 45 loss: 0.2563\n", - "The minimum value of the loss function is: 0.25196530073166423\n" + "iter: 0 loss: 0.7704\n", + "iter: 5 loss: 0.6964\n", + "iter: 10 loss: 0.5480\n", + "iter: 15 loss: 0.4297\n", + "iter: 20 loss: 0.3643\n", + "iter: 25 loss: 0.2958\n", + "iter: 30 loss: 0.2372\n", + "iter: 35 loss: 0.2104\n", + "iter: 40 loss: 0.2025\n", + "iter: 45 loss: 0.2006\n", + "The minimum value of the loss function is: 0.20016689983553002\n" ] } ], @@ -1443,162 +1907,6 @@ "---" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Quantum Machine Learning Case Study\n", - "\n", - "## Variational Quantum Eigensolver - Unsupervised Learning\n", - "\n", - "At this stage, large-scale fault-tolerant quantum computers are still far from us. We can only build noisy intermediate-scale quantum (NISQ) computing devices. A promising type of algorithm suitable for NISQ devices is the quantum-classical hybrid algorithm, or variational quantum algorithms. People expect that this approach could surpass the performance of classical computers in certain applications. Among which, the Variational Quantum Eigensolver (VQE) is such an important application. It uses a parameterized circuit to search the vast Hilbert space and uses the gradient descent or other classical optimization methods to find the optimal parameters, which yield a state that is close to the ground state of a given Hamiltonian (find the minimum eigenvalue of a Hermitian matrix). Let's go through the following two-qubit example.\n", - "\n", - "Suppose we want to find the ground state of the following Hamiltonian:\n", - "\n", - "$$\n", - "H = 0.4 \\, Z \\otimes I + 0.4 \\, I \\otimes Z + 0.2 \\, X \\otimes X.\n", - "\\tag{30}\n", - "$$\n", - "\n", - "Given the following quantum neural network architecture\n", - "\n", - "![intro-fig-vqeAnsatz](./figures/intro-fig-vqeAnsatz.png)\n", - "\n", - "We have learned how to build this circuit. If you forget, please go to section **Quantum Neural Network**." - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": { - "ExecuteTime": { - "end_time": "2021-03-09T03:56:15.148775Z", - "start_time": "2021-03-09T03:56:15.092238Z" - } - }, - "outputs": [], - "source": [ - "# First generate the Hamiltonian under Pauli string representation\n", - "# H_info is equivalent to 0.4*kron(I, Z) + 0.4*kron(Z, I) + 0.2*kron(X, X)\n", - "# Among them, X, Y, Z are the Pauli matrix and I is the identity matrix\n", - "H_info = [[0.4,'z0'], [0.4,'z1'], [0.2,'x0,x1']]\n", - "\n", - "# Set hyper parameter\n", - "num_qubits = 2\n", - "theta_size = 4\n", - "ITR = 60\n", - "LR = 0.4\n", - "SEED = 999\n", - "paddle.seed(SEED)\n", - "\n", - "# Convert the Hamiltonian into matrix representation\n", - "H_matrix = pauli_str_to_matrix(H_info, num_qubits)" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": { - "ExecuteTime": { - "end_time": "2021-03-09T03:56:15.789743Z", - "start_time": "2021-03-09T03:56:15.776313Z" - } - }, - "outputs": [], - "source": [ - "class vqe_demo(paddle.nn.Layer):\n", - " \n", - " def __init__(self, shape, dtype='float64'):\n", - " super(vqe_demo, self).__init__()\n", - " \n", - " # Initialize a list of learnable parameters with length theta_size\n", - " # Use the uniform distribution of [0, 2*pi] to fill the initial value\n", - " self.theta = self.create_parameter(shape=shape, \n", - " default_initializer=paddle.nn.initializer.Uniform(low=0., high=2*np.pi), \n", - " dtype=dtype, is_bias=False)\n", - " \n", - " # Define loss function and forward propagation mechanism\n", - " def forward(self):\n", - " \n", - " # Initial quantum circuit\n", - " cir = UAnsatz(num_qubits)\n", - " \n", - " # Add quantum gates\n", - " cir.ry(self.theta[0], 0)\n", - " cir.ry(self.theta[1], 1)\n", - " cir.cnot([0, 1])\n", - " cir.ry(self.theta[2], 0)\n", - " cir.ry(self.theta[3], 1)\n", - " \n", - " # Choose state vector operation mode\n", - " cir.run_state_vector()\n", - " \n", - " # Calculate the expected value of H_info in the current quantum state\n", - " # The formula is given by \n", - " loss = cir.expecval(H_info)\n", - " \n", - " return loss" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": { - "ExecuteTime": { - "end_time": "2021-03-09T03:56:27.823274Z", - "start_time": "2021-03-09T03:56:20.363130Z" - } - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "iter: 0 loss: -0.2202\n", - "iter: 10 loss: -0.7239\n", - "iter: 20 loss: -0.8156\n", - "iter: 30 loss: -0.8172\n", - "iter: 40 loss: -0.8205\n", - "iter: 50 loss: -0.8241\n", - "The calculated ground state energy is: -0.8243637430772154\n", - "The real ground state energy is: -0.8246211251235321\n" - ] - } - ], - "source": [ - "loss_list = []\n", - "parameter_list = []\n", - "\n", - "# Define network dimensions\n", - "vqe = vqe_demo([theta_size])\n", - "\n", - "# We usually use Adam optimizer to get relatively good convergence\n", - "# Of course you can change it to SGD, Adagrad, or RMS prop as we did here.\n", - "opt = paddle.optimizer.Adam(\n", - " learning_rate = LR, parameters = vqe.parameters())\n", - "\n", - "# Optimization cycle\n", - "for itr in range(ITR):\n", - "\n", - " # Forward propagation calculates loss function\n", - " loss = vqe()\n", - "\n", - " # Back propagation minimizes the loss function\n", - " loss.backward()\n", - " opt.minimize(loss)\n", - " opt.clear_grad()\n", - "\n", - " # Record the learning curve\n", - " loss_list.append(loss.numpy()[0])\n", - " parameter_list.append(vqe.parameters()[0].numpy())\n", - " if itr % 10 == 0:\n", - " print('iter:', itr, 'loss: %.4f'% loss.numpy())\n", - "\n", - "\n", - "print('The calculated ground state energy is:', loss_list[-1])\n", - "print('The real ground state energy is:', np.linalg.eigh(H_matrix)[0][0])" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -1643,7 +1951,7 @@ "name": 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zBp9MBbI-&eJAK<_t6S3g?rM?rQSIa2qb-5LlA%%FP`!OvF<)%HHY)q&)ef4$Ds4*&vb z;-bgP&nK#v!H6T`Ar8jL=EESSL`2!&E*h0S@#;b(xscIY0wgR%yf{#gfVBu$5Jn0E z%XShFv`3{tU!nhY;nF|-|9|_=self.n,'扩展后量子比特数要大于原量子比特数' - diff = new_n-self.n - dim = 2**diff - if self.__state is not None: - if self.__run_mode=='density_matrix': - shape = (dim,dim) - _state = paddle.to_tensor(density_op(diff)) - elif self.__run_mode=='state_vector': - shape = (dim,) - _state = paddle.to_tensor(vec(0,diff)) - - _state= paddle.reshape(_state,shape) - _state = kron(self.__state,_state) - self.__state = _state - self.n = new_n - def __add__(self, cir): r"""重载加法 ‘+’ 运算符，用于拼接两个维度相同的电路 Args: cir (UAnsatz): 拼接到现有电路上的电路 - + Returns: UAnsatz: 拼接后的新电路 - + 代码示例: .. code-block:: python @@ -113,19 +90,19 @@ class UAnsatz: print(cir3) :: - cir1: + cir1: --H-- - + --H-- - - cir2: + + cir2: --*-- - | + | --x-- - - cir3: + + cir3: --H----*-- - | + | --H----x-- """ @@ -304,13 +281,13 @@ class UAnsatz: The printed circuit is: --H----Ry(-0.14)----*-------------------X----Ry(-0.77)----*-------------------X-- - | | | | + | | | | --H----Ry(-1.00)----X----*--------------|----Ry(-0.83)----X----*--------------|-- - | | | | + | | | | --H----Ry(-1.88)---------X----*---------|----Ry(-0.98)---------X----*---------|-- - | | | | + | | | | --H----Ry(1.024)--------------X----*----|----Ry(-0.37)--------------X----*----|-- - | | | | + | | | | --H----Ry(1.905)-------------------X----*----Ry(-1.82)-------------------X----*-- """ length, gate = self._count_history() @@ -419,6 +396,29 @@ class UAnsatz: return return_str + def expand(self, qubit_num): + """ + 为原来的量子电路进行比特数扩展 + + Args: + qubit_num (int): 扩展后的量子比特数 + """ + assert qubit_num >= self.n, '扩展后量子比特数要大于原量子比特数' + diff = qubit_num - self.n + dim = 2 ** diff + if self.__state is not None: + if self.__run_mode == 'density_matrix': + shape = (dim, dim) + _state = paddle.to_tensor(density_op(diff)) + elif self.__run_mode == 'state_vector': + shape = (dim,) + _state = paddle.to_tensor(vec(0, diff)) + + _state = paddle.reshape(_state, shape) + _state = kron(self.__state, _state) + self.__state = _state + self.n = qubit_num + def run_state_vector(self, input_state=None, store_state=True): r"""运行当前的量子电路，输入输出的形式为态矢量。 @@ -1160,7 +1160,7 @@ class UAnsatz: .. math:: \begin{align} - CNOT &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes X\\ + CY &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes Y\\ &= \begin{bmatrix} 1 & 0 & 0 & 0 \\ @@ -1197,7 +1197,7 @@ class UAnsatz: .. math:: \begin{align} - CNOT &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes X\\ + CZ &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes Z\\ &= \begin{bmatrix} 1 & 0 & 0 & 0 \\ @@ -1915,9 +1915,9 @@ class UAnsatz: :: ------------x----Rx(3.142)----Ryy(1.57)--------------- - | | + | | ------------|-----------------Ryy(1.57)----Rz(0.785)-- - | + | --H---SDG---*--------H-------------------------------- """ history, param = self._get_history() @@ -1975,15 +1975,15 @@ class UAnsatz: :: --Rx(3.142)----Ryy(1.57)-------------*------ - | | + | | ---------------Ryy(1.57)----z----Rz(0.785)-- - | + | ------H-----------SDG-------*--------H------ --Rx(3.142)----Ryy(1.57)----z-------------*------ - | | | + | | | ---------------Ryy(1.57)----|----z----Rz(0.785)-- - | | + | | ------H------------S--------*----*--------H------ """ history, param = self._get_history() @@ -2035,9 +2035,9 @@ class UAnsatz: :: ------------z----U-- - | + | ------------|------- - | + | --H---SDG---*----H-- """ history, param = self._get_history() @@ -2101,15 +2101,15 @@ class UAnsatz: :: -----------------x-- - | + | ------------z----U-- - | + | --H---SDG---*----H-- ------------z---------x-- - | | + | | ------------|----z----U-- - | | + | | --H----S----*----*----H-- """ history, param = self._get_history() @@ -3098,7 +3098,7 @@ class UAnsatz: def update_param(self, new_param): r"""用得到的新参数列表更新电路参数列表中的可训练的参数。 - + Args: new_param (list): 新的参数列表 @@ -3108,8 +3108,11 @@ class UAnsatz: j = 0 for i in range(len(self.__param)): if not self.__param[i].stop_gradient: - self.__param[i] = paddle.to_tensor(new_param[j], 'float64') - self.__param[i].stop_gradient = False + if not isinstance(new_param[j], paddle.Tensor): + self.__param[i] = paddle.to_tensor(new_param[j], 'float64') + self.__param[i].stop_gradient = False + else: + self.__param[i] = new_param[j] j += 1 self.run_state_vector() return self.__param diff --git a/paddle_quantum/dataset.py b/paddle_quantum/dataset.py new file mode 100644 index 0000000..81bee22 --- /dev/null +++ b/paddle_quantum/dataset.py @@ -0,0 +1,1027 @@ +# Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + + +""" +dataset: To learn more about the functions and properties of this application, +you could check the corresponding Jupyter notebook under the Tutorial folder. +""" + +import math +import random +from math import sqrt +import time +import paddle.vision.transforms as transform +import numpy as np +import paddle +from paddle_quantum.circuit import UAnsatz +from paddle.fluid.layers import reshape + +from sklearn.model_selection import train_test_split +from sklearn import datasets + +__all__ = [ + "VisionDataset", + "SimpleDataset", + "MNIST", + "FashionMNIST", + "Iris", + "BreastCancer" +] + +# data modes +DATAMODE_TRAIN = "train" +DATAMODE_TEST = "test" + +# encoding methods +ANGLE_ENCODING = "angle_encoding" +AMPLITUDE_ENCODING = "amplitude_encoding" +PAULI_ROTATION_ENCODING = "pauli_rotation_encoding" + +LINEAR_ENTANGLED_ENCODING = "linear_entangled_encoding" +REAL_ENTANGLED_ENCODING = "real_entangled_encoding" +COMPLEX_ENTANGLED_ENCODING = "complex_entangled_encoding" +IQP_ENCODING = "IQP_encoding" + +# downscaling method +DOWNSCALINGMETHOD_PCA = "PCA" +DOWNSCALINGMETHOD_RESIZE = "resize" + + +def _normalize(x): + r"""normalize vector ``x`` and the maximum will be pi. This is an internal function. + + Args: + x (ndarray): 需要归一化的向量 + + Returns: + ndarray: 归一化之后的向量 + """ + xx = np.abs(x) + if xx.max() > 0: + return x * np.pi / xx.max() + else: + return x + + +def _normalize_image(x): + r"""normalize image vector ``x`` and the maximum will be pi. This is an internal function. + + Args: + x (ndarray): 需要归一化的图片向量 + + Returns: + ndarray: 归一化之后的向量 + """ + return x * np.pi / 256 + + +def _crop(images, border): + r"""crop ``images`` according to ``border``. This is an internal function. + + Args: + images (list/ndarray): 每一个元素是拉成一维的图片向量 + border(list): 裁剪的边界，从第一个元素切到第二个元素，比如说[4,24]就是从图片的第四行第四列到第24行第24列 + + Returns: + new_images(list): 裁剪之后被拉成一维的图片向量组成的list + """ + new_images = [] + for i in range(len(images)): + size = int(sqrt(len(images[i]))) + temp_image = images[i].reshape((size, size)) + temp_image = temp_image[border[0]:border[1], border[0]:border[1]] + new_images.append(temp_image.flatten()) + return new_images + + +class Dataset(object): + r"""所有数据集的基类，集成了多种量子编码方法。 + """ + def __init__(self): + return + + def data2circuit(self, classical_data, encoding, num_qubits, can_describe_dimension, split_circuit, + return_state, is_image=False): + r"""将输入的经典数据 ``classical_data`` 用编码方式 ``encoding`` 编码成量子态，这里的经典数据经过了截断或者补零，因而可以正好被编码。 + + Args: + classical_data (list): 待编码的向量，ndarray 组成的 list，经过了截断或者补零，刚好可以被编码 + encoding (str): 编码方式，参见 MNIST 编码注释 + num_qubits (int): 量子比特数目 + can_describe_dimension (int): 以 ``encoding`` 编码方式可以编码的数目，比如说振幅编码为 ``2 ** n`` ，其他编码因为可以进行层层堆叠需要计算 + split_circuit (bool): 是否切分电路 + return_state (bool): 是否返回量子态 + is_image (bool): 是否是图片，如果是图片，归一化方法不太一样 + + Returns: + List: 如果 ``return_state == True`` ，返回编码后的量子态，否则返回编码的电路 + """ + quantum_states = classical_data.copy() + quantum_circuits = classical_data.copy() + if encoding == AMPLITUDE_ENCODING: + # Not support to return circuit in amplitude encoding + if return_state is False or split_circuit is True: + raise Exception("Not support to return circuit in amplitude encoding") + for i in range(len(classical_data)): + built_in_amplitude_enc = UAnsatz(num_qubits) + x = paddle.to_tensor(_normalize(classical_data[i])) + if is_image: + x = paddle.to_tensor(_normalize_image(classical_data[i])) + state = built_in_amplitude_enc.amplitude_encoding(x, 'state_vector') + quantum_states[i] = state.numpy() + + elif encoding == ANGLE_ENCODING: + for i in range(len(classical_data)): + one_block_param = 1 * num_qubits + depth = int(can_describe_dimension / one_block_param) + param = paddle.to_tensor(_normalize(classical_data[i])) + if is_image: + param = paddle.to_tensor(_normalize_image(classical_data[i])) + param = reshape(param, (depth, num_qubits, 1)) + which_qubits = [k for k in range(num_qubits)] + if split_circuit: + quantum_circuits[i] = [] + for repeat in range(depth): + circuit = UAnsatz(num_qubits) + for k, q in enumerate(which_qubits): + circuit.ry(param[repeat][k][0], q) + + quantum_circuits[i].append(circuit) + else: + circuit = UAnsatz(num_qubits) + for repeat in range(depth): + for k, q in enumerate(which_qubits): + circuit.ry(param[repeat][k][0], q) + state_out = circuit.run_state_vector() + quantum_states[i] = state_out.numpy() + quantum_circuits[i] = [circuit] + + elif encoding == IQP_ENCODING: + for i in range(len(classical_data)): + one_block_param = 1 * num_qubits + depth = int(can_describe_dimension / one_block_param) + param = paddle.to_tensor(_normalize(classical_data[i])) + if is_image: + param = paddle.to_tensor(_normalize_image(classical_data[i])) + param = reshape(param, (depth, num_qubits)) + if split_circuit: + quantum_circuits[i] = [] + for repeat in range(depth): + circuit = UAnsatz(num_qubits) + S = [] + for k in range(num_qubits - 1): + S.append([k, k + 1]) + # r 是 U 重复的次数 + r = 1 + circuit.iqp_encoding(param[repeat], r, S) + quantum_circuits[i].append(circuit) + else: + circuit = UAnsatz(num_qubits) + for repeat in range(depth): + temp_circuit = UAnsatz(num_qubits) + S = [] + for k in range(num_qubits - 1): + S.append([k, k + 1]) + # r 是 U 重复的次数 + r = 1 + temp_circuit.iqp_encoding(param[repeat], r, S) + circuit = circuit + temp_circuit + state_out = circuit.run_state_vector() + quantum_states[i] = state_out.numpy() + quantum_circuits[i] = [circuit] + + elif encoding == PAULI_ROTATION_ENCODING: + for i in range(len(classical_data)): + one_block_param = 3 * num_qubits + depth = int(can_describe_dimension / one_block_param) + param = paddle.to_tensor(_normalize(classical_data[i])) + if is_image: + param = paddle.to_tensor(_normalize_image(classical_data[i])) + param = reshape(param, (depth, num_qubits, 3)) + which_qubits = [k for k in range(num_qubits)] + if split_circuit: + quantum_circuits[i] = [] + for repeat in range(depth): + circuit = UAnsatz(num_qubits) + for k, q in enumerate(which_qubits): + circuit.ry(param[repeat][k][0], q) + circuit.rz(param[repeat][k][1], q) + circuit.ry(param[repeat][k][2], q) + quantum_circuits[i].append(circuit) + else: + circuit = UAnsatz(num_qubits) + for repeat in range(depth): + for k, q in enumerate(which_qubits): + circuit.ry(param[repeat][k][0], q) + circuit.rz(param[repeat][k][1], q) + circuit.ry(param[repeat][k][2], q) + state_out = circuit.run_state_vector() + quantum_states[i] = state_out.numpy() + quantum_circuits[i] = [circuit] + + elif encoding == LINEAR_ENTANGLED_ENCODING: + for i in range(len(classical_data)): + one_block_param = 2 * num_qubits + depth = int(can_describe_dimension / one_block_param) + param = paddle.to_tensor(_normalize(classical_data[i])) + if is_image: + param = paddle.to_tensor(_normalize_image(classical_data[i])) + param = reshape(param, (depth, num_qubits, 2)) + which_qubits = [k for k in range(num_qubits)] + if split_circuit: + quantum_circuits[i] = [] + for j in range(depth): + circuit = UAnsatz(num_qubits) + for k, q in enumerate(which_qubits): + circuit.ry(param[j][k][0], q) + for k in range(len(which_qubits) - 1): + circuit.cnot([which_qubits[k], which_qubits[k + 1]]) + for k, q in enumerate(which_qubits): + circuit.rz(param[j][k][1], q) + for k in range(len(which_qubits) - 1): + circuit.cnot([which_qubits[k + 1], which_qubits[k]]) + quantum_circuits[i].append(circuit) + else: + circuit = UAnsatz(num_qubits) + for j in range(depth): + for k, q in enumerate(which_qubits): + circuit.ry(param[j][k][0], q) + for k in range(len(which_qubits) - 1): + circuit.cnot([which_qubits[k], which_qubits[k + 1]]) + for k, q in enumerate(which_qubits): + circuit.rz(param[j][k][1], q) + for k in range(len(which_qubits) - 1): + circuit.cnot([which_qubits[k + 1], which_qubits[k]]) + state_out = circuit.run_state_vector() + quantum_states[i] = state_out.numpy() + quantum_circuits[i] = [circuit] + + elif encoding == REAL_ENTANGLED_ENCODING: + for i in range(len(classical_data)): + one_block_param = 1 * num_qubits + depth = int(can_describe_dimension / one_block_param) + param = paddle.to_tensor(_normalize(classical_data[i])) + if is_image: + param = paddle.to_tensor(_normalize_image(classical_data[i])) + param = reshape(param, (depth, num_qubits, 1)) + which_qubits = [k for k in range(num_qubits)] + if split_circuit: + quantum_circuits[i] = [] + for repeat in range(depth): + circuit = UAnsatz(num_qubits) + for k, q in enumerate(which_qubits): + circuit.ry(param[repeat][k][0], q) + for k in range(len(which_qubits) - 1): + circuit.cnot([which_qubits[k], which_qubits[k + 1]]) + circuit.cnot([which_qubits[-1], which_qubits[0]]) + quantum_circuits[i].append(circuit) + else: + circuit = UAnsatz(num_qubits) + for repeat in range(depth): + for k, q in enumerate(which_qubits): + circuit.ry(param[repeat][k][0], q) + for k in range(len(which_qubits) - 1): + circuit.cnot([which_qubits[k], which_qubits[k + 1]]) + circuit.cnot([which_qubits[-1], which_qubits[0]]) + state_out = circuit.run_state_vector() + quantum_states[i] = state_out.numpy() + quantum_circuits[i] = [circuit] + + elif encoding == COMPLEX_ENTANGLED_ENCODING: + for i in range(len(classical_data)): + one_block_param = 3 * num_qubits + depth = int(can_describe_dimension / one_block_param) + param = paddle.to_tensor(_normalize(classical_data[i])) + if is_image: + param = paddle.to_tensor(_normalize_image(classical_data[i])) + param = reshape(param, (depth, num_qubits, 3)) + which_qubits = [k for k in range(num_qubits)] + if split_circuit: + quantum_circuits[i] = [] + for repeat in range(depth): + circuit = UAnsatz(num_qubits) + for k, q in enumerate(which_qubits): + circuit.u3(param[repeat][k][0], param[repeat][k][1], param[repeat][k][2], q) + for k in range(len(which_qubits) - 1): + circuit.cnot([which_qubits[k], which_qubits[k + 1]]) + circuit.cnot([which_qubits[-1], which_qubits[0]]) + quantum_circuits[i].append(circuit) + else: + circuit = UAnsatz(num_qubits) + for repeat in range(depth): + for k, q in enumerate(which_qubits): + circuit.u3(param[repeat][k][0], param[repeat][k][1], param[repeat][k][2], q) + for k in range(len(which_qubits) - 1): + circuit.cnot([which_qubits[k], which_qubits[k + 1]]) + circuit.cnot([which_qubits[-1], which_qubits[0]]) + state_out = circuit.run_state_vector() + quantum_states[i] = state_out.numpy() + quantum_circuits[i] = [circuit] + return quantum_states, quantum_circuits + + def filter_class(self, x, y, classes, data_num, need_relabel, seed=0): + r"""将输入的 ``x`` , ``y`` 按照 ``classes`` 给出的类别进行筛选，数目为 ``data_num`` 。 + + Args: + x (ndarray/list): 样本的特征 + y (ndarray/list): 样本标签， ``classes`` 是其中某几个标签的取值 + classes (list): 需要筛选的类别 + data_num (int): 筛选出来的样本数目 + need_relabel (bool): 将原有类别按照顺序重新标记为 0、1、2 等新的名字，比如传入 ``[1,2]`` ， 重新标记之后变为 ``[0,1]`` 主要用于二分类 + seed (int): 随机种子，默认为 ``0`` + + Returns: + tuple: 包含如下元素: + - new_x (list): 筛选出的特征 + - new_y (list): 对应于 ``new_x`` 的标签 + + """ + new_x = [] + new_y = [] + if need_relabel: + for i in range(len(x)): + if y[i] in classes: + new_x.append(x[i]) + new_y.append(classes.index(y[i])) + else: + for i in range(len(x)): + if y[i] in classes: + new_x.append(x[i]) + new_y.append(y[i]) + + # sample to data_num randomly + if data_num > 0 and data_num < len(new_x): + random_index = [k for k in range(len(new_x))] + random.seed(seed) + random.shuffle(random_index) + random_index = random_index[:data_num] + filter_x = [] + filter_y = [] + for index in random_index: + filter_x.append(new_x[index]) + filter_y.append(new_y[index]) + return filter_x, filter_y + return new_x, new_y + + +class VisionDataset(Dataset): + r"""图片数据集类，通过继承 VisionDataset 类，用户可以快速生成自己的图片量子数据。 + + Attributes: + original_images (ndarray): 图片经过类别过滤，但是还没有降维、补零的特征，是一个一维向量（可调用 ``reshape()`` 函数转成图片） + classical_image_vectors (ndarray): 经过类别过滤和降维、补零等操作之后的特征，并未编码为量子态 + quantum_image_states (paddle.tensor): 经过类别过滤之后的所有特征经编码形成的量子态 + quantum_image_circuits (list): 所有特征编码的电路 + """ + + def __init__(self, figure_size): + r"""构造函数 + + Args: + figure_size (int): 图片大小，也就是长和高的数值 + """ + Dataset.__init__(self) + self.figure_size = figure_size + return + + # The encode function only needs to import images to form one-dimensional vector features. + # The pre-processing of images (except dimensionality reduction) is completed before the import of features + def encode(self, feature, encoding, num_qubits, split_circuit=False, + downscaling_method=DOWNSCALINGMETHOD_RESIZE, target_dimension=-1, return_state=True, full_return=False): + r"""根据降尺度方式、目标尺度、编码方式、量子比特数目进行编码。只需要输入一维图片向量就行。 + + Args: + feature (list/ndarray): 一维图片向量组成的list/ndarray + encoding (str): ``"angle_encoding"`` 表示角度编码，一个量子比特编码一个旋转门； ``"amplitude_encoding"`` 表示振幅编码； + ``"pauli_rotation_encoding"`` 表示SU(3)的角度编码; 还有 ``"linear_entangled_encoding"`` , + ``"real_entangled_encoding"`` , ``"complex_entangled_encoding"`` 三种纠缠编码和 ``"IQP_encoding"`` 编码 + num_qubits (int): 编码后的量子比特数目 + split_circuit (bool): 是否需要切分电路。除了振幅之外的所有电路都会存在堆叠的情况，如果选择 ``True`` 就将块与块分开 + downscaling_method (str): 包括 ``"PCA"`` 和 ``"resize"`` + target_dimension (int): 降维之后的尺度大小，如果是 ``"PCA"`` ，不能超过图片大小；如果是 ``"resize"`` ，不能超过原图大小 + return_state (bool): 是否返回量子态，如果是 ``False`` 返回量子电路 + + Returns: + tuple: 包含如下元素: + - quantum_image_states (paddle.tensor): 量子态，只有 ``full_return==True`` 或者 ``return_state==True`` 的时候会返回 + - quantum_image_circuits (list): 所有特征编码的电路， 只有 ``full_return==False`` 或者 ``return_state==True`` 的时候会返回 + - original_images (ndarray): 图片经过类别过滤，但是还没有降维、补零的特征，是一个一维向量（可以 reshape 成图片），只有 ``return_state==True`` 的时候会返回 + - classical_image_vectors (ndarray): 经过类别过滤和降维、补零等操作之后的特征，并未编码为量子态，只有 ``return_state==True`` 的时候会返回 + + """ + assert num_qubits > 0 + if encoding in [IQP_ENCODING, COMPLEX_ENTANGLED_ENCODING, REAL_ENTANGLED_ENCODING, + LINEAR_ENTANGLED_ENCODING]: + assert num_qubits > 1 + + if type(feature) == np.ndarray: + feature = list(feature) + + # The first step: judge whether `target_dimension` is reasonable + if target_dimension > -1: + if downscaling_method == DOWNSCALINGMETHOD_PCA: + if target_dimension > self.figure_size: + raise Exception("PCA dimension should be less than {}.".format(self.figure_size)) + elif downscaling_method == DOWNSCALINGMETHOD_RESIZE: + if int(sqrt(target_dimension)) ** 2 != target_dimension: # not a square + raise Exception("Resize dimension should be a square.") + else: + raise Exception("Downscaling methods can only be resize and PCA.") + else: + if downscaling_method == DOWNSCALINGMETHOD_PCA: + target_dimension = self.figure_size + elif downscaling_method == DOWNSCALINGMETHOD_RESIZE: + target_dimension = self.figure_size ** 2 + + # The second step: calculate `can_describe_dimension` + if encoding == AMPLITUDE_ENCODING: # amplitude encoding, encoding 2^N-dimension feature + self.can_describe_dimension = 2 ** num_qubits + + elif encoding == LINEAR_ENTANGLED_ENCODING: + one_block_param = 2 * num_qubits + self.can_describe_dimension = math.ceil(target_dimension / one_block_param) * one_block_param + + elif encoding in [REAL_ENTANGLED_ENCODING, ANGLE_ENCODING, IQP_ENCODING]: + one_block_param = 1 * num_qubits + self.can_describe_dimension = math.ceil(target_dimension / one_block_param) * one_block_param + + elif encoding in [COMPLEX_ENTANGLED_ENCODING, PAULI_ROTATION_ENCODING]: + one_block_param = 3 * num_qubits + self.can_describe_dimension = math.ceil(target_dimension / one_block_param) * one_block_param + + else: + raise Exception("Invalid encoding methods!") + self.dimension = target_dimension + + # The third step: download MNIST data from paddlepaddle and crop or fill the vector to ``can_describe_vector`` + self.original_images = np.array(feature) + self.classical_image_vectors = feature.copy() + + # What need to mention if ``Resize`` needs uint8, but MNIST in paddle is float32, so we should change its type. + if downscaling_method == DOWNSCALINGMETHOD_RESIZE: + # iterating all items + for i in range(len(self.classical_image_vectors)): + cur_image = self.classical_image_vectors[i].astype(np.uint8) + new_size = int(sqrt(self.dimension)) + cur_image = transform.resize(cur_image.reshape((self.figure_size, self.figure_size)), + (new_size, new_size)) + self.classical_image_vectors[i] = cur_image.reshape(-1).astype(np.float64) # now it is one-dimension + + if self.can_describe_dimension < len(self.classical_image_vectors[i]): + self.classical_image_vectors[i] = self.classical_image_vectors[i][:self.can_describe_dimension] + else: + self.classical_image_vectors[i] = np.append(self.classical_image_vectors[i], np.array( + [0.0] * (self.can_describe_dimension - len(self.classical_image_vectors[i])))) + + elif downscaling_method == DOWNSCALINGMETHOD_PCA: + for i in range(len(self.classical_image_vectors)): + U, s, V = np.linalg.svd(self.classical_image_vectors[i].reshape((self.figure_size, self.figure_size))) + s = s[:self.dimension].astype(np.float64) + if self.can_describe_dimension > self.dimension: + self.classical_image_vectors[i] = np.append(s, np.array( + [0.0] * (self.can_describe_dimension - self.dimension))) + else: + self.classical_image_vectors[i] = s[:self.can_describe_dimension] + + # Step 4: Encode the data, which must be of float64 type(needed in paddle quantum) + self.quantum_image_states, self.quantum_image_circuits = self.data2circuit( + self.classical_image_vectors, encoding, num_qubits, self.can_describe_dimension, split_circuit, + return_state, is_image=True) + self.classical_image_vectors = np.array(self.classical_image_vectors) + if return_state: + self.quantum_image_states = paddle.to_tensor(np.array(self.quantum_image_states)) # transfer to tensor + + if full_return: + return self.quantum_image_states, self.quantum_image_circuits, self.original_images, \ + self.classical_image_vectors + else: + if return_state: + return self.quantum_image_states + else: + return self.quantum_image_circuits + + +class MNIST(VisionDataset): + r"""MNIST 数据集，它继承了 VisionDataset 图片数据集类。 + + Attributes: + original_images(ndarray): 图片经过类别过滤，但是还没有降维、补零的特征，是一个一维向量（可调用 ``reshape()`` 方法转成图片） + classical_image_vectors(ndarray): 经过类别过滤和降维、补零等操作之后的特征，并未编码为量子态 + quantum_image_states(paddle.tensor): 经过类别过滤之后的所有特征经编码形成的量子态 + quantum_image_circuits(list): 所有特征编码的电路 + labels(ndarray): 经过类别过滤之后的所有标签 + + 代码示例: + + .. code-block:: python + + from paddle_quantum.dataset import MNIST + + # main parameters + training_data_num = 80 + testing_data_num = 20 + qubit_num = 4 + + # acquiring training dataset + train_dataset = MNIST(mode='train', encoding='pauli_rotation_encoding', num_qubits=qubit_num, classes=[3,6], + data_num=training_data_num,need_cropping=True, + downscaling_method='resize', target_dimension=16, return_state=True) + + # acquiring testing dataset + val_dataset = MNIST(mode='test', encoding='pauli_rotation_encoding', num_qubits=qubit_num, classes=[3,6], + data_num=testing_data_num,need_cropping=True, + downscaling_method='resize', target_dimension=16,return_state=True) + + # acquiring features and labels + train_x, train_y = train_dataset.quantum_image_states, train_dataset.labels # paddle.tensor, ndarray + test_x, test_y = val_dataset.quantum_image_states, val_dataset.labels + + print(train_x[0]) + print(train_y[0]) + + """ + + def __init__(self, mode, encoding, num_qubits, classes, data_num=-1, split_circuit=False, + downscaling_method=DOWNSCALINGMETHOD_RESIZE, target_dimension=-1, need_cropping=True, + need_relabel=True, return_state=True, seed=0): + r"""构造函数 + + Args: + mode (str): 数据模式，包括 ``"train"`` 和 ``"test"`` + encoding (str): ``"angle_encoding"`` 表示角度编码，一个量子比特编码一个旋转门； ``"amplitude_encoding"`` 表示振幅编码； + ``"pauli_rotation_encoding"`` 表示SU(3)的角度编码; 还有 ``"linear_entangled_encoding"`` , + ``"real_entangled_encoding"`` , ``"complex_entangled_encoding"`` 三种纠缠编码和 ``"IQP_encoding"`` 编码 + num_qubits (int): 编码后的量子比特数目 + classes (list): 用列表给出需要的类别，类别用数字标签表示，不支持传入名字 + data_num (int): 使用的数据量大小，这样可以不用所有数据都进行编码，这样会很慢 + split_circuit (bool): 是否需要切分电路。除了振幅之外的所有电路都会存在堆叠的情况，如果选择 ``True`` 就将块与块分开 + need_cropping (bool): 是否需要裁边，如果为 ``True`` ，则从 ``image[0:27][0:27]`` 裁剪为 ``image[4:24][4:24]`` + need_relabel (bool): 将原有类别按照顺序重新标记为 0，1，2 等新的名字，比如传入 ``[1,2]`` ，重新标记之后变为 ``[0,1]`` ，主要用于二分类 + downscaling_method (str): 包括 ``"PCA"`` 和 ``"resize"`` + target_dimension (int): 降维之后的尺度大小，如果是 ``"PCA"`` ，不能超过图片大小；如果是 ``"resize"`` ，不能超过原图大小 + return_state (bool): 是否返回量子态，如果是 ``False`` 返回量子电路 + seed (int): 筛选样本的随机种子，默认为 ``0`` + """ + VisionDataset.__init__(self, 28) + + if need_cropping: + self.figure_size = 20 + + # Download data from paddlepaddle + if mode == DATAMODE_TRAIN: + train_dataset = paddle.vision.datasets.MNIST(mode='train') + feature, self.labels = self.filter_class(train_dataset.images, train_dataset.labels, + classes=classes, + data_num=data_num, need_relabel=need_relabel, seed=seed) + if need_cropping: + feature = _crop(feature, [4, 24]) + + elif mode == DATAMODE_TEST: + test_dataset = paddle.vision.datasets.MNIST(mode='test') + # test_dataset.images is now a list of (784,1) shape + feature, self.labels = self.filter_class(test_dataset.images, test_dataset.labels, + classes=classes, + data_num=data_num, need_relabel=need_relabel, seed=seed) + if need_cropping: + feature = _crop(feature, [4, 24]) + + else: + raise Exception("data mode can only be train and test.") + + # Start to encode + self.quantum_image_states, self.quantum_image_circuits, self.original_images, self.classical_image_vectors = \ + self.encode(feature, encoding, num_qubits, split_circuit, downscaling_method, target_dimension, + return_state, True) + self.labels = np.array(self.labels) + + def __len__(self): + return len(self.quantum_image_states) + + +class FashionMNIST(VisionDataset): + r""" FashionMNIST 数据集，它继承了 VisionDataset 图片数据集类 + + Attributes: + original_images (ndarray): 图片经过类别过滤，但是还没有降维、补零的特征，是一个一维向量（可调用 ``reshape()`` 方法转成图片） + classical_image_vectors (ndarray): 经过类别过滤和降维、补零等操作之后的特征，并未编码为量子态 + quantum_image_states (paddle.tensor): 经过类别过滤之后的所有特征经编码形成的量子态 + quantum_image_circuits (list): 所有特征编码的电路 + labels (ndarray): 经过类别过滤之后的所有标签 + + 代码示例: + + .. code-block:: python + + from paddle_quantum.dataset import FashionMNIST + + training_data_num=80 + testing_data_num=20 + qubit_num=4 + + # acquiring training dataset + train_dataset = FashionMNIST(mode='train', encoding='pauli_rotation_encoding', num_qubits=qubit_num, classes=[3,6], + data_num=training_data_num,downscaling_method='resize', target_dimension=16, return_state=True) + + # 验acquiring testing dataset + val_dataset = FashionMNIST(mode='test', encoding='pauli_rotation_encoding', num_qubits=qubit_num, classes=[3,6], + data_num=testing_data_num,downscaling_method='resize', target_dimension=16,return_state=True) + + # acquiring features and labels + train_x, train_y = train_dataset.quantum_image_states, train_dataset.labels # paddle.tensor, ndarray + test_x, test_y = val_dataset.quantum_image_states, val_dataset.labels + + print(train_x[0]) + print(train_y[0]) + """ + + def __init__(self, mode, encoding, num_qubits, classes, data_num=-1, split_circuit=False, + downscaling_method=DOWNSCALINGMETHOD_RESIZE, target_dimension=-1, + need_relabel=True, return_state=True, seed=0): + r""" 构造函数 + + Args: + mode (str): 数据模式，包括 ``"train"`` 和 ``"test"`` + encoding (str): ``"angle_encoding"`` 表示角度编码，一个量子比特编码一个旋转门； ``"amplitude_encoding"`` 表示振幅编码； + ``"pauli_rotation_encoding"`` 表示SU(3)的角度编码；还有 ``"linear_entangled_encoding"`` 、 + ``"real_entangled_encoding"`` 、 ``"complex_entangled_encoding"`` 三种纠缠编码和 ``"IQP_encoding"`` 编码 + num_qubits (int): 编码后的量子比特数目 + classes (list): 用列表给出需要的类别，类别用数字标签表示，不支持传入名字 + data_num (int): 使用的数据量大小，这样可以不用所有数据都进行编码，这样会很慢 + split_circuit (bool): 是否需要切分电路。除了振幅之外的所有电路都会存在堆叠的情况，如果选择true就将块与块分开 + need_relabel (bool): 将原有类别按照顺序重新标记为0，1，2等新的名字，比如传入 ``[1,2]`` ，重新标记之后变为 ``[0,1]`` ，主要用于二分类 + downscaling_method (str): 包括 ``"PCA"`` 和 ``"resize"`` + target_dimension (int): 降维之后的尺度大小，如果是 ``"PCA"`` ，不能超过图片大小；如果是 ``"resize"`` ，不能超过原图大小 + return_state (bool): 是否返回量子态，如果是 ``False`` 返回量子电路 + seed (int): 随机种子，默认为 ``0`` + """ + VisionDataset.__init__(self, 28) + + # Download data from paddlepaddle + if mode == DATAMODE_TRAIN: + train_dataset = paddle.vision.datasets.FashionMNIST(mode='train') + feature, self.labels = self.filter_class(train_dataset.images, train_dataset.labels, + classes=classes, + data_num=data_num, need_relabel=need_relabel, seed=seed) + + elif mode == DATAMODE_TEST: + test_dataset = paddle.vision.datasets.FashionMNIST(mode='test') + # test_dataset.images is now a list of (784,1) shape + feature, self.labels = self.filter_class(test_dataset.images, test_dataset.labels, + classes=classes, + data_num=data_num, need_relabel=need_relabel, seed=seed) + + else: + raise Exception("data mode can only be train and test.") + + # Start to encode + self.quantum_image_states, self.quantum_image_circuits, self.original_images, self.classical_image_vectors = \ + self.encode(feature, encoding, num_qubits, split_circuit, downscaling_method, target_dimension, + return_state, True) + self.labels = np.array(self.labels) + + def __len__(self): + return len(self.quantum_image_states) + + +class SimpleDataset(Dataset): + r""" 用于不需要降维的简单分类数据。用户可以通过继承 ``SimpleDataset`` ，将自己的分类数据变为量子态。下面的几个属性也会被继承。 + + Attributes: + quantum_states (ndarray): 经过类别过滤之后的所有特征经编码形成的量子态 + quantum_circuits (list): 所有特征编码的电路 + origin_feature (ndarray): 经过类别过滤之后的所有特征，并未编码为量子态 + feature (ndarray): ``origin_feature`` 经过了补零之后的特征， ``quantum_states`` 就是将 ``feature`` 编码之后的结果 + + 代码示例: + + .. code-block:: python + + from paddle_quantum.dataset import SimpleDataset + + def circle_data_point_generator(Ntrain, Ntest, boundary_gap, seed_data): + # generate binary classification data with circle boundaries + # The former Ntrain samples are training data, the latter Ntest samples are testing data. + + train_x, train_y = [], [] + num_samples, seed_para = 0, 0 + while num_samples < Ntrain + Ntest: + np.random.seed((seed_data + 10) * 1000 + seed_para + num_samples) + data_point = np.random.rand(2) * 2 - 1 # generator two-dimension vectors in [-1, 1] + + # If the norm is below (0.7 - gap), the data point is mark as zero + if np.linalg.norm(data_point) < 0.7 - boundary_gap / 2: + train_x.append(data_point) + train_y.append(0.) + num_samples += 1 + + # If the norm is over (0.7 + gap), the data point is mark as one + elif np.linalg.norm(data_point) > 0.7 + boundary_gap / 2: + train_x.append(data_point) + train_y.append(1.) + num_samples += 1 + else: + seed_para += 1 + + train_x = np.array(train_x).astype("float64") + train_y = np.array([train_y]).astype("float64").T + + print("The dimension of the training data: x {} 和 y {}".format(np.shape(train_x[0:Ntrain]), np.shape(train_y[0:Ntrain]))) + print("The dimension of the testing data: x {} 和 y {}".format(np.shape(train_x[Ntrain:]), np.shape(train_y[Ntrain:])), "\n") + + return train_x[0:Ntrain], train_y[0:Ntrain], train_x[Ntrain:], train_y[Ntrain:] + + Ntrain = 200 # the size of the training dataset + Ntest = 100 # the size of the testing dataset + boundary_gap = 0.5 # the gap between two classes + seed_data = 2 # fixed seed + + # generate a new dataset + train_x, train_y, test_x, test_y = circle_data_point_generator(Ntrain, Ntest, boundary_gap, seed_data) + encoding="angle_encoding" + num_qubit=2 + dimension=2 + train_x=SimpleDataset(dimension).encode(train_x,encoding,num_qubit) + test_x=SimpleDataset(dimension).encode(test_x,encoding,num_qubit) + + print(train_x[0]) + print(test_x[0]) + + :: + """ + + def __init__(self, dimension): + r""" 构造函数 + + Args: + dimension (int): 编码数据的维度。 + """ + Dataset.__init__(self) + self.dimension = dimension + return + + def encode(self, feature, encoding, num_qubits, return_state=True, full_return=False): + r""" 进行编码 + + Args: + feature (list/ndarray): 编码的特征，每一个分量都是一个 ndarray 的特征向量 + encoding (str): 编码方法 + num_qubits (int): 编码的量子比特数目 + return_state (bool): 是否返回量子态 + + Returns: + tuple: 包含如下元素: + - quantum_states (ndarray): 量子态，只有 ``full_return==True`` 或者 ``return_state==True`` 的时候会返回 + - quantum_circuits (list): 所有特征编码的电路，只有 ``full_return==False`` 或者 ``return_state==True`` 的时候会返回 + - origin_feature (ndarray): 经过类别过滤之后的所有特征，并未编码为量子态，只有 ``return_state==True`` 的时候会返回 + - feature (ndarray): ``origin_feature`` 经过了补零之后的特征， ``quantum_states`` 就是将 ``feature`` 编码之后的结果。 只有 ``return_state==True`` 的时候会返回 + """ + + assert num_qubits > 0 + if encoding in [IQP_ENCODING, COMPLEX_ENTANGLED_ENCODING, REAL_ENTANGLED_ENCODING, + LINEAR_ENTANGLED_ENCODING]: + assert num_qubits > 1 + + if type(feature) == np.ndarray: + self.feature = list(feature) + elif type(feature) is list: + self.feature = feature + else: + raise Exception("invalid type of feature") + + self.origin_feature = np.array(feature) + + # The first step, calculate ``self.can_describe_dimension``, and judge whether the qubit number is small + if encoding == AMPLITUDE_ENCODING: # amplitude encoding, encoding 2^N-dimension feature + self.can_describe_dimension = 2 ** num_qubits + # For these three kinds of entanglement encoding: lay these parameters block by block. + elif encoding == LINEAR_ENTANGLED_ENCODING: + one_block_param = 2 * num_qubits + self.can_describe_dimension = math.ceil(self.dimension / one_block_param) * one_block_param + + elif encoding in [REAL_ENTANGLED_ENCODING, IQP_ENCODING, ANGLE_ENCODING]: + one_block_param = 1 * num_qubits + self.can_describe_dimension = math.ceil(self.dimension / one_block_param) * one_block_param + + elif encoding in [COMPLEX_ENTANGLED_ENCODING, PAULI_ROTATION_ENCODING]: + one_block_param = 3 * num_qubits + self.can_describe_dimension = math.ceil(self.dimension / one_block_param) * one_block_param + + else: + raise Exception("Invalid encoding methods!") + + if self.can_describe_dimension < self.dimension: + raise Exception("The qubit number is not enough to encode the features.") + + # The second step: fill the vector to ``can_describe_dimension`` using zero + for i in range(len(self.feature)): + self.feature[i] = self.feature[i].reshape(-1).astype( + np.float64) # now self.images[i] is a numpy with (new_size*new_size,1) shape + self.feature[i] = np.append(self.feature[i], + np.array([0.0] * ( + self.can_describe_dimension - self.dimension))) # now self.images[i] is filled to ``self.can_describe_dimension`` + + # Step 3: Encode the data, which must be of float64 type(needed in paddle quantum) + self.quantum_states, self.quantum_circuits = self.data2circuit( + self.feature, encoding, num_qubits, self.can_describe_dimension, False, # split_circuit=False + return_state) + + self.feature = np.array(self.feature) + self.quantum_states = np.array(self.quantum_states) + + if full_return: + return self.quantum_states, self.quantum_circuits, self.origin_feature, self.feature + else: + if return_state: + return self.quantum_states + else: + return self.quantum_circuits + + +class Iris(SimpleDataset): + r""" Iris 数据集 + + Attributes: + quantum_states (ndarray): 经过类别过滤之后的所有特征经编码形成的量子态 + quantum_circuits (list): 所有特征编码的电路 + origin_feature (ndarray): 经过类别过滤之后的所有特征，并未编码为量子态 + feature (ndarray): ``origin_feature`` 经过了补零之后的特征， ``quantum_states`` 就是将 ``feature`` 编码之后的结果 + target (ndarray): 经过类别过滤之后的所有标签 + train_x (paddle.tensor): 从 ``quantum_states`` 中选出的训练集 + test_x (paddle.tensor): 从 ``quantum_states`` 中选出的测试集 + train_circuits (list): 对应于 ``train_x`` 的编码电路 + test_circuits (list): 对应于 ``test_x`` 的编码电路 + origin_train_x (ndarray): 和 ``train_x`` 对应的经典数据 + origin_test_x (ndarray): 和 ``test_x`` 对应的经典数据 + train_y (ndarray): 对应于 ``train_x`` 的标签 + test_y (ndarray): 对应于 ``test_x`` 的标签 + + 代码示例: + + .. code-block:: python + + from paddle_quantum.dataset import Iris + + test_rate=0.2 + qubit_num=4 + + # Get Iris data, select two classes 0,1, and encode the data into four qubits using angle coding and return the quantum state. + # The proportion of the test set is 0.2. + iris =Iris (encoding='angle_encoding', num_qubits=qubit_num, test_rate=test_rate,classes=[0,1], return_state=True) + + # Get the features and labels of the classical Iris dataset + origin_feature=iris.origin_feature # ndarray + origin_target=iris.target + + # Gets the quantum states and labels of the training and test datasets + train_x, train_y = iris.train_x, iris.train_y # paddle.tensor, ndarray + test_x, test_y = iris.test_x, iris.test_y + + testing_data_num=len(test_y) + training_data_num=len(train_y) + print(training_data_num) + print(testing_data_num) + """ + + def __init__(self, encoding, num_qubits, classes, test_rate=0.2, need_relabel=True, return_state=True): + r""" 构造函数 + + Args: + encoding (str): ``"angle_encoding"`` 表示角度编码，一个量子比特编码一个旋转门； ``"amplitude_encoding"`` 表示振幅编码； + ``"pauli_rotation_encoding"`` 表示SU(3)的角度编码；还有 ``"linear_entangled_encoding"`` 、 + ``"real_entangled_encoding"`` 、 ``"complex_entangled_encoding"`` 三种纠缠编码和 ``"IQP_encoding"`` 编码 + num_qubits (int): 量子比特数目 + classes (list): 用列表给出需要的类别，类别用数字标签表示，不支持传入名字 + test_rate (float): 测试集的占比 + need_relabel (bool): 将原有类别按照顺序重标记为 0、1、2 等新的名字，比如传入 ``[1,2]`` ，重标记之后变为 ``[0,1]`` ，主要用于二分类 + return_state (bool): 是否返回量子态，如果是 ``False`` 返回量子电路 + """ + + SimpleDataset.__init__(self, dimension=4) + + # Download data from scikit-learn + iris = datasets.load_iris() + self.dimension = 4 # dimension of Iris dataset + feature, self.target = self.filter_class(iris.data, iris.target, classes, -1, + need_relabel) # here -1 means all data + self.target = np.array(self.target) + + # Start to encode + self.quantum_states, self.quantum_circuits, self.origin_feature, self.feature = \ + self.encode(feature, encoding, num_qubits, return_state, True) + + # Divide training and testing dataset + seed = int(time.time()) + self.train_x, self.test_x, self.train_y, self.test_y = \ + train_test_split(self.quantum_states, self.target, test_size=test_rate, + random_state=seed) + + self.train_circuits, self.test_circuits, temp1, temp2 = \ + train_test_split(self.quantum_circuits, self.target, test_size=test_rate, + random_state=seed) + + self.origin_train_x, self.origin_test_x, temp1, temp2 = \ + train_test_split(self.origin_feature, self.target, test_size=test_rate, + random_state=seed) + if return_state: + self.train_x = paddle.to_tensor(self.train_x) + self.test_x = paddle.to_tensor(self.test_x) + + +class BreastCancer(SimpleDataset): + r"""BreastCancer 数据集，569 组数据 30 维，只有两类。 + + Attributes: + quantum_states (ndarray): 经过类别过滤之后的所有特征经编码形成的量子态 + quantum_circuits (list): 所有特征编码的电路 + origin_feature (ndarray): 经过类别过滤之后的所有特征，并未编码为量子态 + feature (ndarray): ``origin_feature`` 经过了补零之后的特征， ``quantum_states`` 就是将 ``feature`` 编码之后的结果 + target (ndarray): 经过类别过滤之后的所有标签 + train_x (paddle.tensor): 从 ``quantum_states`` 中选出的训练集 + test_x (paddle.tensor): 从 ``quantum_states`` 中选出的测试集 + train_circuits (list): 对应于 ``train_x`` 的编码电路 + test_circuits (list): 对应于 ``test_x`` 的编码电路 + origin_train_x (ndarray): 和 ``train_x`` 对应的经典数据 + origin_test_x (ndarray): 和 ``test_x`` 对应的经典数据 + train_y (ndarray): 对应于 ``train_x`` 的标签 + test_y (ndarray): 对应于 ``test_x`` 的标签 + + 代码示例: + + .. code-block:: python + + from paddle_quantum.dataset import BreastCancer + + test_rate = 0.2 + qubit_num = 4 + + # Get BreastCancer data, select two classes 0,1, and encode the data into four qubits using angle coding and return the quantum state. + # The proportion of the test set is 0.2. + breast_cancer =BreastCancer(encoding='angle_encoding', num_qubits=qubit_num, test_rate=test_rate, return_state=True) + + # Get the features and labels of the classical BreastCancer dataset + origin_feature=breast_cancer.origin_feature # ndarray + origin_target=breast_cancer.target + + # Gets the quantum states and labels of the training and test datasets + train_x, train_y = breast_cancer.train_x, breast_cancer.train_y # paddle.tensor, ndarray + test_x, test_y = breast_cancer.test_x, breast_cancer.test_y + + testing_data_num=len(test_y) + training_data_num=len(train_y) + print(training_data_num) + print(testing_data_num) + """ + + def __init__(self, encoding, num_qubits, test_rate=0.2, return_state=True): + r"""构造函数 + + Args: + encoding (str): ``"angle_encoding"`` 表示角度编码，一个量子比特编码一个旋转门； ``"amplitude_encoding"`` 表示振幅编码； + ``"pauli_rotation_encoding"`` 表示SU(3)的角度编码；还有 ``"linear_entangled_encoding"`` 、 + ``"real_entangled_encoding"`` 、 ``"complex_entangled_encoding"`` 三种纠缠编码和 ``"IQP_encoding"`` 编码 + num_qubits (int): 量子比特数目 + test_rate (float): 测试集的占比 + return_state (bool): 是否返回量子态，如果是 ``False`` 返回量子电路 + """ + SimpleDataset.__init__(self, dimension=30) # The dimension is 30 + self.dimension = 30 + + # Download data from scikit-learn + breast_cancer = datasets.load_breast_cancer() + feature = breast_cancer["data"] + self.target = breast_cancer["target"] + + self.target = np.array(self.target) + + # Start to encode + self.quantum_states, self.quantum_circuits, self.origin_feature, self.feature = \ + self.encode(feature, encoding, num_qubits, return_state, True) + + # Divide training and testing dataset + seed = int(time.time()) + self.train_x, self.test_x, self.train_y, self.test_y = \ + train_test_split(self.quantum_states, self.target, test_size=test_rate, + random_state=seed) + + self.train_circuits, self.test_circuits, temp1, temp2 = \ + train_test_split(self.quantum_circuits, self.target, test_size=test_rate, + random_state=seed) + + self.origin_train_x, self.origin_test_x, temp1, temp2 = \ + train_test_split(self.origin_feature, self.target, test_size=test_rate, + random_state=seed) + if return_state: + self.train_x = paddle.to_tensor(self.train_x) + self.test_x = paddle.to_tensor(self.test_x) diff --git a/paddle_quantum/gradtool.py b/paddle_quantum/gradtool.py new file mode 100644 index 0000000..8ec169e --- /dev/null +++ b/paddle_quantum/gradtool.py @@ -0,0 +1,429 @@ +# Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +""" +梯度分析工具模块 +""" + + +import numpy as np +import paddle +from paddle import reshape +from random import choice +from tqdm import tqdm +import matplotlib.pyplot as plt + +__all__ = [ + "StateNet", + "show_gradient", + "random_sample", + "random_sample_supervised", + "plot_loss_grad", + "plot_supervised_loss_grad", + "plot_distribution" +] + + +class StateNet(paddle.nn.Layer): + r"""定义用于量子机器学习的量子神经网络模型 + + 用户可以通过实例化该类定义自己的量子神经网络模型。 + """ + + def __init__(self, shape, dtype='float64'): + r"""构造函数，用于实例化一个 ``StateNet`` 对象 + + Args: + shape (paddle.Tensor): 表示传入的量子电路中的需要被优化的参数个数 + """ + super(StateNet, self).__init__() + self.theta = self.create_parameter(shape=shape, + default_initializer=paddle.nn.initializer.Uniform(low=0.0, high=2*np.pi), + dtype=dtype, is_bias=False) + + def forward(self, circuit, loss_func, *args): + r"""用于更新电路参数并计算该量子神经网络的损失值。 + + Args: + circuit (UAnsatz): 表示传入的参数化量子电路，即要训练的量子神经网络 + loss_func (function): 表示计算该量子神经网络损失值的函数 + *args (list): 表示用于损失函数计算的额外参数列表 + + Note: + 这里的 ``loss_func`` 是一个用户自定义的计算损失值的函数，参数为电路和一个可变参数列表。 + + Returns: + tuple: 包含如下两个元素: + - loss (paddle.Tensor): 表示该量子神经网络损失值 + - circuit (UAnsatz): 更新参数后的量子电路 + """ + circuit.update_param(self.theta) + circuit.run_state_vector() + loss = loss_func(circuit, *args) + return loss, circuit + + +def show_gradient(circuit, loss_func, ITR, LR, *args): + r"""计算量子神经网络中各可变参数的梯度值和损失函数值 + + Args: + circuit (UAnsatz): 表示传入的参数化量子电路，即要训练的量子神经网络 + loss_func (function): 表示计算该量子神经网络损失值的函数 + ITR (int): 表示训练的次数 + LR (float): 表示学习训练的速率 + *args (list): 表示用于损失函数计算的额外参数列表 + + Returns: + tuple: 包含如下两个元素: + - loss_list (list): 表示损失函数值随训练次数变化的列表 + - grad_list(list): 表示各参数梯度随训练次变化的列表 + """ + + grad_list = [] + loss_list = [] + shape = paddle.shape(circuit.get_param()) + net = StateNet(shape=shape) + opt = paddle.optimizer.Adam(learning_rate=LR, parameters=net.parameters()) + + pbar = tqdm( + desc="Training: ", total=ITR, ncols=100, ascii=True + ) + + for itr in range(ITR): + pbar.update(1) + loss, cir = net(circuit, loss_func, *args) + loss.backward() + grad = net.theta.grad.numpy() + grad_list.append(grad) + loss_list.append(loss.numpy()[0]) + opt.minimize(loss) + opt.clear_grad() + pbar.close() + + return loss_list, grad_list + + +def plot_distribution(grad): + r"""根据输入的梯度的列表，画出梯度的分布图 + + Args: + grad (np.array): 表示量子神经网络某参数的梯度列表 + """ + + grad = np.abs(grad) + grad_list = [0, 0, 0, 0, 0] + x = ['<0.0001', ' (0.0001,0.001)', '(0.001,0.01)', '(0.01,0.1)', '>0.1'] + for g in grad: + if g > 0.1: + grad_list[4] += 1 + elif g > 0.01: + grad_list[3] += 1 + elif g > 0.001: + grad_list[2] += 1 + elif g > 0.0001: + grad_list[1] += 1 + else: + grad_list[0] += 1 + grad_list = np.array(grad_list) / len(grad) + + plt.figure() + plt.bar(x, grad_list, width=0.5) + plt.title('The gradient distribution of variables') + plt.ylabel('ratio') + plt.show() + + +def random_sample(circuit, loss_func, sample_num, *args, mode='single', if_plot=True, param=0): + r"""表示对模型进行随机采样，根据不同的计算模式，获得对应的平均值和方差 + + Args: + circuit (UAnsatz): 表示传入的参数化量子电路，即要训练的量子神经网络 + loss_func (function): 表示计算该量子神经网络损失值的函数 + sample_num (int): 表示随机采样的次数 + mode (string): 表示随机采样后的计算模式，默认为 'single' + if_plot(boolean): 表示是否对梯度进行画图表示 + param (int): 表示 ``Single`` 模式中对第几个参数进行画图，默认为第一个参数 + *args (list): 表示用于损失函数计算的额外参数列表 + + Note: + 在本函数中提供了三种计算模式，``mode`` 分别可以选择 ``'single'``, ``'max'``, 以及 ``'random'`` + - mode='single': 表示计算电路中的每个可变参数梯度的平均值和方差 + - mode='max': 表示对电路中每轮采样的所有参数梯度的最大值求平均值和方差 + - mode='random': 表示对电路中每轮采样的所有参数随机取一个梯度，求平均值和方差 + + Returns: + tuple: 包含如下两个元素: + - loss_list (list): 表示多次采样后损失函数值的列表 + - grad_list(list): 表示多次采样后各参数梯度的列表 + """ + + loss_list, grad_list = [], [] + pbar = tqdm( + desc="Sampling: ", total=sample_num, ncols=100, ascii=True + ) + for itr in range(sample_num): + pbar.update(1) + shape = paddle.shape(circuit.get_param()) + net = StateNet(shape=shape) + loss, cir = net(circuit, loss_func, *args) + loss.backward() + grad = net.theta.grad.numpy() + loss_list.append(loss.numpy()[0]) + grad_list.append(grad) + + pbar.close() + + if mode == 'single': + grad_list = np.array(grad_list) + grad_list = grad_list.transpose() + grad_variance_list = [] + grad_mean_list = [] + for idx in range(len(grad_list)): + grad_variance_list.append(np.var(grad_list[idx])) + grad_mean_list.append(np.mean(grad_list[idx])) + + print("Mean of gradient for all parameters: ") + for i in range(len(grad_mean_list)): + print("theta", i+1, ": ", grad_mean_list[i]) + print("Variance of gradient for all parameters: ") + for i in range(len(grad_variance_list)): + print("theta", i+1, ": ", grad_variance_list[i]) + + if if_plot: + plot_distribution(grad_list[param]) + + return grad_mean_list, grad_variance_list + + if mode == 'max': + max_grad_list = [] + for idx in range(len(grad_list)): + max_grad_list.append(np.max(np.abs(grad_list[idx]))) + + print("Mean of max gradient") + print(np.mean(max_grad_list)) + print("Variance of max gradient") + print(np.var(max_grad_list)) + + if if_plot: + plot_distribution(max_grad_list) + + return np.mean(max_grad_list), np.var(max_grad_list) + + if mode == 'random': + random_grad_list = [] + for idx in range(len(grad_list)): + random_grad = choice(grad_list[idx]) + random_grad_list.append(random_grad) + print("Mean of random gradient") + print(np.mean(random_grad_list)) + print("Variance of random gradient") + print(np.var(random_grad_list)) + + if if_plot: + plot_distribution(random_grad_list) + + return np.mean(random_grad_list), np.var(random_grad_list) + + return loss_list, grad_list + + +def plot_loss_grad(circuit, loss_func, ITR, LR, *args): + r"""绘制损失值和梯度随训练次数变化的图 + + Args: + circuit (UAnsatz): 表示传入的参数化量子电路，即要训练的量子神经网络 + loss_func (function): 表示计算该量子神经网络损失值的函数 + ITR (int): 表示训练的次数 + LR (float): 表示学习训练的速率 + *args (list): 表示用于损失函数计算的额外参数列表 + + """ + loss, grad = show_gradient(circuit, loss_func, ITR, LR, *args) + plt.xlabel(r"Iteration") + plt.ylabel(r"Loss") + plt.plot(range(1, ITR+1), loss, 'r', label='loss') + plt.legend() + plt.show() + + max_grad = [np.max(np.abs(i)) for i in grad] + plt.xlabel(r"Iteration") + plt.ylabel(r"Gradient") + plt.plot(range(1, ITR+1), max_grad, 'b', label='gradient') + plt.legend() + plt.show() + + +def plot_supervised_loss_grad(circuit, loss_func, N, EPOCH, LR, BATCH, TRAIN_X, TRAIN_Y, *args): + r"""绘制监督学习中损失值和梯度随训练次数变化的图 + + Args: + circuit (UAnsatz): 表示传入的参数化量子电路，即要训练的量子神经网络 + loss_func (function): 表示计算该量子神经网络损失值的函数 + N (int): 表示量子比特的数量 + EPOCH (int): 表示训练的轮数 + LR (float): 表示学习训练的速率 + BATCH (int): 表示训练时 batch 的大小 + TRAIN_X (paddle.Tensor): 表示训练数据集 + TRAIN_Y (list): 表示训练数据集的标签 + *args (list): 表示用于损失函数计算的额外参数列表 + + Returns: + tuple: 包含如下两个元素: + - loss_list (list): 表示多次训练的损失函数值列表 + - grad_list(list): 表示多次训练后各参数梯度的列表 + """ + grad_list = [] + loss_list = [] + + if type(TRAIN_X) != paddle.Tensor: + raise Exception("Training data should be paddle.Tensor type") + + shape = paddle.shape(circuit.get_param()) + net = StateNet(shape=shape) + opt = paddle.optimizer.Adam(learning_rate=LR, parameters=net.parameters()) + + for ep in range(EPOCH): + for itr in range(len(TRAIN_X)//BATCH): + input_state = TRAIN_X[itr*BATCH:(itr+1)*BATCH] + input_state = reshape(input_state, [-1, 1, 2**N]) + label = TRAIN_Y[itr * BATCH:(itr + 1) * BATCH] + loss, circuit = net(circuit, loss_func, input_state, label) + loss.backward() + grad = net.theta.grad.numpy() + grad_list.append(grad) + loss_list.append(loss.numpy()[0]) + opt.minimize(loss) + opt.clear_grad() + + max_grad = [np.max(np.abs(i)) for i in grad_list] + plt.xlabel(r"Iteration") + plt.ylabel(r"Loss") + plt.plot(range(1, EPOCH*len(TRAIN_X)//BATCH+1), loss_list, 'r', label='loss') + plt.legend() + plt.show() + + plt.xlabel(r"Iteration") + plt.ylabel(r"Gradient") + plt.plot(range(1, EPOCH*len(TRAIN_X)//BATCH+1), max_grad, 'b', label='gradient') + plt.legend() + plt.show() + + return loss_list, grad_list + + +def random_sample_supervised(circuit, loss_func, N, sample_num, BATCH, TRAIN_X, TRAIN_Y, *args, mode='single', if_plot=True, param=0): + r"""表示对监督学习模型进行随机采样，根据不同的计算模式，获得对应的平均值和方差 + + Args: + circuit (UAnsatz): 表示传入的参数化量子电路，即要训练的量子神经网络 + loss_func (function): 表示计算该量子神经网络损失值的函数 + N (int): 表示量子比特的数量 + sample_num (int): 表示随机采样的次数 + BATCH (int): 表示训练时 batch 的大小 + TRAIN_X (paddle.Tensor): 表示训练数据集 + TRAIN_Y (list): 表示训练数据集的标签 + mode (string): 表示随机采样后的计算模式，默认为 'single' + if_plot(boolean): 表示是否对梯度进行画图表示 + param (int): 表示 ``Single`` 模式中对第几个参数进行画图，默认为第一个参数 + *args (list): 表示用于损失函数计算的额外参数列表 + + Note: + 在本函数中提供了三种计算模式，``mode`` 分别可以选择 ``'single'``, ``'max'``, 以及 ``'random'`` + - mode='single': 表示计算电路中的每个可变参数梯度的平均值和方差 + - mode='max': 表示对电路中所有参数梯度的最大值求平均值和方差 + - mode='random': 表示随机对电路中采样的所有参数随机取一个梯度，求平均值和方差 + + Returns: + tuple: 包含如下两个元素: + - loss_list (list): 表示多次采样后损失函数值的列表 + - grad_list(list): 表示多次采样后各参数梯度的列表 + """ + grad_list = [] + loss_list = [] + input_state = TRAIN_X[0:BATCH] + input_state = reshape(input_state, [-1, 1, 2**N]) + label = TRAIN_Y[0: BATCH] + + if type(TRAIN_X) != paddle.Tensor: + raise Exception("Training data should be paddle.Tensor type") + + label = TRAIN_Y[0: BATCH] + + pbar = tqdm( + desc="Sampling: ", total=sample_num, ncols=100, ascii=True + ) + for idx in range(sample_num): + pbar.update(1) + shape = paddle.shape(circuit.get_param()) + net = StateNet(shape=shape) + + loss, circuit = net(circuit, loss_func, input_state, label) + loss.backward() + grad = net.theta.grad.numpy() + grad_list.append(grad) + loss_list.append(loss.numpy()[0]) + pbar.close() + + if mode == 'single': + grad_list = np.array(grad_list) + grad_list = grad_list.transpose() + grad_variance_list = [] + grad_mean_list = [] + for idx in range(len(grad_list)): + grad_variance_list.append(np.var(grad_list[idx])) + grad_mean_list.append(np.mean(grad_list[idx])) + + print("Mean of gradient for all parameters: ") + for i in range(len(grad_mean_list)): + print("theta", i+1, ": ", grad_mean_list[i]) + print("Variance of gradient for all parameters: ") + for i in range(len(grad_variance_list)): + print("theta", i+1, ": ", grad_variance_list[i]) + + if if_plot: + plot_distribution(grad_list[param]) + + return grad_mean_list, grad_variance_list + + if mode == 'max': + max_grad_list = [] + for idx in range(len(grad_list)): + max_grad_list.append(np.max(np.abs(grad_list[idx]))) + + print("Mean of max gradient") + print(np.mean(max_grad_list)) + print("Variance of max gradient") + print(np.var(max_grad_list)) + + if if_plot: + plot_distribution(max_grad_list) + + return np.mean(max_grad_list), np.var(max_grad_list) + + if mode == 'random': + random_grad_list = [] + for idx in range(len(grad_list)): + random_grad = choice(grad_list[idx]) + random_grad_list.append(random_grad) + print("Mean of random gradient") + print(np.mean(random_grad_list)) + print("Variance of random gradient") + print(np.var(random_grad_list)) + + if if_plot: + plot_distribution(random_grad_list) + + return np.mean(random_grad_list), np.var(random_grad_list) + + return loss_list, grad_list diff --git a/paddle_quantum/locc.py b/paddle_quantum/locc.py index f3f740e..df6bc5e 100644 --- a/paddle_quantum/locc.py +++ b/paddle_quantum/locc.py @@ -68,7 +68,7 @@ class LoccStatus(object): return self.measured_result else: raise ValueError("too many values to unpack (expected 3)") - + def __repr__(self): return f"state: {self.state.numpy()}\nprob: {self.prob.numpy()[0]}\nmeasured_result: {self.measured_result}" diff --git a/paddle_quantum/mbqc/utils.py b/paddle_quantum/mbqc/utils.py index 4e7783c..48074c7 100644 --- a/paddle_quantum/mbqc/utils.py +++ b/paddle_quantum/mbqc/utils.py @@ -967,9 +967,12 @@ def print_progress(current_progress, progress_name, track=True): assert 0 <= current_progress <= 1, "'current_progress' must be between 0 and 1" assert isinstance(track, bool), "'track' must be a bool." if track: - print("\r" + f"{progress_name.ljust(30)}" - f"|{'■' * int(50 * current_progress):{50}s}| " - f"\033[94m {'{:6.2f}'.format(100 * current_progress)}% \033[0m ", flush=True, end="") + print( + "\r" + f"{progress_name.ljust(30)}" + f"|{'■' * int(50 * current_progress):{50}s}| " + f"\033[94m {'{:6.2f}'.format(100 * current_progress)}% \033[0m ", flush=True, end="" + ) if current_progress == 1: print(" (Done)") diff --git a/paddle_quantum/optimizer/conjugate_gradient.py b/paddle_quantum/optimizer/conjugate_gradient.py index 8f4ef1d..cc75e28 100644 --- a/paddle_quantum/optimizer/conjugate_gradient.py +++ b/paddle_quantum/optimizer/conjugate_gradient.py @@ -19,6 +19,7 @@ CG optimizer from scipy import optimize from .custom_optimizer import CustomOptimizer + class ConjugateGradient(CustomOptimizer): r"""ConjugateGradient Optimizer @@ -57,6 +58,6 @@ class ConjugateGradient(CustomOptimizer): method='CG', jac=self.grad_func, options={'maxiter': iterations}, - callback=lambda xk: print('loss: ', (self.loss_func(xk, self.cir, self.hamiltonian, self.shots))) - ) + callback=lambda xk: print('loss: ', self.loss_func(xk, self.cir, self.hamiltonian, self.shots)) + ) print(opt_res.message) diff --git a/paddle_quantum/optimizer/newton_cg.py b/paddle_quantum/optimizer/newton_cg.py index c281a75..fc5285e 100644 --- a/paddle_quantum/optimizer/newton_cg.py +++ b/paddle_quantum/optimizer/newton_cg.py @@ -19,6 +19,7 @@ Newton-CG optimizer from scipy import optimize from .custom_optimizer import CustomOptimizer + class NewtonCG(CustomOptimizer): r"""Newton-CG Optimizer @@ -57,6 +58,6 @@ class NewtonCG(CustomOptimizer): method='Newton-CG', jac=self.grad_func, options={'maxiter': iterations}, - callback=lambda xk: print('loss: ', (self.loss_func(xk, self.cir, self.hamiltonian, self.shots))) - ) + callback=lambda xk: print('loss: ', self.loss_func(xk, self.cir, self.hamiltonian, self.shots)) + ) print(opt_res.message) diff --git a/paddle_quantum/optimizer/powell.py b/paddle_quantum/optimizer/powell.py index a91dbff..8669f2f 100644 --- a/paddle_quantum/optimizer/powell.py +++ b/paddle_quantum/optimizer/powell.py @@ -19,6 +19,7 @@ Powell optimizer from scipy import optimize from .custom_optimizer import CustomOptimizer + class Powell(CustomOptimizer): r"""Powell Optimizer @@ -54,5 +55,5 @@ class Powell(CustomOptimizer): method='Powell', options={'maxiter': iterations}, callback=lambda xk: print('loss: ', self.loss_func(xk, self.cir, self.hamiltonian, self.shots)) - ) + ) print(opt_res.message) diff --git a/paddle_quantum/optimizer/slsqp.py b/paddle_quantum/optimizer/slsqp.py index e508cef..037dec8 100644 --- a/paddle_quantum/optimizer/slsqp.py +++ b/paddle_quantum/optimizer/slsqp.py @@ -19,6 +19,7 @@ SLSQP optimizer from scipy import optimize from .custom_optimizer import CustomOptimizer + class SLSQP(CustomOptimizer): r"""SLSQP Optimizer @@ -53,5 +54,5 @@ class SLSQP(CustomOptimizer): method='SLSQP', options={'maxiter': iterations}, callback=lambda xk: print('loss: ', self.loss_func(xk, self.cir, self.hamiltonian, self.shots)) - ) + ) print(opt_res.message) diff --git a/paddle_quantum/qchem/__init__.py b/paddle_quantum/qchem/__init__.py new file mode 100755 index 0000000..f4e8f18 --- /dev/null +++ b/paddle_quantum/qchem/__init__.py @@ -0,0 +1,43 @@ +# Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +""" +量桨平台的量子化学模块 +""" + +from .qmodel import QModel +from . import ansatz +from .run import run_chem +from .qchem import * +import platform +import warnings + +__all__ = [ + "run_chem", + "QModel", + "ansatz", + "geometry", + "get_molecular_data", + "active_space", + # forward compatible with original qchem module + "fermionic_hamiltonian", + "spin_hamiltonian" +] + +if platform.system() == "Windows": + warning_msg = ("Currently, Windows' users can't use 'hartree fock' ansatz " + "for ground state energy calculation in `run_chem`, " + "since it depends on pyscf, which is not available on Windows. " + "We will work it out in the near future, sorry for the inconvenience.") + warnings.warn(message=warning_msg) diff --git a/paddle_quantum/qchem/ansatz/__init__.py b/paddle_quantum/qchem/ansatz/__init__.py new file mode 100755 index 0000000..7300cef --- /dev/null +++ b/paddle_quantum/qchem/ansatz/__init__.py @@ -0,0 +1,21 @@ +# Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +r""" +化学模块的 ansatz +""" + + +from .hardware_efficient import HardwareEfficientModel +from .rhf import RestrictHartreeFockModel diff --git a/paddle_quantum/qchem/ansatz/hardware_efficient.py b/paddle_quantum/qchem/ansatz/hardware_efficient.py new file mode 100755 index 0000000..60c0d8f --- /dev/null +++ b/paddle_quantum/qchem/ansatz/hardware_efficient.py @@ -0,0 +1,78 @@ +# Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the 'License'); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an 'AS IS' BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +""" +Hardware efficient ansatz 量子电路，以 +`Hardware-efficient variational quantum eigensolver +for small molecules and quantum magnets` 方式构建。 +具体细节可以参见 https://arxiv.org/abs/1704.05018 + +该模块依赖于 + - paddlepaddle + - paddle_quantum + - ../layers + - ../qmodel +""" + +import paddle +from paddle import nn +from paddle_quantum.circuit import UAnsatz + +from ..qmodel import QModel +from .. import layers + + +class HardwareEfficientModel(QModel): + r"""面向硬件的量子线路。 + + Args: + num_qubit (int): 量子线路的量子比特数量。 + circuit_depth (int): Cross resonance 和 Euler 转动层的数量。 + """ + + def __init__(self, num_qubit: int, circuit_depth: int) -> None: + super().__init__(num_qubit) + + mid_layers = [] + for i in range(circuit_depth): + mid_layers.append(layers.CrossResonanceLayer(num_qubit)) + mid_layers.append(layers.EulerRotationLayer(num_qubit)) + + self.model = nn.Sequential( + layers.RotationLayer(num_qubit, "X"), + layers.RotationLayer(num_qubit, "Z"), + *mid_layers, + ) + + def forward( + self, + state: "paddle.Tensor[paddle.complex128]" + ) -> "paddle.Tensor[paddle.complex128]": + r"""运行量子电路 + + Args: + state (paddle.Tensor[paddle.complex128]): 传入量子线路的量子态。 + + Returns: + paddle.Tensor[paddle.complex128]: 运行电路后的量子态 + """ + + out = self.model(state) + + cir0 = UAnsatz(self._n_qubit) + for subcir in self.model: + cir0 += subcir.circuit + self._circuit = cir0 + + return out diff --git a/paddle_quantum/qchem/ansatz/rhf.py b/paddle_quantum/qchem/ansatz/rhf.py new file mode 100755 index 0000000..0209b8a --- /dev/null +++ b/paddle_quantum/qchem/ansatz/rhf.py @@ -0,0 +1,133 @@ +# Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the 'License'); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an 'AS IS' BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +""" +Restrict Hartree Fock 模块 +""" + +from collections import OrderedDict +from copy import deepcopy +import numpy as np +import paddle +from paddle.nn import initializer +from paddle_quantum.circuit import UAnsatz +from ..linalg import givens_decomposition, parameters_to_givens_matrix2 +from ..qmodel import QModel +from .. import functional + + +class _MakeGivensMatrix(paddle.autograd.PyLayer): + r"""Construct Givens rotation matrix G from parameters \theta and \phi. + + .. math:: + G[j-1,j-1] = \cos(\theta) + G[j,j] = \cos(\theta) + G[j-1,j] = -\phi\sin(\theta) + G[j,j-1] = \phi\sin(\theta) + + We define this function since paddle doesn't fully support differentiate over + copy and slice operation, e.g. A[i,j] = \theta, where \theta is the parameter + to be differentiated. + """ + + @staticmethod + def forward(ctx, theta: paddle.Tensor, phi: paddle.Tensor, j: int, n: int): + G = parameters_to_givens_matrix2(theta, phi, j, n) + ctx.saved_index = j + ctx.save_for_backward(theta, phi) + return G + + @staticmethod + def backward(ctx, dG): + j = ctx.saved_index + theta, phi = ctx.saved_tensor() + dtheta = (-1.0 * (dG[j - 1, j - 1] + dG[j, j]) * paddle.sin(theta) + + (dG[j, j - 1] - dG[j - 1, j]) * phi * paddle.cos(theta)) + return dtheta, None + + +class RestrictHartreeFockModel(QModel): + r"""限制性 Hartree Fock (RHF) 波函数的量子线路。 + + Args: + num_qubits (int): RHF 计算中需要使用的量子比特数量。 + n_electrons (int): 待模拟的量子化学系统中的电子数量。 + onebody (paddle.Tensor(dtype=paddle.float64)): 经过 L\"owdin 正交化之后的单体积分。 + """ + + def __init__( + self, + num_qubits: int, + n_electrons: int, + onebody: paddle.Tensor + ) -> None: + super().__init__(num_qubits) + + self.nocc = n_electrons // 2 + self.norb = num_qubits // 2 + self.nvir = self.norb - self.nocc + + givens_angles = self.get_init_givens_angles(onebody) + models = [] + for ij, (theta, phi) in givens_angles.items(): + models.append((ij, _GivensBlock(self.n_qubit, -theta, phi))) + + self.models = paddle.nn.Sequential(*models) + + def get_init_givens_angles(self, onebody: paddle.Tensor) -> OrderedDict: + r"""利用单体积分来初始化 Givens 旋转的角度。 + + Args: + onebody (paddle.Tensor): 经过 L\"owdin 正交化之后的单体积分。 + + Returns: + OrderedDict + """ + assert type(onebody) == paddle.Tensor, "The onebody integral must be a paddle.Tensor." + _, U = np.linalg.eigh(onebody.numpy()) + U_tensor = paddle.to_tensor(U) + return givens_decomposition(U_tensor) + + def forward(self, state: paddle.Tensor) -> paddle.Tensor: + r"""运行量子电路 + + Args: + state (paddle.Tensor[paddle.complex128]): 传入量子线路的量子态矢量。 + + Returns: + paddle.Tensor[paddle.complex128]: 运行电路后的量子态 + """ + s = deepcopy(state) + self._circuit = UAnsatz(self.n_qubit) + for ij, givens_ops in self.models.named_children(): + i, j = [int(p) for p in ij.split(",")] + s = givens_ops(s, 2 * i, 2 * j) + self._circuit += givens_ops.circuit + s = givens_ops(s, 2 * i + 1, 2 * j + 1) + self._circuit += givens_ops.circuit + + return s + + def single_particle_U(self): + r"""获取 Hartree Fock 轨道旋转矩阵 + + Returns: + paddle.Tensor, Hartree Fock 轨道旋转矩阵，:math:`n_{orbitals}\times n_{occ}` + """ + self.register_buffer("_U", paddle.eye(int(self.norb), dtype=paddle.float64)) + for ij, givens_ops in self.models.named_children(): + j = int(ij.split(",")[1]) + self._U = givens_ops.single_particle_U(j, self.norb) @ self._U + + return self._U[:, :self.nocc] diff --git a/paddle_quantum/qchem/functional.py b/paddle_quantum/qchem/functional.py new file mode 100755 index 0000000..bcc9158 --- /dev/null +++ b/paddle_quantum/qchem/functional.py @@ -0,0 +1,180 @@ +# !/usr/bin/env python3 +# Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the 'License'); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an 'AS IS' BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +""" +用于构建量子电路层的函数操作。 +该模块依赖于 paddlepaddle 和 paddle_quantum +""" + +import paddle +from paddle_quantum.circuit import UAnsatz + + +# Rotation layer function +def rot_layer( + cir: UAnsatz, + parameters: "paddle.Tensor[paddle.float64]", + gate_type: str +) -> UAnsatz: + r"""该函数用来在量子线路上添加一层单比特旋转门，"Rx", "Ry", "Rz" + + Args: + cir (UAnsatz): 量子线路 + parameters (paddle.Tensor[paddle.float64]): 旋转门的旋转角度 + gate_type (str): "X", "Y" 和 "Z"，例如：如果是 "Rx" 门，则添 "X" + + Returns: + UAnsatz + """ + + n_qubits = cir.n + assert n_qubits == len(parameters), \ + "length of the parameters must equal the number of qubits" + + for i in range(n_qubits): + if gate_type == "X": + cir.rx(parameters[i], i) + elif gate_type == "Y": + cir.ry(parameters[i], i) + elif gate_type == "Z": + cir.rz(parameters[i], i) + + return cir + + +# Euler rotation gate function +def euler_rotation( + cir: UAnsatz, + which_qubit: int, + angles: "paddle.Tensor[paddle.float64]", +) -> UAnsatz: + r"""该函数定义了单比特的 Euler 旋转门（使用 ZXZ 规范） + + .. math:: + U(\theta,\phi,\gamma)=e^{-i\gamma/2\hat{Z}}e^{-i\phi/2\hat{X}}e^{-i\theta/2\hat{X}}. + + Args: + cir (UAnsatz): 量子线路 + which (int): Euler 旋转门作用的量子比特编号 + angles (paddle.Tensor[paddle.float64]): Euler 角，存储顺序与 ZXZ 操作的顺序相反。 + + Returns: + UAnsatz + """ + cir.rz(angles[0], which_qubit) + cir.rx(angles[1], which_qubit) + cir.rz(angles[2], which_qubit) + return cir + + +# Euler rotation layer function +def euler_rotation_layer( + cir: UAnsatz, + parameters: "paddle.Tensor[paddle.float64]", +) -> UAnsatz: + r"""该函数会在给定的量子线路上添加一层 Euler 旋转门。 + + Args: + cir (UAnsatz): 量子线路。 + parameters (paddle.Tensor[paddle.float64]): Euler 角参数集合。 + """ + n_qubits = cir.n + assert len( + parameters) == 3 * n_qubits, "length of parameter should be 3 times of the number of qubits in the circuit." + + for i in range(n_qubits): + cir = euler_rotation(cir, i, parameters[3 * i:3 * (i + 1)]) + + return cir + + +# Cross resonance gate function +def cross_resonance( + cir: UAnsatz, + ctrl_targ: "list[int]", + phase_angle: paddle.Tensor +) -> UAnsatz: + r"""该函数定义了一个双比特的 cross resonance (CR) 门。 + + .. math:: + U(\theta) = \exp(-i\frac{\theta}{2}\hat{X}\otimes\hat{Z}) + + Args: + cir (UAnsatz): 量子线路。 + ctrl_targ (list[int]): 控制比特和目标比特对应的比特编号。 + phase_angle (paddle.Tensor[paddle.float64]): 旋转角度。 + + Returns: + UAnsatz + """ + cir.h(ctrl_targ[0]) + cir.rzz(phase_angle, ctrl_targ) + cir.h(ctrl_targ[0]) + return cir + + +# Cross resonance layer function +def cr_layer( + cir: UAnsatz, + parameters: "paddle.Tensor[paddle.float64]", + ctrl_qubit_index: "list[int]", + targ_qubit_index: "list[int]" +) -> UAnsatz: + """该函数在给定线路上按照给定的控制和目标比特编号添加一层 cross resonance (CR) 门。 + + Args: + cir (UAnsatz): 量子线路。 + parameters (paddle.Tensor[paddle.float64]): CR 门中的角度。 + ctrl_qubit_index (list[int]): 控制比特序号。 + targ_qubit_index (list[int]): 目标比特序号。 + + Returns: + UAnsatz + """ + assert len(parameters) == len(ctrl_qubit_index) and len(ctrl_qubit_index) == len(targ_qubit_index), \ + "length of parameter must be the same as the number of cr gates" + + for i, ct_index in enumerate(zip(ctrl_qubit_index, targ_qubit_index)): + cir = cross_resonance(cir, list(ct_index), parameters[i]) + + return cir + + +# Nearest neighbor Givens rotation gate function +def givens_rotation( + cir: UAnsatz, + theta: "paddle.Tensor[paddle.float64]", + q1_index: int, + q2_index: int +) -> UAnsatz: + r"""该函数定义了两个相邻比特之间的 Givens 旋转门。详细信息参见 https://arxiv.org/abs/1711.05395. + + Note: + 在 paddlequantum :math:`Ry(\theta)=e^{-i\frac{\theta}{2}\hat{Y}}`. + + Args: + cir (UAnsatz): 量子线路。 + theta (paddle.Tensor[paddle.float64]): 操作中 Ry 门的角度。 + q1_index (int): 第一个 qubit 的编号。 + q2_index (int): 第二个 qubit 的编号。 + + Returns: + UAnsatz + """ + + cir.cnot([q2_index, q1_index]) + cir.cry(-2 * theta, [q1_index, q2_index]) + cir.cnot([q2_index, q1_index]) + return cir diff --git a/paddle_quantum/qchem/layers.py b/paddle_quantum/qchem/layers.py new file mode 100755 index 0000000..406b9d0 --- /dev/null +++ b/paddle_quantum/qchem/layers.py @@ -0,0 +1,183 @@ +# !/usr/bin/env python3 +# Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the 'License'); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an 'AS IS' BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +""" +量子电路层，该模块依赖于 paddlepaddle，paddle_quantum 和 math 包。 +同时依赖于 qmodel 和 functional 模块。 +""" + +import math +import paddle +from paddle.nn import initializer + +from paddle_quantum.circuit import UAnsatz + +from .qmodel import QModel +from . import functional + + +# Rotation layer +class RotationLayer(QModel): + r"""单比特旋转门层。 + + Args: + num_qubits (int): 量子线路的量子比特数。 + gate_type (str): 量子门的类型，"X", "Y" 和 "Z" 中的一个。 + trainable (bool): 层中的角度参数是否可训练。 + """ + def __init__(self, num_qubits: int, gate_type: str, trainable: bool = True): + super().__init__(num_qubits) + + self._angle_attr = paddle.ParamAttr( + initializer=initializer.Uniform(0.0, 2*math.pi), + trainable=trainable + ) + + self.angles = self.create_parameter( + shape=[num_qubits], + attr=self._angle_attr, + dtype="float64" + ) + + self._gate_type = gate_type + + def forward( + self, + state: "paddle.Tensor[paddle.complex128]" + ) -> "paddle.Tensor[paddle.complex128]": + r"""获取运行后的量子态 + + Args: + state (paddle.Tensor[paddle.complex128, shape=[n]]): 送入电路的量子态 + + Returns: + paddle.Tensor[paddle.complex128, shape=[n]]: 运行电路后的量子态 + """ + cir0 = UAnsatz(self._n_qubit) + self._circuit = functional.rot_layer(cir0, self.angles, self._gate_type) + return self.circuit.run_state_vector(state) + + def extra_repr(self): + r"""额外表示 + """ + return "gate={:s}, dtype={:s}".format( + self._gate_type, + self.angles.dtype.name) + + +# Euler rotation layer +class EulerRotationLayer(QModel): + r"""Euler 旋转门层。 + + Args: + num_qubits (int): 量子线路中的量子比特数量。 + trainable (bool): 层中的参数是否是可训练的。 + """ + + def __init__(self, num_qubits: int, trainable: bool = True) -> None: + super().__init__(num_qubits) + self._angle_attr = paddle.ParamAttr( + initializer=initializer.Uniform(0.0, 2*math.pi), + trainable=trainable + ) + self.euler_angles = self.create_parameter( + shape=[3*num_qubits], + attr=self._angle_attr, + dtype="float64" + ) + + def forward( + self, + state: "paddle.Tensor[paddle.complex128]" + ) -> "paddle.Tensor[paddle.complex128]": + r"""获取运行后的量子态 + + Args: + state (paddle.Tensor[paddle.complex128, shape=[n]]): 送入电路的量子态 + + Returns: + paddle.Tensor[paddle.complex128, shape=[n]]: 运行电路后的量子态 + """ + cir0 = UAnsatz(self._n_qubit) + self._circuit = functional.euler_rotation_layer(cir0, self.euler_angles) + return self._circuit.run_state_vector(state) + + def extra_repr(self): + r"""额外表示 + """ + return "dtype={:s}".format(self.euler_angles.dtype.name) + + +# Cross resonance layer +class CrossResonanceLayer(QModel): + r"""在量子线路中按照给定的控制和目标比特添加一层 cross resonance 门。 + + Args: + num_qubits (int): 量子比特数目。 + ctrl_qubit_index (list[int]): 控制比特的序号。 + targ_qubit_index (list[int]): 目标比特的序号。 + trainable (bool): 层中的参数是否可训练。 + """ + def __init__( + self, + num_qubits: int, + ctrl_qubit_index: "list[int]" = None, + targ_qubit_index: "list[int]" = None, + trainable: bool = True + ) -> None: + super().__init__(num_qubits) + + if ctrl_qubit_index is None: + ctrl_qubit_index = list(range(num_qubits)) + if targ_qubit_index is None: + targ_qubit_index = list(range(1, num_qubits)) + [0] + + self._ctrl_qubit_index = ctrl_qubit_index + self._targ_qubit_index = targ_qubit_index + + self._phase_attr = paddle.ParamAttr( + initializer=initializer.Uniform(0.0, 2*math.pi), + trainable=trainable + ) + self.phase = self.create_parameter( + shape=[len(ctrl_qubit_index)], + attr=self._phase_attr, + dtype="float64" + ) + + def forward( + self, + state: "paddle.Tensor[paddle.complex128]" + ) -> "paddle.Tensor[paddle.complex128]": + r"""获取运行后的量子态 + + Args: + state (paddle.Tensor[paddle.complex128, shape=[n]]): 送入电路的量子态 + + Returns: + paddle.Tensor[paddle.complex128, shape=[n]]: 运行电路后的量子态 + """ + cir0 = UAnsatz(self._n_qubit) + self._circuit = functional.cr_layer( + cir0, + self.phase, + self._ctrl_qubit_index, + self._targ_qubit_index) + return self._circuit.run_state_vector(state) + + def extra_repr(self): + r"""额外表示 + """ + return "dtype={:s}".format(self.phase.dtype.name) diff --git a/paddle_quantum/qchem/linalg.py b/paddle_quantum/qchem/linalg.py new file mode 100755 index 0000000..7def15d --- /dev/null +++ b/paddle_quantum/qchem/linalg.py @@ -0,0 +1,154 @@ +# !/usr/bin/env python3 +# Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the 'License'); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an 'AS IS' BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +""" +qchem 开发所需的线性代数操作 +""" + +from typing import OrderedDict, Tuple +from collections import OrderedDict +import math +from copy import deepcopy +import paddle + + +DEFAULT_TOL = 1e-8 + + +def get_givens_rotation_parameters( + a: paddle.Tensor, + b: paddle.Tensor +) -> Tuple[paddle.Tensor]: + r"""计算 Givens 旋转的 (c,s) 参数。 + 详细过程参见：https://www.netlib.org/lapack/lawnspdf/lawn148.pdf + + Note: + :math:`r = \operatorname{sign}(a)\sqrt{a^2+b^2}, c = |a|/|r|, s = \operatorname{sign}(a)*b/|r|` + + Args: + a (paddle.Tensor(dtype=float64)): 计算所用参数 + b (paddle.Tensor(dtype=float64)): 计算所用参数 + + Returns: + tuple: + - c (paddle.Tensor(dtype=float64)) + - s (paddle.Tensor(dtype=float64)) + """ + assert a.dtype is paddle.float64 and b.dtype is paddle.float64,\ + "dtype not match, require dtype of a, b be paddle.float64!" + + if math.isclose(b.item(), 0.0, abs_tol=DEFAULT_TOL): + r = a + c = paddle.to_tensor(1.0, dtype=paddle.float64) + s = paddle.to_tensor(0.0, dtype=paddle.float64) + elif math.isclose(a.item(), 0.0, abs_tol=DEFAULT_TOL): + r = b.abs() + c = paddle.to_tensor(0.0, dtype=paddle.float64) + s = paddle.sign(b) + else: + abs_r = paddle.sqrt(a.abs()**2+b.abs()**2) + r = paddle.sign(a)*abs_r + c = a.abs()/abs_r + s = paddle.sign(a)*b/abs_r + return r, c, s + + +def parameter_to_givens_matrix1(c: paddle.Tensor, s: paddle.Tensor, j: int, n_size: int): + r"""该函数可利用 (c,s) 参数来构造 Givens 旋转矩阵以消去 A[i,j] 上的元素。 + + Args: + c (paddle.Tensor): :math:`|A[i,j-1]|/r`, 其中 :math:`r=\sqrt{A[i,j-1]^2+A[i,j]^2}`; + s (paddle.Tensor): :math:`\operatorname{sign}{(A[i,j]*A[i,j-1])*A[i,j]/r)}`; + j (int): 计算所用参数 + n_size (int): Givens 旋转矩阵的维度 + + Returns: + Givens 旋转矩阵 (paddle.Tensor) + """ + G = paddle.eye(n_size, dtype=paddle.float64) + + G[j - 1, j - 1] = c + G[j, j] = c + G[j - 1, j] = -s + G[j, j - 1] = s + + return G + + +def givens_decomposition(A: paddle.Tensor) -> OrderedDict: + r"""对于一个给定的矩阵 A，该函数会返回一个 Givens 旋转操作的 list，用户可以使用其中的 Givens 旋转操作消除掉 A 的上三角的元素。 + + Note: + :math:`r = \operatorname{sign}(a)\sqrt{a^2+b^2}, c = |a|/|r|` + + :math:`s = \operatorname{sign}(a)*b/|r| , \theta = arc\cos(c), phi = \operatorname{sign}(a*b)` + + :math:`A^{\prime}[:,j-1] = c*A[:,j-1]+s*A[:,j]` + + :math:`A^{\prime}[:,j] = -s*A[:,j-1]+c*A[:,j]` + + Args: + A (paddle.Tensor(dtype=paddle.float64)): 矩阵 + + Returns: + OrderedDict, 包含 Givens 旋转操作以及其对应的参数。 + """ + n = A.shape[0] + assert n == A.shape[1], "The input tensor should be a square matrix." + assert A.dtype is paddle.float64, "dtype of input tensor must be paddle.float64!" + + # The givens rotations are not parallel !!! + A1 = deepcopy(A) + rotations = [] + for i in range(n): + for j in range(n-1, i, -1): + _, c, s = get_givens_rotation_parameters(A1[i, j - 1], A1[i, j]) + theta = paddle.acos(c) + phi = paddle.sign(A1[i, j - 1]*A1[i, j]) + rotations.append((f"{i:>d},{j:>d}", (theta, phi))) + + # update A matrix + A1_jprev = c*A1[:, j - 1] + s*A1[:, j] + A1_j = -s*A1[:, j-1] + c*A1[:, j] + A1[:, j-1] = A1_jprev + A1[:, j] = A1_j + + return OrderedDict(rotations) + + +def parameters_to_givens_matrix2( + theta: paddle.Tensor, + phi: paddle.Tensor, + j: int, + n_size: int +) -> paddle.Tensor: + r"""该函数用来从 :math:`(\theta,\phi)` 参数中构建 Givens 旋转矩阵消去 :math:`A[i,j]`。 + + Args: + theta (paddle.Tensor): arccos(c); + phi (paddle.Tensor): :math:`\operatorname{sign}(A[i,j-1]*A[i,j])`; + j (int): 计算所用参数 + n_size (int): Givens 旋转矩阵的维度。 + + Returns: + paddle.Tensor, Givens 旋转矩阵 + """ + G = paddle.eye(int(n_size), dtype=paddle.float64) + + G[j - 1, j - 1] = paddle.cos(theta) + G[j, j] = paddle.cos(theta) + G[j - 1, j] = -phi*paddle.sin(theta) + G[j, j - 1] = phi*paddle.sin(theta) + + return G diff --git a/paddle_quantum/qchem/molecule.py b/paddle_quantum/qchem/molecule.py new file mode 100755 index 0000000..8272206 --- /dev/null +++ b/paddle_quantum/qchem/molecule.py @@ -0,0 +1,102 @@ +# !/usr/bin/env python3 +# Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the 'License'); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an 'AS IS' BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +""" +从分子结构等信息中提取量子化学需要的输入。 +""" + +from typing import Tuple, List +import numpy as np +from pyscf import gto, scf +from pyscf.lo import lowdin + + +# Transform one and two body integral into L\"owdin basis +def lowdin_transform( + ovlp: np.array, + onebody: np.array, + twobody: np.array +) -> Tuple[np.array]: + r"""该函数会将 pyscf 中得到的高斯积分利用 L\"owdin 正交化方法进行变换。 + + Note: + L\"owdin 正交化: + :math:`S_{ij}=\langle\phi_i^{\text{G}}|\phi_j^{\text{G}}\rangle`, + :math:`X = S^{-1/2}` + + Operators 的变换方式: + :math:`A^{\prime}_{ij}=\sum_{pq}A_{pq}X_{ip}X_{qj}` + :math:`B^{\prime}_{iklj}=\sum_{pqrs}B_{prsq}X_{ip}X_{kr}X_{sl}X_{qj}` + + 分子轨道的变换方式: + :math:`C^{\prime}_{ij}=\sum_{p}C_{pj}X^{-1}_{ip}` + + Args: + ovlp (np.array): 交叠积分，`mol.intor("int1e_ovlp")`。 + onebody (np.array): 单体积分，`mol.intor("int1e_kin")+mol.intor("int1e_nuc")`。 + twobody (np.array): 两体积分，`mol.intor("int2e")`。 + + Returns: + Tuple[np.array]: + - 变换之后的单体积分。 + - 变换之后的两体积分。 + """ + + inv_half_ovlp = lowdin(ovlp) + t_onebody = inv_half_ovlp @ onebody @ inv_half_ovlp + t_twobody = np.einsum( + "pqrs,ip,qj,kr,sl->ijkl", + twobody, inv_half_ovlp, inv_half_ovlp, inv_half_ovlp, inv_half_ovlp + ) + return t_onebody, t_twobody + + +# Molecular information +def get_molecular_information( + geometry: List[Tuple[str, List]], + basis: str = "sto-3g", + charge: int = 0, + debug: bool = False +) -> Tuple: + r"""该函数会返回量子化学（目前是 "hartree fock" 方法）计算所需要的分子信息，包括有计算需要的量子比特的数量，分子中的电子数，分子积分和 pyscf 平均场结果 (optional)。 + + Args: + geometry (List[Tuple[str,List]]): 分子中各原子笛卡尔坐标； + basis (str): 基函数名称，例如："sto-3g"； + charge (int): 分子的电荷； + debug (bool): 是否使用 debug 模式。debug 模式会返回 pyscf 的平均场计算结果。 + + Returns: + Tuple: + - 量子比特数目； + - 分子中的电子数； + - 原子核之间的排斥能、单体积分、双体积分； + - pyscf 的平均场计算结果 (可选，只有 debug=True 才会返回)。 + """ + mol = gto.M(atom=geometry, basis=basis, charge=charge, unit="angstrom") + mol.build() + if debug: + mf_mol = scf.RHF(mol).run() + + int_ovlp = mol.intor("int1e_ovlp") + nuc_energy = mol.energy_nuc() + onebody = mol.intor("int1e_kin") + mol.intor("int1e_nuc") + twobody = mol.intor("int2e") + + orth_onebody, orth_twobody = lowdin_transform(int_ovlp, onebody, twobody) + + if debug: + return 2*mol.nao, mol.nelectron, (nuc_energy, orth_onebody, 0.5*orth_twobody), mf_mol + else: + return 2*mol.nao, mol.nelectron, (nuc_energy, orth_onebody, 0.5*orth_twobody) diff --git a/paddle_quantum/qchem.py b/paddle_quantum/qchem/qchem.py old mode 100644 new mode 100755 similarity index 89% rename from paddle_quantum/qchem.py rename to paddle_quantum/qchem/qchem.py index 2e5a54f..ebabfbf --- a/paddle_quantum/qchem.py +++ b/paddle_quantum/qchem/qchem.py @@ -1,3 +1,4 @@ +# !/usr/bin/env python3 # Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. # # Licensed under the Apache License, Version 2.0 (the "License"); @@ -13,7 +14,7 @@ # limitations under the License. """ -Quantum chemistry module +量子化学模块 """ import os @@ -73,14 +74,14 @@ def _hamiltonian_transformation(spin_h, tol=1e-8): def _geo_str(geometry): - r"""创建分子几何信息的字符串。 + r"""创建分子几何信息的字符串 Args: geometry (list): 包含了分子的几何信息，以 H2 分子为例 - [['H', [-1.68666, 1.79811, 0.0]], ['H', [-1.12017, 1.37343, 0.0]]]。 + [['H', [-1.68666, 1.79811, 0.0]], ['H', [-1.12017, 1.37343, 0.0]]] Returns: - str: 分子几何信息的字符串。 + str: 分子几何信息的字符串 """ geo_str = '' for item in geometry: @@ -98,26 +99,26 @@ def _geo_str(geometry): def _run_psi4( - molecule, - charge, - multiplicity, - method, - basis, - if_print, - if_save + molecule, + charge, + multiplicity, + method, + basis, + if_print, + if_save ): r"""计算分子的必要信息，包括单体积分 (one-body integrations) 和双体积分 (two-body integrations)， 以及用 scf 和 fci 的方法计算基态的能量。 Args: - molecule (MolecularData object): 包含分子所有信息的类 (class)。 - charge (int): 分子的电荷。 - multiplicity (int): 分子的多重度。 - method (str): 用于计算基态能量的方法，包括 'scf'和 'fci'。 - basis (str): 常用的基组是 'sto-3g', '6-31g'等。更多的基组选择可以参考网站。 - https://psicode.org/psi4manual/master/basissets_byelement.html#apdx-basiselement。 - if_print (Boolean): 是否需要打印出选定方法 (method) 计算出的分子基态能量。 - if_save (Boolean): 是否需要将分子信息存储成 .hdf5 文件。 + molecule (MolecularData object): 包含分子所有信息的类 (class) + charge (int): 分子的电荷 + multiplicity (int): 分子的多重度 + method (str): 用于计算基态能量的方法，包括 'scf'和 'fci' + basis (str): 常用的基组是 'sto-3g', '6-31g'等。更多的基组选择可以参考网站 + https://psicode.org/psi4manual/master/basissets_byelement.html#apdx-basiselement + if_print (Boolean): 是否需要打印出选定方法 (method) 计算出的分子基态能量 + if_save (Boolean): 是否需要将分子信息存储成 .hdf5 文件 """ psi4.set_memory('500 MB') psi4.set_options({'soscf': 'false', @@ -182,7 +183,7 @@ def _run_psi4( def geometry(structure=None, file=None): - r"""读取分子的几何信息。 + r"""读取分子的几何信息 Args: structure (string, optional): 分子几何信息的字符串形式，以 H2 分子为例 @@ -193,9 +194,9 @@ def geometry(structure=None, file=None): str: 分子的几何信息 Raises: - AssertionError: 两个输入参数不可以同时为 ``None`` 。 + AssertionError: 两个输入参数不可以同时为 ``None`` """ - if ((structure is None) and (file is None)): + if structure is None and file is None: raise AssertionError('Input must be structure or .xyz file') elif file is None: shape = np.array(structure).shape @@ -221,15 +222,15 @@ def geometry(structure=None, file=None): def get_molecular_data( - geometry, - charge=0, - multiplicity=1, - basis='sto-3g', - method='scf', - if_save=True, - if_print=True, - name="", - file_path="." + geometry, + charge=0, + multiplicity=1, + basis='sto-3g', + method='scf', + if_save=True, + if_print=True, + name="", + file_path="." ): r"""计算分子的必要信息，包括单体积分（one-body integrations）和双体积分（two-body integrations）， 以及用选定的方法计算基态的能量。 @@ -270,28 +271,34 @@ def get_molecular_data( else: filename = name + '.hdf5' - molecule = MolecularData(geometry, - basis=basis, - multiplicity=multiplicity, - charge=charge, - filename=filename) + molecule = MolecularData( + geometry, + basis=basis, + multiplicity=multiplicity, + charge=charge, + filename=filename + ) - _run_psi4(molecule, - charge, - multiplicity, - method, - basis, - if_print, - if_save) + _run_psi4( + molecule, + charge, + multiplicity, + method, + basis, + if_print, + if_save + ) return molecule -def active_space(electrons, - orbitals, - multiplicity=1, - active_electrons=None, - active_orbitals=None): +def active_space( + electrons, + orbitals, + multiplicity=1, + active_electrons=None, + active_orbitals=None +): r"""对于给定的活跃电子和活跃轨道计算相应的活跃空间（active space）。 Args: @@ -340,11 +347,13 @@ def active_space(electrons, return core_orbitals, active_orbitals -def fermionic_hamiltonian(molecule, - filename=None, - multiplicity=1, - active_electrons=None, - active_orbitals=None): +def fermionic_hamiltonian( + molecule, + filename=None, + multiplicity=1, + active_electrons=None, + active_orbitals=None +): r"""计算给定分子的费米哈密顿量。 Args: @@ -375,12 +384,14 @@ def fermionic_hamiltonian(molecule, return fermionic_hamiltonian -def spin_hamiltonian(molecule, - filename=None, - multiplicity=1, - mapping_method='jordan_wigner', - active_electrons=None, - active_orbitals=None): +def spin_hamiltonian( + molecule, + filename=None, + multiplicity=1, + mapping_method='jordan_wigner', + active_electrons=None, + active_orbitals=None +): r"""生成 Paddle Quantum 格式的哈密顿量 Args: diff --git a/paddle_quantum/qchem/qmodel.py b/paddle_quantum/qchem/qmodel.py new file mode 100755 index 0000000..fd6321c --- /dev/null +++ b/paddle_quantum/qchem/qmodel.py @@ -0,0 +1,51 @@ +# !/usr/bin/env python3 +# Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the 'License'); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an 'AS IS' BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +""" +用于构建量子电路层的基类 +该模块依赖 paddlepaddle。 +""" + +from paddle import nn + + +class QModel(nn.Layer): + r"""量子化学用量子线路的基类，任何自定义量子线路都需要继承自这个类。 + """ + def __init__(self, num_qubit: int): + r"""构造函数 + + Args: + num_qubit (int): 量子比特数目 + """ + super().__init__(name_scope="QModel") + self._n_qubit = num_qubit + self._circuit = None + + @property + def n_qubit(self): + r"""量子比特数目 + """ + return self._n_qubit + + @property + def circuit(self): + r"""量子电路 + """ + if self._circuit is None: + print("Circuit is not built, please run `forward` to build the circuit first.") + return None + else: + return self._circuit diff --git a/paddle_quantum/qchem/run.py b/paddle_quantum/qchem/run.py new file mode 100755 index 0000000..cb2c9f5 --- /dev/null +++ b/paddle_quantum/qchem/run.py @@ -0,0 +1,180 @@ +# !/usr/bin/env python3 +# Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the 'License'); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an 'AS IS' BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. +""" +利用不同的 ansatz 运行量子化学计算。 +""" + +from typing import List, Tuple, Callable +import numpy as np +import paddle +from paddle.optimizer import Optimizer, Adam +from . import qchem as pq_chem +import paddle_quantum.state as pq_state +from paddle_quantum.intrinsic import vec_expecval + +from .ansatz.rhf import RestrictHartreeFockModel +from .qmodel import QModel +from .ansatz import HardwareEfficientModel + + +def _minimize( + model: QModel, + loss_fn: Callable[[QModel], Tuple[float, QModel]], + optimizer: Optimizer, + max_iters: int, + a_tol: float +) -> Tuple[float, QModel]: + loss_prev = -np.inf + for i in range(max_iters): + with paddle.no_grad(): + loss = loss_fn(model) + print(f"Iteration {i+1:>d}, {model.__class__.__name__} energy {loss.item():>.5f}.") + + if np.abs(loss.item() - loss_prev) < a_tol: + print(f"Converge after {(i+1):>d} number of iterations.") + break + else: + loss_prev = loss.item() + + optimizer.clear_grad() + loss = loss_fn(model) + loss.backward() + optimizer.step() + + with paddle.no_grad(): + loss = loss_fn(model) + + return loss.item(), model + + +def run_chem( + geometry: List[Tuple[str, List[float]]], + ansatz: str, + basis_set: str = "sto-3g", + charge: int = 0, + max_iters: int = 100, + a_tol: float = 1e-6, + optimizer_option: dict = {}, + ansatz_option: dict = {} +) -> Tuple[float, QModel]: + r"""根据输入的分子信息进行量子化学计算。 + + Args: + geometry (List[Tuple[str, List[float]]]): 分子的几何结构，例如：[("H", [0.0, 0.0, 0.0]), ("H", [0.0, 0.0, 0.74])]。定义结构时使用的长度单位是 Angstrom。 + ansatz (str): 表示多体波函数的量子线路，目前我们支持 "hardware efficient" 和 "hartree fock"。 + basis_set (str): 用来展开原子轨道的量子化学的基函数，例如："sto-3g"。注意，复杂的基函数会极大占用计算资源。 + charge (int): 分子的电荷量。 + max_iters (int): 优化过程的最大迭代次数。 + a_tol (float): 优化收敛的判断依据，当 :math:`|e_{i+1} - e_i| < a_{tol}` 时，优化结束。 + optimizer_options (dict): 优化器的可选参数，例如：学习率 (learning_rate)、权重递减 (weight_decay)。 + ansatz_option (dict): 定义 ansatz 量子线路的可选参数。目前，对于 "hardware efficient" 方法，可选参数为 "cir_depth"（线路深度）。"hartree fock" 方法没有可选参数。 + + Returns: + tuple: + - 基态能量 + - 优化后的 ansatz 量子线路 + """ + + if ansatz == "hardware efficient": + return run_hardware( + geometry, basis_set, charge, + max_iters, a_tol, optimizer_option, **ansatz_option + ) + + if ansatz == "hartree fock": + return run_rhf( + geometry, basis_set, charge, + max_iters, a_tol, optimizer_option, **ansatz_option + ) + + else: + raise NotImplementedError( + """ + Currently, we only support "hardware efficient" or "hartree fock" for `ansatz` parameter, we will add more in the future. You can open an issue here + https://github.com/PaddlePaddle/Quantum/issues to report the ansatz you're interested in. + """) + + +def run_hardware( + geometry: List[Tuple[str, List[float]]], + basis_set: str, + charge: int, + max_iters: int, + a_tol: float, + optimizer_option: dict = {}, + cir_depth: int = 3 +) -> Tuple[float, QModel]: + r"""hardware efficient 方法的 run 函数。 + + """ + mol_data = pq_chem.get_molecular_data(geometry, basis=basis_set, charge=charge, if_print=False) + mol_qubitH = pq_chem.spin_hamiltonian(mol_data) + + n_qubits = mol_qubitH.n_qubits + ansatz = HardwareEfficientModel(n_qubits, cir_depth) + optimizer = Adam(parameters=ansatz.parameters(), **optimizer_option) + + s0 = paddle.to_tensor(pq_state.vec(0, n_qubits)) + s0 = paddle.reshape(s0, [2**n_qubits]) + + def loss_fn(model: QModel) -> paddle.Tensor: + s = model(s0) + return paddle.real(vec_expecval(mol_qubitH.pauli_str, s)) + + mol_gs_en, updated_ansatz = _minimize(ansatz, loss_fn, optimizer, max_iters, a_tol) + return mol_gs_en, updated_ansatz + + +def run_rhf( + geometry: List[Tuple[str, List[float]]], + basis_set: str, + charge: int, + max_iters: int, + a_tol: float, + optimizer_option: dict = {} +) -> Tuple[float, QModel]: + r"""hartree fock 方法的 run 函数。 + """ + try: + import pyscf + except ModuleNotFoundError as e: + raise ModuleNotFoundError( + """ + Hartree Fock method needs `pyscf`, + please run `pip install -U pyscf` to first install pyscf. + """) + + from .molecule import get_molecular_information + + n_qubits, n_electrons, integrals = get_molecular_information(geometry, basis_set, charge) + nuc_energy, onebody, twobody = [paddle.to_tensor(t) for t in integrals] + ansatz = RestrictHartreeFockModel(n_qubits, n_electrons, onebody) + optimizer = Adam(parameters=ansatz.parameters(), **optimizer_option) + + # run model to build the circuit + bstr = "1"*n_electrons+"0"*(n_qubits-n_electrons) + _s0 = paddle.to_tensor(pq_state.vec(int(bstr, 2), n_qubits)) + _s0 = paddle.reshape(_s0, [2**n_qubits]) + ansatz(_s0) + + def loss_fn(model: QModel) -> paddle.Tensor: + U_hf = model.single_particle_U() + rdm1 = U_hf @ U_hf.conj().t() + return nuc_energy + 2*paddle.einsum("pq,qp->", onebody, rdm1)\ + + 4*paddle.einsum("pqrs,qp,sr->", twobody, rdm1, rdm1)\ + - 2*paddle.einsum("pqrs,sp,qr->", twobody, rdm1, rdm1) + + mol_gs_en, updated_ansatz = _minimize(ansatz, loss_fn, optimizer, max_iters, a_tol) + return mol_gs_en, updated_ansatz diff --git a/paddle_quantum/shadow.py b/paddle_quantum/shadow.py index 478929b..4aef814 100644 --- a/paddle_quantum/shadow.py +++ b/paddle_quantum/shadow.py @@ -19,6 +19,7 @@ shadow sample module import numpy as np import paddle import re +import math from paddle_quantum import circuit from paddle_quantum.utils import Hamiltonian @@ -27,6 +28,120 @@ __all__ = [ ] +def random_pauli_sample(num_qubits, beta=None): + r"""根据概率分布 beta, 随机选取 pauli 测量基 + + Args: + num_qubits (int): 量子比特数目 + beta (list, optional): 量子位上不同 pauli 测量基的概率分布 + + Returns: + str: 返回随机选择的 pauli 测量基 + + Note: + 这是内部函数，你并不需要直接调用到该函数。 + """ + # assume beta obeys a uniform distribution if it is not given + if beta is None: + beta = list() + for _ in range(0, num_qubits): + beta.append([1 / 3] * 3) + pauli_sample = str() + for qubit_idx in range(num_qubits): + sample = np.random.choice(['x', 'y', 'z'], 1, p=beta[qubit_idx]) + pauli_sample += sample[0] + return pauli_sample + + +def measure_by_pauli_str(pauli_str, phi, num_qubits, mode, method): + r"""搭建 pauli 测量电路，返回测量结果 + + Args: + pauli_str (str): 输入的是随机选取的num_qubits pauli 测量基 + phi (numpy.ndarray): 输入量子态，支持态矢量和密度矩阵形式 + num_qubits (int): 量子比特数量 + mode (str): 输入量子态的表示方式，``"state_vector"`` 表示态矢量形式， ``"density_matrix"`` 表示密度矩阵形式 + method (str): 进行测量的方法，有 "CS"、"LBCS"、"APS" + + Returns: + str: 返回测量结果 + + Note: + 这是内部函数，你并不需要直接调用到该函数。 + """ + if method == "clifford": + # Add the clifford function + pass + else: + # Other method are transformed as follows + # Convert to tensor form + input_state = paddle.to_tensor(phi) + cir = circuit.UAnsatz(num_qubits) + for qubit in range(num_qubits): + if pauli_str[qubit] == 'x': + cir.h(qubit) + elif pauli_str[qubit] == 'y': + cir.h(qubit) + cir.s(qubit) + cir.h(qubit) + if mode == 'state_vector': + cir.run_state_vector(input_state) + else: + cir.run_density_matrix(input_state) + result = cir.measure(shots=1) + bit_string, = result + return bit_string + + +def paulistr_to_matrix(paulistr): + r"""识别随机选取的 pauli 并转换成作用于 Z 测量的酉变换的矩阵形式 + + Args: + paulistr (str): 输入的是某一量子位上随机选取的 Pauli 测量基 + + Returns: + numpy.ndarray: 返回酉变换的矩阵形式 + + Note: + 这是内部函数，你并不需要直接调用到该函数。 + """ + + # Define the matrix form of H, S gates + a = math.pow(2, 0.5) + H_matrix = np.array([[1 / a, 1 / a], [1 / a, -1 / a]]) + S_matrix = np.array([[1, 0], [0, 1j]]) + I_matrix = np.array([[1, 0], [0, 1]]) + + if paulistr == 'x': + paulistr_matrix = H_matrix + elif paulistr == 'y': + paulistr_matrix = np.dot(np.dot(H_matrix, S_matrix), H_matrix) + elif paulistr == 'z': + paulistr_matrix = I_matrix + return paulistr_matrix + + +def measure_result_to_matrix(measure_str): + r"""将单个量子位上测量的结果转换为密度矩阵形式 + + Args: + measure_str (str): 输入的是某一量子位上的测量结果 + + Returns: + numpy.ndarray: 返回测量结果的密度矩阵形式 + Note: + 这是内部函数，你并不需要直接调用到该函数。 + """ + + ket_0 = np.array([[1, 0]]).T + ket_1 = np.array([[0, 1]]).T + if measure_str == '0': + b_matrix = np.kron(ket_0, ket_0.conj().T) + elif measure_str == '1': + b_matrix = np.kron(ket_1, ket_1.conj().T) + return b_matrix + + def shadow_sample(state, num_qubits, sample_shots, mode, hamiltonian=None, method='CS'): r"""对给定的量子态进行随机的泡利测量并返回测量结果。 @@ -108,68 +223,6 @@ def shadow_sample(state, num_qubits, sample_shots, mode, hamiltonian=None, metho pauli2index = {'x': 0, 'y': 1, 'z': 2} - def random_pauli_sample(num_qubits, beta=None): - r"""根据概率分布 beta, 随机选取 pauli 测量基 - - Args: - num_qubits (int): 量子比特数目 - beta (list, optional): 量子位上不同 pauli 测量基的概率分布 - - Returns: - str: 返回随机选择的 pauli 测量基 - - Note: - 这是内部函数，你并不需要直接调用到该函数。 - """ - # assume beta obeys a uniform distribution if it is not given - if beta is None: - beta = list() - for _ in range(0, num_qubits): - beta.append([1 / 3] * 3) - pauli_sample = str() - for qubit_idx in range(num_qubits): - sample = np.random.choice(['x', 'y', 'z'], 1, p=beta[qubit_idx]) - pauli_sample += sample[0] - return pauli_sample - - def measure_by_pauli_str(pauli_str, phi, num_qubits, method): - r"""搭建 pauli 测量电路，返回测量结果 - - Args: - pauli_str (str): 输入的是随机选取的num_qubits pauli 测量基 - phi (numpy.ndarray): 输入量子态，支持态矢量和密度矩阵形式 - num_qubits (int): 量子比特数量 - method (str): 进行测量的方法，有 "CS"、"LBCS"、"APS" - - Returns: - str: 返回测量结果 - - Note: - 这是内部函数，你并不需要直接调用到该函数。 - """ - if method == "clifford": - # Add the clifford function - pass - else: - # Other method are transformed as follows - # Convert to tensor form - input_state = paddle.to_tensor(phi) - cir = circuit.UAnsatz(num_qubits) - for qubit in range(num_qubits): - if pauli_str[qubit] == 'x': - cir.h(qubit) - elif pauli_str[qubit] == 'y': - cir.h(qubit) - cir.s(qubit) - cir.h(qubit) - if mode == 'state_vector': - cir.run_state_vector(input_state) - else: - cir.run_density_matrix(input_state) - result = cir.measure(shots=1) - bit_string, = result - return bit_string - # Define the function used to update the beta of the LBCS algorithm def calculate_diagonal_product(pauli_str, beta): r"""迭代 LBCS beta 公式中的一部分 @@ -424,7 +477,7 @@ def shadow_sample(state, num_qubits, sample_shots, mode, hamiltonian=None, metho if method == "CS": for _ in range(sample_shots): random_pauli_str = random_pauli_sample(num_qubits, beta=None) - measurement_result = measure_by_pauli_str(random_pauli_str, state, num_qubits, method) + measurement_result = measure_by_pauli_str(random_pauli_str, state, num_qubits, mode, method) sample_result.append((random_pauli_str, measurement_result)) return sample_result elif method == "LBCS": @@ -441,12 +494,91 @@ def shadow_sample(state, num_qubits, sample_shots, mode, hamiltonian=None, metho sample_result = list() for _ in range(sample_shots): random_pauli_str = random_pauli_sample(num_qubits, beta) - measurement_result = measure_by_pauli_str(random_pauli_str, state, num_qubits, method) + measurement_result = measure_by_pauli_str(random_pauli_str, state, num_qubits, mode, method) sample_result.append((random_pauli_str, measurement_result)) return sample_result, beta elif method == "APS": for _ in range(sample_shots): random_pauli_str = random_pauli_sample_in_aps(hamiltonian) - measurement_result = measure_by_pauli_str(random_pauli_str, state, num_qubits, method) + measurement_result = measure_by_pauli_str(random_pauli_str, state, num_qubits, mode, method) sample_result.append((random_pauli_str, measurement_result)) return sample_result + + +def classical_shadow(state, num_qubits, sample_shots, mode, method=None): + r"""获得量子态 state 的经典影子 + + Args: + state (numpy.ndarray): 输入量子态，支持态矢量和密度矩阵形式 + num_qubits (int): 量子比特数量 + sample_shots (int): 随机采样的次数 + mode (str): 输入量子态的表示方式，``"state_vector"`` 表示态矢量形式， ``"density_matrix"`` 表示密度矩阵形式 + method (str, optional): 可选方法 restructure (R)，获得量子态的密度矩阵形式；或默认为None (即 not restructure, NR)，获得量子态的密度矩阵形式 + + Returns: + tuple: 包含如下两个元素 + - state_hat (list): 返回量子态 state 的经典影子 (method = 'NR') + - reconstructed_state (numpy.ndarray): 返回估计的量子态 state 的密度矩阵 (method = 'R') + + 代码示例: + + .. code-block:: python + + from paddle_quantum.shadow import classical_shadow + from paddle_quantum.state import vec_random + + n_qubit = 2 + sample_shots = 2 + state = vec_random(n_qubit) + state_shadow = classical_shadow(state, n_qubit, sample_shots, mode='state_vector', method='NR') + state_density_matrix = classical_shadow(state, n_qubit, sample_shots, mode='state_vector', method='R') + + print('classical shadow of quantum state = ', state_shadow) + print('density matrix of quantum state = ', state_density_matrix) + + :: + classical shadow of quantum state = [array([[ 0.25+0.j , 0. +0.75j, -0.75+0.j , -0. -2.25j], + [ 0. -0.75j, 0.25+0.j , 0. +2.25j, -0.75+0.j ], + [-0.75+0.j , -0. -2.25j, 0.25+0.j , 0. +0.75j], + [ 0. +2.25j, -0.75+0.j , 0. -0.75j, 0.25+0.j ]]), + array([[0.25+0.j , 0. -0.75j, 0.75+0.j , 0. -2.25j], + [0. +0.75j, 0.25+0.j , 0. +2.25j, 0.75+0.j ], + [0.75+0.j , 0. -2.25j, 0.25+0.j , 0. -0.75j], + [0. +2.25j, 0.75+0.j , 0. +0.75j, 0.25+0.j ]])] + density matrix of quantum state = [[ 0.625+0.j 0.375+0.j -1.5 +0.375j 0. +1.125j] + [ 0.375+0.j -0.125+0.j 0. +1.125j 0.75 +0.375j] + [-1.5 -0.375j 0. -1.125j 0.625+0.j 0.375+0.j ] + [ 0. -1.125j 0.75 -0.375j 0.375+0.j -0.125+0.j ]] + + """ + # Used to store the classic shadow for each sample + state_hat = [] + I_matrix = np.array([[1, 0], [0, 1]]) + + for _ in range(sample_shots): + # Randomly selected Pauli + random_pauli_str = random_pauli_sample(num_qubits, beta=None) + # Measure according to the selected Pauli + measurement_result = measure_by_pauli_str(random_pauli_str, state, num_qubits, mode, None) + # Generate a 1×1 matrix, convenient tensor product + hat_state = np.eye(1) + for i in range(num_qubits): + single_pauli_matrix = paulistr_to_matrix(random_pauli_str[i]) + single_b_matrix = measure_result_to_matrix(measurement_result[i]) + # The classical shadow on a single qubit is obtained according to the derived M inverse + single_qubit_state_left = np.dot(np.dot(single_pauli_matrix.conj().T, single_b_matrix), single_pauli_matrix) + single_qubit_state = 3 * single_qubit_state_left - I_matrix + # The classical shadow of quantum state is obtained + hat_state = np.kron(hat_state, single_qubit_state) + + # Store classical shadows + state_hat.append(hat_state) + + if method == 'R': + # Returns the density matrix of the quantum state + reconstructed_state = sum(state_hat)/len(state_hat) + return reconstructed_state + + else: + # Returns the classical shadow of the quantum state + return state_hat diff --git a/paddle_quantum/simulator.py b/paddle_quantum/simulator.py index 09b8d88..ee49078 100644 --- a/paddle_quantum/simulator.py +++ b/paddle_quantum/simulator.py @@ -69,38 +69,9 @@ def init_state_gen(n, i=0): """ assert 0 <= i < 2 ** n, 'Invalid index' - if n == 1: - state1 = paddle.ones([1], 'float64') - state0 = paddle.zeros([2 ** n - 1], 'float64') - - if i == 0: - state = paddle.concat([state1, state0]) - else: - state = paddle.concat([state0, state1]) - else: - if i == 0: - state1 = paddle.ones([1], 'float64') - state0 = paddle.zeros([2 ** n - 1], 'float64') - state = paddle.concat([state1, state0]) - elif i == 2 ** n - 1: - state1 = paddle.ones([1], 'float64') - state0 = paddle.zeros([2 ** n - 1], 'float64') - state = paddle.concat([state0, state1]) - else: - state1 = paddle.ones([1], 'float64') - state0 = paddle.zeros([i], 'float64') - state00 = paddle.zeros([2 ** n - i - 1], 'float64') - state = paddle.concat([state0, state1, state00]) - - del state1, state0 - try: - del state00 - except NameError: - pass - gc.collect() # free the intermediate big data immediately - - state = paddle.cast(state, 'complex128') - gc.collect() # free the intermediate big data immediately + state = np.zeros([2 ** n], dtype=np.complex128) + state[i] = 1 + state = paddle.to_tensor(state) return state diff --git a/paddle_quantum/trotter.py b/paddle_quantum/trotter.py index 39bb51d..6c70f48 100644 --- a/paddle_quantum/trotter.py +++ b/paddle_quantum/trotter.py @@ -28,15 +28,15 @@ PI = paddle.to_tensor(np.pi, dtype='float64') def construct_trotter_circuit( - circuit: UAnsatz, - hamiltonian: Hamiltonian, - tau: float, - steps: int, - method: str = 'suzuki', - order: int = 1, - grouping: str = None, - coefficient: np.ndarray or paddle.Tensor = None, - permutation: np.ndarray = None + circuit: UAnsatz, + hamiltonian: Hamiltonian, + tau: float, + steps: int, + method: str = 'suzuki', + order: int = 1, + grouping: str = None, + coefficient: np.ndarray or paddle.Tensor = None, + permutation: np.ndarray = None ): r"""向 circuit 的后面添加 trotter 时间演化电路，即给定一个系统的哈密顿量 H，该电路可以模拟系统的时间演化 :math:`U_{cir}~ e^{-iHt}` 。 @@ -249,7 +249,7 @@ def _add_custom_block(circuit, tau, grouped_hamiltonian, custom_coefficients, pe add_n_pauli_gate(circuit, 2 * tau * coeff, pauli_word, site) -def __add_first_order_trotter_block(circuit, tau, grouped_hamiltonian, reverse=False): +def __add_first_order_trotter_block(circuit, tau, grouped_hamiltonian, reverse=False, optimization=False): r""" 添加一阶 trotter-suzuki 分解的时间演化块 Notes: @@ -258,54 +258,57 @@ def __add_first_order_trotter_block(circuit, tau, grouped_hamiltonian, reverse=F if not reverse: for hamiltonian in grouped_hamiltonian: assert isinstance(hamiltonian, Hamiltonian) - - #将原哈密顿量中相同site的XX，YY，ZZ组合到一起 - grouped_hamiltonian = [] - coeffs, pauli_words, sites = hamiltonian.decompose_with_sites() - grouped_terms_indices = [] - left_over_terms_indices = [] - d = defaultdict(list) - #合并相同site的XX,YY,ZZ - for term_index in range(len(coeffs)): - site = sites[term_index] - pauli_word = pauli_words[term_index] - for pauli in ['XX', 'YY', 'ZZ']: - assert isinstance(pauli_word, str), "Each pauli word should be a string type" - if (pauli_word==pauli or pauli_word==pauli.lower()): - key = tuple(sorted(site)) - d[key].append((pauli,term_index)) - if len(d[key])==3: - terms_indices_to_be_grouped = [x[1] for x in d[key]] - grouped_terms_indices.extend(terms_indices_to_be_grouped) - grouped_hamiltonian.append(hamiltonian[terms_indices_to_be_grouped]) - #其他的剩余项 - for term_index in range(len(coeffs)): - if term_index not in grouped_terms_indices: - left_over_terms_indices.append(term_index) - if len(left_over_terms_indices): - for term_index in left_over_terms_indices: - grouped_hamiltonian.append(hamiltonian[term_index]) - #得到新的哈密顿量 - res = grouped_hamiltonian[0] - for i in range(1,len(grouped_hamiltonian)): - res+=grouped_hamiltonian[i] - hamiltonian = res - + if optimization: + # Combine XX, YY, ZZ of the same site in the original Hamiltonian quantity + grouped_hamiltonian = [] + coeffs, pauli_words, sites = hamiltonian.decompose_with_sites() + grouped_terms_indices = [] + left_over_terms_indices = [] + d = defaultdict(list) + # Merge XX,YY,ZZ of the same site + for term_index in range(len(coeffs)): + site = sites[term_index] + pauli_word = pauli_words[term_index] + for pauli in ['XX', 'YY', 'ZZ']: + assert isinstance(pauli_word, str), "Each pauli word should be a string type" + if (pauli_word == pauli or pauli_word == pauli.lower()): + key = tuple(sorted(site)) + d[key].append((pauli, term_index)) + if len(d[key]) == 3: + terms_indices_to_be_grouped = [x[1] for x in d[key]] + grouped_terms_indices.extend(terms_indices_to_be_grouped) + grouped_hamiltonian.append(hamiltonian[terms_indices_to_be_grouped]) + # Other remaining sites + for term_index in range(len(coeffs)): + if term_index not in grouped_terms_indices: + left_over_terms_indices.append(term_index) + if len(left_over_terms_indices): + for term_index in left_over_terms_indices: + grouped_hamiltonian.append(hamiltonian[term_index]) + # Get the new Hamiltonian + res = grouped_hamiltonian[0] + for i in range(1, len(grouped_hamiltonian)): + res += grouped_hamiltonian[i] + hamiltonian = res # decompose the Hamiltonian into 3 lists coeffs, pauli_words, sites = hamiltonian.decompose_with_sites() # apply rotational gate of each term + # for term_index in range(len(coeffs)): + # # get the sorted pauli_word and site (an array of qubit indices) according to their qubit indices + # pauli_word, site = __sort_pauli_word(pauli_words[term_index], sites[term_index]) + # add_n_pauli_gate(circuit, 2 * tau * coeffs[term_index], pauli_word, site) term_index = 0 - while term_index 1e-13) + c = c[:k] + u = u.T[:k].reshape([k, -1, 1]) + v = v[:k].reshape([k, -1, 1]) + return c, u, v - Returns: - list : 哈密顿量对应的 Pauli string - """ - return self.__pauli_str - @property - def terms(self): - r"""返回哈密顿量中的每一项构成的列表 +def __density_matrix_convert_to_bloch_vector(density_matrix): + r"""该函数将密度矩阵转化为bloch球面上的坐标 - Returns: - list :哈密顿量中的每一项，i.e. ``[['Z0, Z1'], ['I']]`` - """ - if self.__update_flag: - self.__decompose() - return self.__terms - else: - return self.__terms + Args: + density_matrix (numpy.ndarray): 输入的密度矩阵 - @property - def coefficients(self): - r""" 返回哈密顿量中的每一项对应的系数构成的列表 + Returns: + bloch_vector (numpy.ndarray): 存储bloch向量的 x,y,z 坐标，向量的模长，向量的颜色 + """ - Returns: - list :哈密顿量中每一项的系数，i.e. ``[1.0, 2.0]`` - """ - if self.__update_flag: - self.__decompose() - return self.__coefficients - else: - return self.__coefficients + # Pauli Matrix + pauli_x = np.array([[0, 1], [1, 0]]) + pauli_y = np.array([[0, -1j], [1j, 0]]) + pauli_z = np.array([[1, 0], [0, -1]]) - @property - def pauli_words(self): - r"""返回哈密顿量中每一项对应的 Pauli word 构成的列表 + # Convert a density matrix to a Bloch vector. + ax = np.trace(np.dot(density_matrix, pauli_x)).real + ay = np.trace(np.dot(density_matrix, pauli_y)).real + az = np.trace(np.dot(density_matrix, pauli_z)).real - Returns: - list :每一项对应的 Pauli word，i.e. ``['ZIZ', 'IIX']`` - """ - if self.__update_flag: - self.__decompose() - return self.__pauli_words - else: - return self.__pauli_words + # Calc the length of bloch vector + length = ax ** 2 + ay ** 2 + az ** 2 + length = sqrt(length) + if length > 1.0: + length = 1.0 - @property - def pauli_words_r(self): - r"""返回哈密顿量中每一项对应的简化（不包含 I） Pauli word 组成的列表 + # Calc the color of bloch vector, the value of the color is proportional to the length + color = length - Returns: - list :不包含 "I" 的 Pauli word 构成的列表，i.e. ``['ZXZZ', 'Z', 'X']`` - """ - if self.__update_flag: - self.__decompose() - return self.__pauli_words_r - else: - return self.__pauli_words_r + bloch_vector = [ax, ay, az, length, color] - @property - def sites(self): - r"""返回该哈密顿量中的每一项对应的量子比特编号组成的列表 + # You must use an array, which is followed by slicing and taking a column + bloch_vector = np.array(bloch_vector) - Returns: - list :哈密顿量中每一项所对应的量子比特编号构成的列表，i.e. ``[[1, 2], [0]]`` - """ - if self.__update_flag: - self.__decompose() - return self.__sites - else: - return self.__sites + return bloch_vector - @property - def n_qubits(self): - r"""返回该哈密顿量对应的量子比特数 - Returns: - int :量子比特数 - """ - if self.__update_flag: - self.__decompose() - return self.__nqubits - else: - return self.__nqubits +def __plot_bloch_sphere( + ax, + bloch_vectors=None, + show_arrow=False, + clear_plt=True, + rotating_angle_list=None, + view_angle=None, + view_dist=None, + set_color=None +): + r"""将 Bloch 向量展示在 Bloch 球面上 - def __decompose(self): - r"""将哈密顿量分解为不同的形式 + Args: + ax (Axes3D(fig)): 画布的句柄 + bloch_vectors (numpy.ndarray): 存储bloch向量的 x,y,z 坐标，向量的模长，向量的颜色 + show_arrow (bool): 是否展示向量的箭头，默认为 False + clear_plt (bool): 是否要清空画布，默认为 True，每次画图的时候清空画布再画图 + rotating_angle_list (list): 旋转角度的列表，用于展示旋转轨迹 + view_angle (list): 视图的角度， + 第一个元素为关于xy平面的夹角[0-360],第二个元素为关于xz平面的夹角[0-360], 默认为 (30, 45) + view_dist (int): 视图的距离，默认为 7 + set_color (str): 设置指定的颜色，请查阅cmap表，默认为 "红-黑-根据向量的模长渐变" 颜色方案 + """ + # Assign a value to an empty variable + if view_angle is None: + view_angle = (30, 45) + if view_dist is None: + view_dist = 7 + # Define my_color + if set_color is None: + color = 'rainbow' + black_code = '#000000' + red_code = '#F24A29' + if bloch_vectors is not None: + black_to_red = mplcolors.LinearSegmentedColormap.from_list( + 'my_color', + [(0, black_code), (1, red_code)], + N=len(bloch_vectors[:, 4]) + ) + map_vir = plt.get_cmap(black_to_red) + color = map_vir(bloch_vectors[:, 4]) + else: + color = set_color - Notes: - 这是一个内部函数，你不需要直接使用它 - 这是一个比较基础的函数，它负责将输入的 Pauli string 拆分为不同的形式并存储在内部变量中 - """ - self.__pauli_words = [] - self.__pauli_words_r = [] - self.__sites = [] - self.__terms = [] - self.__coefficients = [] - self.__nqubits = 1 - new_pauli_str = [] - for coefficient, pauli_term in self.__pauli_str: - pauli_word_r = '' - site = [] - single_pauli_terms = re.split(r',\s*', pauli_term.upper()) - self.__coefficients.append(float(coefficient)) - self.__terms.append(single_pauli_terms) - for single_pauli_term in single_pauli_terms: - match_I = re.match(r'I', single_pauli_term, flags=re.I) - if match_I: - assert single_pauli_term[0].upper() == 'I', \ - 'The offset is defined with a sole letter "I", i.e. (3.0, "I")' - pauli_word_r += 'I' - site.append('') - else: - match = re.match(r'([XYZ])([0-9]+)', single_pauli_term, flags=re.I) - if match: - pauli_word_r += match.group(1).upper() - assert int(match.group(2)) not in site, 'each Pauli operator should act on different qubit' - site.append(int(match.group(2))) - else: - raise Exception( - 'Operators should be defined with a string composed of Pauli operators followed' + - 'by qubit index on which it act, separated with ",". i.e. "Z0, X1"') - self.__nqubits = max(self.__nqubits, int(match.group(2)) + 1) - self.__pauli_words_r.append(pauli_word_r) - self.__sites.append(site) - new_pauli_str.append([float(coefficient), pauli_term.upper()]) - - for term_index in range(len(self.__pauli_str)): - pauli_word = ['I' for _ in range(self.__nqubits)] - site = self.__sites[term_index] - for site_index in range(len(site)): - if type(site[site_index]) == int: - pauli_word[site[site_index]] = self.__pauli_words_r[term_index][site_index] - self.__pauli_words.append(''.join(pauli_word)) - self.__pauli_str = new_pauli_str - self.__update_flag = False - - def __compress(self): - r""" 对同类项进行合并。 - - Notes: - 这是一个内部函数，你不需要直接使用它 - """ - if self.__update_flag: - self.__decompose() - else: - pass - new_pauli_str = [] - flag_merged = [False for _ in range(self.n_terms)] - for term_idx_1 in range(self.n_terms): - if not flag_merged[term_idx_1]: - for term_idx_2 in range(term_idx_1 + 1, self.n_terms): - if not flag_merged[term_idx_2]: - if self.pauli_words[term_idx_1] == self.pauli_words[term_idx_2]: - self.__coefficients[term_idx_1] += self.__coefficients[term_idx_2] - flag_merged[term_idx_2] = True - else: - pass - if self.__coefficients[term_idx_1] != 0: - new_pauli_str.append([self.__coefficients[term_idx_1], ','.join(self.__terms[term_idx_1])]) - self.__pauli_str = new_pauli_str - self.__update_flag = True + # Set the view angle and view distance + ax.view_init(view_angle[0], view_angle[1]) + ax.dist = view_dist - def decompose_with_sites(self): - r"""将 pauli_str 分解为系数、泡利字符串的简化形式以及它们分别作用的量子比特下标。 + # Draw the general frame + def draw_general_frame(): - Returns: - tuple: 包含如下元素的 tuple: + # Do not show the grid and original axes + ax.grid(False) + ax.set_axis_off() + ax.view_init(view_angle[0], view_angle[1]) + ax.dist = view_dist - - coefficients (list): 元素为每一项的系数 - - pauli_words_r (list): 元素为每一项的泡利字符串的简化形式，例如 'Z0, Z1, X3' 这一项的泡利字符串为 'ZZX' - - sites (list): 元素为每一项作用的量子比特下标，例如 'Z0, Z1, X3' 这一项的 site 为 [0, 1, 3] + # Set the lower limit and upper limit of each axis + # To make the bloch_ball look less flat, the default is relatively flat + ax.set_xlim3d(xmin=-1.5, xmax=1.5) + ax.set_ylim3d(ymin=-1.5, ymax=1.5) + ax.set_zlim3d(zmin=-1, zmax=1.3) - """ - if self.__update_flag: - self.__decompose() - return self.coefficients, self.__pauli_words_r, self.__sites + # Draw a new axes + coordinate_start_x, coordinate_start_y, coordinate_start_z = \ + np.array([[-1.5, 0, 0], [0, -1.5, 0], [0, 0, -1.5]]) + coordinate_end_x, coordinate_end_y, coordinate_end_z = \ + np.array([[3, 0, 0], [0, 3, 0], [0, 0, 3]]) + ax.quiver( + coordinate_start_x, coordinate_start_y, coordinate_start_z, + coordinate_end_x, coordinate_end_y, coordinate_end_z, + arrow_length_ratio=0.03, color="black", linewidth=0.5 + ) + ax.text(0, 0, 1.7, r"|0⟩", color="black", fontsize=16) + ax.text(0, 0, -1.9, r"|1⟩", color="black", fontsize=16) + ax.text(1.9, 0, 0, r"|+⟩", color="black", fontsize=16) + ax.text(-1.7, 0, 0, r"|–⟩", color="black", fontsize=16) + ax.text(0, 1.7, 0, r"|i+⟩", color="black", fontsize=16) + ax.text(0, -1.9, 0, r"|i–⟩", color="black", fontsize=16) - def decompose_pauli_words(self): - r"""将 pauli_str 分解为系数和泡利字符串。 + # Draw a surface + horizontal_angle = np.linspace(0, 2 * np.pi, 80) + vertical_angle = np.linspace(0, np.pi, 80) + surface_point_x = np.outer(np.cos(horizontal_angle), np.sin(vertical_angle)) + surface_point_y = np.outer(np.sin(horizontal_angle), np.sin(vertical_angle)) + surface_point_z = np.outer(np.ones(np.size(horizontal_angle)), np.cos(vertical_angle)) + ax.plot_surface( + surface_point_x, surface_point_y, surface_point_z, rstride=1, cstride=1, + color="black", linewidth=0.05, alpha=0.03 + ) - Returns: - tuple: 包含如下元素的 tuple: + # Draw circle + def draw_circle(circle_horizon_angle, circle_vertical_angle, linewidth=0.5, alpha=0.2): + r = 1 + circle_point_x = r * np.cos(circle_vertical_angle) * np.cos(circle_horizon_angle) + circle_point_y = r * np.cos(circle_vertical_angle) * np.sin(circle_horizon_angle) + circle_point_z = r * np.sin(circle_vertical_angle) + ax.plot( + circle_point_x, circle_point_y, circle_point_z, + color="black", linewidth=linewidth, alpha=alpha + ) - - coefficients(list): 元素为每一项的系数 - - pauli_words(list): 元素为每一项的泡利字符串，例如 'Z0, Z1, X3' 这一项的泡利字符串为 'ZZIX' - """ - if self.__update_flag: - self.__decompose() - else: - pass - return self.coefficients, self.__pauli_words + # draw longitude and latitude + def draw_longitude_and_latitude(): + # Draw longitude + num = 3 + theta = np.linspace(0, 0, 100) + psi = np.linspace(0, 2 * np.pi, 100) + for i in range(num): + theta = theta + np.pi / num + draw_circle(theta, psi) - def construct_h_matrix(self, n_qubit=None): - r"""构建 Hamiltonian 在 Z 基底下的矩阵。 + # Draw latitude + num = 6 + theta = np.linspace(0, 2 * np.pi, 100) + psi = np.linspace(-np.pi / 2, -np.pi / 2, 100) + for i in range(num): + psi = psi + np.pi / num + draw_circle(theta, psi) - Returns: - np.ndarray: Z 基底下的哈密顿量矩阵形式 - """ - coefs, pauli_words, sites = self.decompose_with_sites() - if n_qubit is None: - n_qubit = 1 - for site in sites: - if type(site[0]) is int: - print(n_qubit,(site)) - n_qubit = max(n_qubit, max(site) + 1) - else: - assert n_qubit>=self.n_qubits,"输入的量子数不小于哈密顿量表达式中所对应的量子比特数" - h_matrix = np.zeros([2 ** n_qubit, 2 ** n_qubit], dtype='complex64') - spin_ops = SpinOps(n_qubit, use_sparse=True) - for idx in range(len(coefs)): - op = coefs[idx] * sparse.eye(2 ** n_qubit, dtype='complex64') - for site_idx in range(len(sites[idx])): - if re.match(r'X', pauli_words[idx][site_idx], re.I): - op = op.dot(spin_ops.sigx_p[sites[idx][site_idx]]) - elif re.match(r'Y', pauli_words[idx][site_idx], re.I): - op = op.dot(spin_ops.sigy_p[sites[idx][site_idx]]) - elif re.match(r'Z', pauli_words[idx][site_idx], re.I): - op = op.dot(spin_ops.sigz_p[sites[idx][site_idx]]) - h_matrix += op - return h_matrix + # Draw equator + theta = np.linspace(0, 2 * np.pi, 100) + psi = np.linspace(0, 0, 100) + draw_circle(theta, psi, linewidth=0.5, alpha=0.2) + # Draw prime meridian + theta = np.linspace(0, 0, 100) + psi = np.linspace(0, 2 * np.pi, 100) + draw_circle(theta, psi, linewidth=0.5, alpha=0.2) -class SpinOps: - r"""矩阵表示下的自旋算符，可以用来构建哈密顿量矩阵或者自旋可观测量。 + # If the number of data points exceeds 20, no longitude and latitude lines will be drawn. + if bloch_vectors is not None and len(bloch_vectors) < 52: + draw_longitude_and_latitude() + elif bloch_vectors is None: + draw_longitude_and_latitude() - """ - def __init__(self, size: int, use_sparse=False): - r"""SpinOps 的构造函数，用于实例化一个 SpinOps 对象。 + # Draw three invisible points + invisible_points = np.array([[0.03440399, 0.30279721, 0.95243384], + [0.70776026, 0.57712403, 0.40743499], + [0.46991358, -0.63717908, 0.61088792]]) + ax.scatter( + invisible_points[:, 0], invisible_points[:, 1], invisible_points[:, 2], + c='w', alpha=0.01 + ) - Args: - size (int): 系统的大小（有几个量子比特） - use_sparse (bool): 是否使用 sparse matrix 计算，默认为 ``False`` - """ - self.size = size - self.id = sparse.eye(2, dtype='complex128') - self.__sigz = sparse.bsr.bsr_matrix([[1, 0], [0, -1]], dtype='complex64') - self.__sigy = sparse.bsr.bsr_matrix([[0, -1j], [1j, 0]], dtype='complex64') - self.__sigx = sparse.bsr.bsr_matrix([[0, 1], [1, 0]], dtype='complex64') - self.__sigz_p = [] - self.__sigy_p = [] - self.__sigx_p = [] - self.__sparse = use_sparse - for i in range(self.size): - self.__sigz_p.append(self.__direct_prod_op(spin_op=self.__sigz, spin_index=i)) - self.__sigy_p.append(self.__direct_prod_op(spin_op=self.__sigy, spin_index=i)) - self.__sigx_p.append(self.__direct_prod_op(spin_op=self.__sigx, spin_index=i)) + # clean plt + if clear_plt: + ax.cla() + draw_general_frame() - @property - def sigz_p(self): - r""" :math:`Z` 基底下的 :math:`S^z_i` 算符。 + # Draw the data points + if bloch_vectors is not None: + ax.scatter( + bloch_vectors[:, 0], bloch_vectors[:, 1], bloch_vectors[:, 2], c=color, alpha=1.0 + ) - Returns: - list : :math:`S^z_i` 算符组成的列表，其中每一项对应不同的 :math:`i` - """ - return self.__sigz_p + # if show the rotating angle + if rotating_angle_list is not None: + bloch_num = len(bloch_vectors) + rotating_angle_theta, rotating_angle_phi, rotating_angle_lam = rotating_angle_list[bloch_num - 1] + rotating_angle_theta = round(rotating_angle_theta, 6) + rotating_angle_phi = round(rotating_angle_phi, 6) + rotating_angle_lam = round(rotating_angle_lam, 6) - @property - def sigy_p(self): - r""" :math:`Z` 基底下的 :math:`S^y_i` 算符。 + # Shown at the top right of the perspective + display_text_angle = [-(view_angle[0] - 10), (view_angle[1] + 10)] + text_point_x = 2 * np.cos(display_text_angle[0]) * np.cos(display_text_angle[1]) + text_point_y = 2 * np.cos(display_text_angle[0]) * np.sin(-display_text_angle[1]) + text_point_z = 2 * np.sin(-display_text_angle[0]) + ax.text(text_point_x, text_point_y, text_point_z, r'$\theta=' + str(rotating_angle_theta) + r'$', + color="black", fontsize=14) + ax.text(text_point_x, text_point_y, text_point_z - 0.1, r'$\phi=' + str(rotating_angle_phi) + r'$', + color="black", fontsize=14) + ax.text(text_point_x, text_point_y, text_point_z - 0.2, r'$\lambda=' + str(rotating_angle_lam) + r'$', + color="black", fontsize=14) - Returns: - list : :math:`S^y_i` 算符组成的列表，其中每一项对应不同的 :math:`i` - """ - return self.__sigy_p + # If show the bloch_vector + if show_arrow: + ax.quiver( + 0, 0, 0, bloch_vectors[:, 0], bloch_vectors[:, 1], bloch_vectors[:, 2], + arrow_length_ratio=0.05, color=color, alpha=1.0 + ) - @property - def sigx_p(self): - r""" :math:`Z` 基底下的 :math:`S^x_i` 算符。 - Returns: - list : :math:`S^x_i` 算符组成的列表，其中每一项对应不同的 :math:`i` - """ - return self.__sigx_p - - def __direct_prod_op(self, spin_op, spin_index): - r"""直积，得到第 n 个自旋（量子比特）上的自旋算符 - - Args: - spin_op: 单体自旋算符 - spin_index: 标记第 n 个自旋（量子比特） - - Returns: - scipy.sparse or np.ndarray: 直积后的自旋算符，其数据类型取决于 self.__use_sparse - """ - s_p = copy.copy(spin_op) - for i in range(self.size): - if i < spin_index: - s_p = sparse.kron(self.id, s_p) - elif i > spin_index: - s_p = sparse.kron(s_p, self.id) - if self.__sparse: - return s_p - else: - return s_p.toarray() - - -def __input_args_dtype_check( - show_arrow, - save_gif, - filename, - view_angle, - view_dist -): - r""" - 该函数实现对输入默认参数的数据类型检查，保证输入函数中的参数为所允许的数据类型 +def plot_state_in_bloch_sphere( + state, + show_arrow=False, + save_gif=False, + filename=None, + view_angle=None, + view_dist=None, + set_color=None +): + r"""将输入的量子态展示在 Bloch 球面上 Args: - show_arrow (bool): 是否展示向量的箭头，默认为 False - save_gif (bool): 是否存储 gif 动图 + state (list(numpy.ndarray or paddle.Tensor)): 输入的量子态列表，可以支持态矢量和密度矩阵 + show_arrow (bool): 是否展示向量的箭头，默认为 ``False`` + save_gif (bool): 是否存储 gif 动图，默认为 ``False`` filename (str): 存储的 gif 动图的名字 view_angle (list or tuple): 视图的角度， - 第一个元素为关于xy平面的夹角[0-360],第二个元素为关于xz平面的夹角[0-360], 默认为 (30, 45) + 第一个元素为关于 xy 平面的夹角 [0-360]，第二个元素为关于 xz 平面的夹角 [0-360], 默认为 ``(30, 45)`` view_dist (int): 视图的距离，默认为 7 + set_color (str): 若要设置指定的颜色，请查阅 ``cmap`` 表。默认为红色到黑色的渐变颜色 """ + # Check input data + __input_args_dtype_check(show_arrow, save_gif, filename, view_angle, view_dist) - if show_arrow is not None: - assert type(show_arrow) == bool, \ - 'the type of "show_arrow" should be "bool".' - if save_gif is not None: - assert type(save_gif) == bool, \ - 'the type of "save_gif" should be "bool".' - if save_gif: - if filename is not None: - assert type(filename) == str, \ - 'the type of "filename" should be "str".' - other, ext = os.path.splitext(filename) - assert ext == '.gif', 'The suffix of the file name must be "gif".' - # If it does not exist, create a folder - path, file = os.path.split(filename) - if not os.path.exists(path): - os.makedirs(path) - if view_angle is not None: - assert type(view_angle) == list or type(view_angle) == tuple, \ - 'the type of "view_angle" should be "list" or "tuple".' - for i in range(2): - assert type(view_angle[i]) == int, \ - 'the type of "view_angle[0]" and "view_angle[1]" should be "int".' - if view_dist is not None: - assert type(view_dist) == int, \ - 'the type of "view_dist" should be "int".' + assert type(state) == list or type(state) == paddle.Tensor or type(state) == np.ndarray, \ + 'the type of "state" must be "list" or "paddle.Tensor" or "np.ndarray".' + if type(state) == paddle.Tensor or type(state) == np.ndarray: + state = [state] + state_len = len(state) + assert state_len >= 1, '"state" is NULL.' + for i in range(state_len): + assert type(state[i]) == paddle.Tensor or type(state[i]) == np.ndarray, \ + 'the type of "state[i]" should be "paddle.Tensor" or "numpy.ndarray".' + if set_color is not None: + assert type(set_color) == str, \ + 'the type of "set_color" should be "str".' + # Assign a value to an empty variable + if filename is None: + filename = 'state_in_bloch_sphere.gif' + if view_angle is None: + view_angle = (30, 45) + if view_dist is None: + view_dist = 7 -def __density_matrix_convert_to_bloch_vector(density_matrix): - r"""该函数将密度矩阵转化为bloch球面上的坐标 + # Convert Tensor to numpy + for i in range(state_len): + if type(state[i]) == paddle.Tensor: + state[i] = state[i].numpy() - Args: - density_matrix (numpy.ndarray): 输入的密度矩阵 + # Convert state_vector to density_matrix + for i in range(state_len): + if state[i].size == 2: + state_vector = state[i] + state[i] = np.outer(state_vector, np.conj(state_vector)) - Returns: - bloch_vector (numpy.ndarray): 存储bloch向量的 x,y,z 坐标，向量的模长，向量的颜色 - """ + # Calc the bloch_vectors + bloch_vector_list = [] + for i in range(state_len): + bloch_vector_tmp = __density_matrix_convert_to_bloch_vector(state[i]) + bloch_vector_list.append(bloch_vector_tmp) - # Pauli Matrix - pauli_x = np.array([[0, 1], [1, 0]]) - pauli_y = np.array([[0, -1j], [1j, 0]]) - pauli_z = np.array([[1, 0], [0, -1]]) + # List must be converted to array for slicing. + bloch_vectors = np.array(bloch_vector_list) - # Convert a density matrix to a Bloch vector. - ax = np.trace(np.dot(density_matrix, pauli_x)).real - ay = np.trace(np.dot(density_matrix, pauli_y)).real - az = np.trace(np.dot(density_matrix, pauli_z)).real + # A update function for animation class + def update(frame): + view_rotating_angle = 5 + new_view_angle = [view_angle[0], view_angle[1] + view_rotating_angle * frame] + __plot_bloch_sphere( + ax, bloch_vectors, show_arrow, clear_plt=True, + view_angle=new_view_angle, view_dist=view_dist, set_color=set_color + ) - # Calc the length of bloch vector - length = ax ** 2 + ay ** 2 + az ** 2 - length = sqrt(length) - if length > 1.0: - length = 1.0 + # Dynamic update and save + if save_gif: + # Helper function to plot vectors on a sphere. + fig = plt.figure(figsize=(8, 8), dpi=100) + fig.subplots_adjust(left=0, right=1, bottom=0, top=1) + ax = fig.add_subplot(111, projection='3d') - # Calc the color of bloch vector, the value of the color is proportional to the length - color = length + frames_num = 7 + anim = animation.FuncAnimation(fig, update, frames=frames_num, interval=600, repeat=False) + anim.save(filename, dpi=100, writer='pillow') + # close the plt + plt.close(fig) - bloch_vector = [ax, ay, az, length, color] + # Helper function to plot vectors on a sphere. + fig = plt.figure(figsize=(8, 8), dpi=100) + fig.subplots_adjust(left=0, right=1, bottom=0, top=1) + ax = fig.add_subplot(111, projection='3d') - # You must use an array, which is followed by slicing and taking a column - bloch_vector = np.array(bloch_vector) + __plot_bloch_sphere( + ax, bloch_vectors, show_arrow, clear_plt=True, + view_angle=view_angle, view_dist=view_dist, set_color=set_color + ) - return bloch_vector + plt.show() -def __plot_bloch_sphere( - ax, - bloch_vectors=None, +def plot_multi_qubits_state_in_bloch_sphere( + state, + which_qubits=None, show_arrow=False, - clear_plt=True, - rotating_angle_list=None, + save_gif=False, + save_pic=True, + filename=None, view_angle=None, view_dist=None, - set_color=None + set_color='#0000FF' ): - r"""将 Bloch 向量展示在 Bloch 球面上 + r"""将输入的多量子比特的量子态展示在 Bloch 球面上 Args: - ax (Axes3D(fig)): 画布的句柄 - bloch_vectors (numpy.ndarray): 存储bloch向量的 x,y,z 坐标，向量的模长，向量的颜色 - show_arrow (bool): 是否展示向量的箭头，默认为 False - clear_plt (bool): 是否要清空画布，默认为 True，每次画图的时候清空画布再画图 - rotating_angle_list (list): 旋转角度的列表，用于展示旋转轨迹 - view_angle (list): 视图的角度， - 第一个元素为关于xy平面的夹角[0-360],第二个元素为关于xz平面的夹角[0-360], 默认为 (30, 45) + state (numpy.ndarray or paddle.Tensor): 输入的量子态，可以支持态矢量和密度矩阵 + which_qubits (list or None): 要展示的量子比特，默认为全展示 + show_arrow (bool): 是否展示向量的箭头，默认为 ``False`` + save_gif (bool): 是否存储 gif 动图，默认为 ``False`` + save_pic (bool): 是否存储静态图片，默认为 ``True`` + filename (str): 存储的图片的名字 + view_angle (list or tuple): 视图的角度，第一个元素为关于 xy 平面的夹角 [0-360]，第二个元素为关于 xz 平面的夹角 [0-360], 默认为 ``(30, 45)`` view_dist (int): 视图的距离，默认为 7 - set_color (str): 设置指定的颜色，请查阅cmap表，默认为 "红-黑-根据向量的模长渐变" 颜色方案 + set_color (str): 若要设置指定的颜色，请查阅 ``cmap`` 表。默认为蓝色 """ + # Check input data + __input_args_dtype_check(show_arrow, save_gif, filename, view_angle, view_dist) + + assert type(state) == paddle.Tensor or type(state) == np.ndarray, \ + 'the type of "state" must be "paddle.Tensor" or "np.ndarray".' + assert type(set_color) == str, \ + 'the type of "set_color" should be "str".' + + n_qubits = int(np.log2(state.shape[0])) + + if which_qubits is None: + which_qubits = list(range(n_qubits)) + else: + assert type(which_qubits) == list, 'the type of which_qubits should be None or list' + assert 1 <= len(which_qubits) <= n_qubits, '展示的量子数量需要小于n_qubits' + for i in range(len(which_qubits)): + assert 0 <= which_qubits[i] < n_qubits, '0= 2 and state.size == state.shape[0]: + state_vector = state + state = np.outer(state_vector, np.conj(state_vector)) - # Do not show the grid and original axes - ax.grid(False) - ax.set_axis_off() - ax.view_init(view_angle[0], view_angle[1]) - ax.dist = view_dist + # multi qubits state decompose + if state.shape[0] > 2: + rho = paddle.to_tensor(state) + tmp_s = [] + for q in which_qubits: + tmp_s.append(partial_trace_discontiguous(rho, [q])) + state = tmp_s + else: + state = [state] + state_len = len(state) - # Set the lower limit and upper limit of each axis - # To make the bloch_ball look less flat, the default is relatively flat - ax.set_xlim3d(xmin=-1.5, xmax=1.5) - ax.set_ylim3d(ymin=-1.5, ymax=1.5) - ax.set_zlim3d(zmin=-1, zmax=1.3) + # Calc the bloch_vectors + bloch_vector_list = [] + for i in range(state_len): + bloch_vector_tmp = __density_matrix_convert_to_bloch_vector(state[i]) + bloch_vector_list.append(bloch_vector_tmp) - # Draw a new axes - coordinate_start_x, coordinate_start_y, coordinate_start_z = \ - np.array([[-1.5, 0, 0], [0, -1.5, 0], [0, 0, -1.5]]) - coordinate_end_x, coordinate_end_y, coordinate_end_z = \ - np.array([[3, 0, 0], [0, 3, 0], [0, 0, 3]]) - ax.quiver( - coordinate_start_x, coordinate_start_y, coordinate_start_z, - coordinate_end_x, coordinate_end_y, coordinate_end_z, - arrow_length_ratio=0.03, color="black", linewidth=0.5 - ) - ax.text(0, 0, 1.7, r"|0⟩", color="black", fontsize=16) - ax.text(0, 0, -1.9, r"|1⟩", color="black", fontsize=16) - ax.text(1.9, 0, 0, r"|+⟩", color="black", fontsize=16) - ax.text(-1.7, 0, 0, r"|–⟩", color="black", fontsize=16) - ax.text(0, 1.7, 0, r"|i+⟩", color="black", fontsize=16) - ax.text(0, -1.9, 0, r"|i–⟩", color="black", fontsize=16) + # List must be converted to array for slicing. + bloch_vectors = np.array(bloch_vector_list) - # Draw a surface - horizontal_angle = np.linspace(0, 2 * np.pi, 80) - vertical_angle = np.linspace(0, np.pi, 80) - surface_point_x = np.outer(np.cos(horizontal_angle), np.sin(vertical_angle)) - surface_point_y = np.outer(np.sin(horizontal_angle), np.sin(vertical_angle)) - surface_point_z = np.outer(np.ones(np.size(horizontal_angle)), np.cos(vertical_angle)) - ax.plot_surface( - surface_point_x, surface_point_y, surface_point_z, rstride=1, cstride=1, - color="black", linewidth=0.05, alpha=0.03 + # A update function for animation class + def update(frame): + view_rotating_angle = 5 + new_view_angle = [view_angle[0], view_angle[1] + view_rotating_angle * frame] + __plot_bloch_sphere( + ax, bloch_vectors, show_arrow, clear_plt=True, + view_angle=new_view_angle, view_dist=view_dist, set_color=set_color ) - # Draw circle - def draw_circle(circle_horizon_angle, circle_vertical_angle, linewidth=0.5, alpha=0.2): - r = 1 - circle_point_x = r * np.cos(circle_vertical_angle) * np.cos(circle_horizon_angle) - circle_point_y = r * np.cos(circle_vertical_angle) * np.sin(circle_horizon_angle) - circle_point_z = r * np.sin(circle_vertical_angle) - ax.plot( - circle_point_x, circle_point_y, circle_point_z, - color="black", linewidth=linewidth, alpha=alpha - ) + # Dynamic update and save + if save_gif: + # Helper function to plot vectors on a sphere. + fig = plt.figure(figsize=(8, 8), dpi=100) + fig.subplots_adjust(left=0, right=1, bottom=0, top=1) + ax = fig.add_subplot(111, projection='3d') - # draw longitude and latitude - def draw_longitude_and_latitude(): - # Draw longitude - num = 3 - theta = np.linspace(0, 0, 100) - psi = np.linspace(0, 2 * np.pi, 100) - for i in range(num): - theta = theta + np.pi / num - draw_circle(theta, psi) + frames_num = 7 + anim = animation.FuncAnimation(fig, update, frames=frames_num, interval=600, repeat=False) + anim.save(filename, dpi=100, writer='pillow') + # close the plt + plt.close(fig) - # Draw latitude - num = 6 - theta = np.linspace(0, 2 * np.pi, 100) - psi = np.linspace(-np.pi / 2, -np.pi / 2, 100) - for i in range(num): - psi = psi + np.pi / num - draw_circle(theta, psi) + # Helper function to plot vectors on a sphere. + fig = plt.figure(figsize=(8, 8), dpi=100) + fig.subplots_adjust(left=0, right=1, bottom=0, top=1) + dim = np.ceil(sqrt(len(which_qubits))) + for i in range(1, len(which_qubits)+1): + ax = fig.add_subplot(dim, dim, i, projection='3d') + bloch_vector = np.array([bloch_vectors[i-1]]) + __plot_bloch_sphere( + ax, bloch_vector, show_arrow, clear_plt=True, + view_angle=view_angle, view_dist=view_dist, set_color=set_color + ) + if save_pic: + plt.savefig('n_qubit_state_in_bloch.png', bbox_inches='tight') + plt.show() - # Draw equator - theta = np.linspace(0, 2 * np.pi, 100) - psi = np.linspace(0, 0, 100) - draw_circle(theta, psi, linewidth=0.5, alpha=0.2) - # Draw prime meridian - theta = np.linspace(0, 0, 100) - psi = np.linspace(0, 2 * np.pi, 100) - draw_circle(theta, psi, linewidth=0.5, alpha=0.2) +def plot_rotation_in_bloch_sphere( + init_state, + rotating_angle, + show_arrow=False, + save_gif=False, + filename=None, + view_angle=None, + view_dist=None, + color_scheme=None, +): + r"""在 Bloch 球面上刻画从初始量子态开始的旋转轨迹 - # If the number of data points exceeds 20, no longitude and latitude lines will be drawn. - if bloch_vectors is not None and len(bloch_vectors) < 52: - draw_longitude_and_latitude() - elif bloch_vectors is None: - draw_longitude_and_latitude() + Args: + init_state (numpy.ndarray or paddle.Tensor): 输入的初始量子态，可以支持态矢量和密度矩阵 + rotating_angle (list(float)): 旋转角度 ``[theta, phi, lam]`` + show_arrow (bool): 是否展示向量的箭头，默认为 ``False`` + save_gif (bool): 是否存储 gif 动图，默认为 ``False`` + filename (str): 存储的 gif 动图的名字 + view_angle (list or tuple): 视图的角度， + 第一个元素为关于 xy 平面的夹角 [0-360]，第二个元素为关于 xz 平面的夹角 [0-360], 默认为 ``(30, 45)`` + view_dist (int): 视图的距离，默认为 7 + color_scheme (list(str,str,str)): 分别是初始颜色，轨迹颜色，结束颜色。若要设置指定的颜色，请查阅 ``cmap`` 表。默认为红色 + """ + # Check input data + __input_args_dtype_check(show_arrow, save_gif, filename, view_angle, view_dist) - # Draw three invisible points - invisible_points = np.array([[0.03440399, 0.30279721, 0.95243384], - [0.70776026, 0.57712403, 0.40743499], - [0.46991358, -0.63717908, 0.61088792]]) - ax.scatter( - invisible_points[:, 0], invisible_points[:, 1], invisible_points[:, 2], - c='w', alpha=0.01 - ) + assert type(init_state) == paddle.Tensor or type(init_state) == np.ndarray, \ + 'the type of input data should be "paddle.Tensor" or "numpy.ndarray".' + assert type(rotating_angle) == tuple or type(rotating_angle) == list, \ + 'the type of rotating_angle should be "tuple" or "list".' + assert len(rotating_angle) == 3, \ + 'the rotating_angle must include [theta=paddle.Tensor, phi=paddle.Tensor, lam=paddle.Tensor].' + for i in range(3): + assert type(rotating_angle[i]) == paddle.Tensor or type(rotating_angle[i]) == float, \ + 'the rotating_angle must include [theta=paddle.Tensor, phi=paddle.Tensor, lam=paddle.Tensor].' + if color_scheme is not None: + assert type(color_scheme) == list and len(color_scheme) <= 3, \ + 'the type of "color_scheme" should be "list" and ' \ + 'the length of "color_scheme" should be less than or equal to "3".' + for i in range(len(color_scheme)): + assert type(color_scheme[i]) == str, \ + 'the type of "color_scheme[i] should be "str".' - # clean plt - if clear_plt: - ax.cla() - draw_general_frame() + # Assign a value to an empty variable + if filename is None: + filename = 'rotation_in_bloch_sphere.gif' - # Draw the data points - if bloch_vectors is not None: - ax.scatter( - bloch_vectors[:, 0], bloch_vectors[:, 1], bloch_vectors[:, 2], c=color, alpha=1.0 - ) + # Assign colors to bloch vectors + color_list = ['orangered', 'lightsalmon', 'darkred'] + if color_scheme is not None: + for i in range(len(color_scheme)): + color_list[i] = color_scheme[i] + set_init_color, set_trac_color, set_end_color = color_list - # if show the rotating angle - if rotating_angle_list is not None: - bloch_num = len(bloch_vectors) - rotating_angle_theta, rotating_angle_phi, rotating_angle_lam = rotating_angle_list[bloch_num - 1] - rotating_angle_theta = round(rotating_angle_theta, 6) - rotating_angle_phi = round(rotating_angle_phi, 6) - rotating_angle_lam = round(rotating_angle_lam, 6) + theta, phi, lam = rotating_angle - # Shown at the top right of the perspective - display_text_angle = [-(view_angle[0] - 10), (view_angle[1] + 10)] - text_point_x = 2 * np.cos(display_text_angle[0]) * np.cos(display_text_angle[1]) - text_point_y = 2 * np.cos(display_text_angle[0]) * np.sin(-display_text_angle[1]) - text_point_z = 2 * np.sin(-display_text_angle[0]) - ax.text(text_point_x, text_point_y, text_point_z, r'$\theta=' + str(rotating_angle_theta) + r'$', - color="black", fontsize=14) - ax.text(text_point_x, text_point_y, text_point_z - 0.1, r'$\phi=' + str(rotating_angle_phi) + r'$', - color="black", fontsize=14) - ax.text(text_point_x, text_point_y, text_point_z - 0.2, r'$\lambda=' + str(rotating_angle_lam) + r'$', - color="black", fontsize=14) + # Convert Tensor to numpy + if type(init_state) == paddle.Tensor: + init_state = init_state.numpy() - # If show the bloch_vector - if show_arrow: - ax.quiver( - 0, 0, 0, bloch_vectors[:, 0], bloch_vectors[:, 1], bloch_vectors[:, 2], - arrow_length_ratio=0.05, color=color, alpha=1.0 - ) - + # Convert state_vector to density_matrix + if init_state.size == 2: + state_vector = init_state + init_state = np.outer(state_vector, np.conj(state_vector)) -def plot_n_qubit_state_in_bloch_sphere( - state, - which_qubits=None, - show_arrow=False, - save_gif=False, - save_pic=True, - filename=None, - view_angle=None, - view_dist=None, - set_color='#0000FF' -): - r"""将输入的多量子比特的量子态展示在 Bloch 球面上 + # Rotating angle + def rotating_operation(rotating_angle_each): + gate_matrix = simulator.u_gate_matrix(rotating_angle_each) + return np.matmul(np.matmul(gate_matrix, init_state), gate_matrix.conj().T) + + # Rotating angle division + rotating_frame = 50 + rotating_angle_list = [] + state = [] + for i in range(rotating_frame + 1): + angle_each = [theta / rotating_frame * i, phi / rotating_frame * i, lam / rotating_frame * i] + rotating_angle_list.append(angle_each) + state.append(rotating_operation(angle_each)) + + state_len = len(state) + # Calc the bloch_vectors + bloch_vector_list = [] + for i in range(state_len): + bloch_vector_tmp = __density_matrix_convert_to_bloch_vector(state[i]) + bloch_vector_list.append(bloch_vector_tmp) + + # List must be converted to array for slicing. + bloch_vectors = np.array(bloch_vector_list) + + # A update function for animation class + def update(frame): + frame = frame + 2 + if frame <= len(bloch_vectors) - 1: + __plot_bloch_sphere( + ax, bloch_vectors[1:frame], show_arrow=show_arrow, clear_plt=True, + rotating_angle_list=rotating_angle_list, + view_angle=view_angle, view_dist=view_dist, set_color=set_trac_color + ) + + # The starting and ending bloch vector has to be shown + # show starting vector + __plot_bloch_sphere( + ax, bloch_vectors[:1], show_arrow=True, clear_plt=False, + view_angle=view_angle, view_dist=view_dist, set_color=set_init_color + ) + + # Show ending vector + if frame == len(bloch_vectors): + __plot_bloch_sphere( + ax, bloch_vectors[frame - 1:frame], show_arrow=True, clear_plt=False, + view_angle=view_angle, view_dist=view_dist, set_color=set_end_color + ) + + if save_gif: + # Helper function to plot vectors on a sphere. + fig = plt.figure(figsize=(8, 8), dpi=100) + fig.subplots_adjust(left=0, right=1, bottom=0, top=1) + ax = fig.add_subplot(111, projection='3d') + + # Dynamic update and save + stop_frames = 15 + frames_num = len(bloch_vectors) - 2 + stop_frames + anim = animation.FuncAnimation(fig, update, frames=frames_num, interval=100, repeat=False) + anim.save(filename, dpi=100, writer='pillow') + # close the plt + plt.close(fig) + + # Helper function to plot vectors on a sphere. + fig = plt.figure(figsize=(8, 8), dpi=100) + fig.subplots_adjust(left=0, right=1, bottom=0, top=1) + ax = fig.add_subplot(111, projection='3d') + + # Draw the penultimate bloch vector + update(len(bloch_vectors) - 3) + # Draw the last bloch vector + update(len(bloch_vectors) - 2) + + plt.show() + + +def plot_density_matrix_graph(density_matrix, size=0.3): + r"""密度矩阵可视化工具。 + + Args: + density_matrix (numpy.ndarray or paddle.Tensor): 多量子比特的量子态的状态向量或者密度矩阵,要求量子数大于 1 + size (float): 条宽度，在 0 到 1 之间，默认为 0.3 + """ + if not isinstance(density_matrix, (np.ndarray, paddle.Tensor)): + msg = f'Expected density_matrix to be np.ndarray or paddle.Tensor, but got {type(density_matrix)}' + raise TypeError(msg) + if isinstance(density_matrix, paddle.Tensor): + density_matrix = density_matrix.numpy() + if density_matrix.shape[0] != density_matrix.shape[1]: + msg = f'Expected density matrix dim0 equal to dim1, but got dim0={density_matrix.shape[0]}, dim1={density_matrix.shape[1]}' + raise ValueError(msg) + + real = density_matrix.real + imag = density_matrix.imag + + figure = plt.figure() + ax_real = figure.add_subplot(121, projection='3d', title="real") + ax_imag = figure.add_subplot(122, projection='3d', title="imag") + + xx, yy = np.meshgrid( + list(range(real.shape[0])), list(range(real.shape[1]))) + xx, yy = xx.ravel(), yy.ravel() + real = real.reshape(-1) + imag = imag.reshape(-1) + + ax_real.bar3d(xx, yy, np.zeros_like(real), size, size, np.abs(real)) + ax_imag.bar3d(xx, yy, np.zeros_like(imag), size, size, np.abs(imag)) + plt.show() + + return + + +def image_to_density_matrix(image_filepath): + r"""将图片编码为密度矩阵 + + Args: + image_filepath (str): 图片文件的路径 + + Return: + rho (numpy.ndarray): 编码得到的密度矩阵 + """ + image_matrix = matplotlib.image.imread(image_filepath) + + # Converting images to grayscale + image_matrix = image_matrix.mean(axis=2) + + # Fill the matrix so that it becomes a matrix whose shape is [2**n,2**n] + length = int(2**np.ceil(np.log2(np.max(image_matrix.shape)))) + image_matrix = np.pad(image_matrix, ((0, length-image_matrix.shape[0]), (0, length-image_matrix.shape[1])), 'constant') + # Density matrix whose trace is 1 + rho = image_matrix@image_matrix.T + rho = rho/np.trace(rho) + return rho + + +def pauli_basis(n): + r"""生成 n 量子比特的泡利基空间 + + Args: + n (int): 量子比特的数量 + + Return: + tuple: + - basis_str: 泡利基空间的一组基底表示（array形式） + - label_str: 泡利基空间对应的一组基底表示（标签形式），形如``[ 'X', 'Y', 'Z', 'I']`` + """ + sigma_x = np.array([[0, 1], [1, 0]], dtype=np.complex128) + sigma_y = np.array([[0, -1j], [1j, 0]], dtype=np.complex128) + sigma_z = np.array([[1, 0], [0, -1]], dtype=np.complex128) + sigma_id = np.array([[1, 0], [0, 1]], dtype=np.complex128) + pauli = [sigma_x, sigma_y, sigma_z, sigma_id] + labels = ['X', 'Y', 'Z', 'I'] + + num_qubits = n + num = 1 + if num_qubits > 0: + basis_str = pauli[:] + label_str = labels[:] + pauli_basis = pauli[:] + pauli_label = labels[:] + while num < num_qubits: + length = len(basis_str) + for i in range(4): + for j in range(length): + basis_str.append(np.kron(basis_str[j], pauli_basis[i])) + label_str.append(label_str[j] + pauli_label[i]) + basis_str = basis_str[-1:-4**(num+1)-1:-1] + label_str = label_str[-1:-4**(num+1)-1:-1] + num += 1 + return basis_str, label_str + + +def decompose(matrix): + r"""生成 n 量子比特的泡利基空间 + + Args: + matrix (numpy.ndarray): 要分解的矩阵 + + Return: + pauli_form (list): 返回矩阵分解后的哈密顿量，形如 ``[[1, 'Z0, Z1'], [2, 'I']]`` + """ + if np.log2(len(matrix)) % 1 != 0: + print("Please input correct matrix!") + return -1 + basis_space, label_str = pauli_basis(np.log2(len(matrix))) + coefficients = [] # 对应的系数 + pauli_word = [] # 对应的label + pauli_form = [] # 输出pauli_str list形式：[[1, 'Z0, Z1'], [2, 'I']] + for i in range(len(basis_space)): + # 求系数 + a_ij = 1/len(matrix) * np.trace(matrix@basis_space[i]) + if a_ij != 0: + if a_ij.imag != 0: + coefficients.append(a_ij) + else: + coefficients.append(a_ij.real) + pauli_word.append(label_str[i]) + for i in range(len(coefficients)): + pauli_site = [] # 临时存放一个基 + pauli_site.append(coefficients[i]) + word = '' + for j in range(len(pauli_word[0])): + if pauli_word[i] == 'I'*int(np.log2(len(matrix))): + word = 'I' # 和Hamiltonian类似，若全是I就用一个I指代 + break + if pauli_word[i][j] == 'I': + continue # 如果是I就不加数字下标 + if j != 0 and len(word) != 0: + word += ',' + word += pauli_word[i][j] + word += str(j) # 对每一个label加标签，说明是作用在哪个比特 + pauli_site.append(word) # 添加上对应作用的门 + pauli_form.append(pauli_site) + + return pauli_form + + +class Hamiltonian: + r""" Paddle Quantum 中的 Hamiltonian ``class``。 + + 用户可以通过一个 Pauli string 来实例化该 ``class``。 + """ + def __init__(self, pauli_str, compress=True): + r""" 创建一个 Hamiltonian 类。 + + Args: + pauli_str (list): 用列表定义的 Hamiltonian，如 ``[(1, 'Z0, Z1'), (2, 'I')]`` + compress (bool): 是否对输入的 list 进行自动合并（例如 ``(1, 'Z0, Z1')`` 和 ``(2, 'Z1, Z0')`` 这两项将被自动合并），默认为 ``True`` + + Note: + 如果设置 ``compress=False``，则不会对输入的合法性进行检验。 + """ + self.__coefficients = None + self.__terms = None + self.__pauli_words_r = [] + self.__pauli_words = [] + self.__sites = [] + self.__nqubits = None + # when internally updating the __pauli_str, be sure to set __update_flag to True + self.__pauli_str = pauli_str + self.__update_flag = True + self.__decompose() + if compress: + self.__compress() + + def __getitem__(self, indices): + new_pauli_str = [] + if isinstance(indices, int): + indices = [indices] + elif isinstance(indices, slice): + indices = list(range(self.n_terms)[indices]) + elif isinstance(indices, tuple): + indices = list(indices) + + for index in indices: + new_pauli_str.append([self.coefficients[index], ','.join(self.terms[index])]) + return Hamiltonian(new_pauli_str, compress=False) + + def __add__(self, h_2): + new_pauli_str = self.pauli_str.copy() + if isinstance(h_2, float) or isinstance(h_2, int): + new_pauli_str.extend([[float(h_2), 'I']]) + else: + new_pauli_str.extend(h_2.pauli_str) + return Hamiltonian(new_pauli_str) + + def __mul__(self, other): + new_pauli_str = copy.deepcopy(self.pauli_str) + for i in range(len(new_pauli_str)): + new_pauli_str[i][0] *= other + return Hamiltonian(new_pauli_str, compress=False) + + def __sub__(self, other): + return self.__add__(other.__mul__(-1)) + + def __str__(self): + str_out = '' + for idx in range(self.n_terms): + str_out += '{} '.format(self.coefficients[idx]) + for _ in range(len(self.terms[idx])): + str_out += self.terms[idx][_] + if _ != len(self.terms[idx]) - 1: + str_out += ', ' + if idx != self.n_terms - 1: + str_out += '\n' + return str_out + + def __repr__(self): + return 'paddle_quantum.Hamiltonian object: \n' + self.__str__() + + @property + def n_terms(self): + r"""返回该哈密顿量的项数 + + Returns: + int :哈密顿量的项数 + """ + return len(self.__pauli_str) + + @property + def pauli_str(self): + r"""返回哈密顿量对应的 Pauli string + + Returns: + list : 哈密顿量对应的 Pauli string + """ + return self.__pauli_str + + @property + def terms(self): + r"""返回哈密顿量中的每一项构成的列表 + + Returns: + list :哈密顿量中的每一项，i.e. ``[['Z0, Z1'], ['I']]`` + """ + if self.__update_flag: + self.__decompose() + return self.__terms + else: + return self.__terms + + @property + def coefficients(self): + r""" 返回哈密顿量中的每一项对应的系数构成的列表 + + Returns: + list :哈密顿量中每一项的系数，i.e. ``[1.0, 2.0]`` + """ + if self.__update_flag: + self.__decompose() + return self.__coefficients + else: + return self.__coefficients + + @property + def pauli_words(self): + r"""返回哈密顿量中每一项对应的 Pauli word 构成的列表 + + Returns: + list :每一项对应的 Pauli word，i.e. ``['ZIZ', 'IIX']`` + """ + if self.__update_flag: + self.__decompose() + return self.__pauli_words + else: + return self.__pauli_words + + @property + def pauli_words_r(self): + r"""返回哈密顿量中每一项对应的简化（不包含 I） Pauli word 组成的列表 + + Returns: + list :不包含 "I" 的 Pauli word 构成的列表，i.e. ``['ZXZZ', 'Z', 'X']`` + """ + if self.__update_flag: + self.__decompose() + return self.__pauli_words_r + else: + return self.__pauli_words_r + + @property + def sites(self): + r"""返回该哈密顿量中的每一项对应的量子比特编号组成的列表 + + Returns: + list :哈密顿量中每一项所对应的量子比特编号构成的列表，i.e. ``[[1, 2], [0]]`` + """ + if self.__update_flag: + self.__decompose() + return self.__sites + else: + return self.__sites + + @property + def n_qubits(self): + r"""返回该哈密顿量对应的量子比特数 + + Returns: + int :量子比特数 + """ + if self.__update_flag: + self.__decompose() + return self.__nqubits + else: + return self.__nqubits + + def __decompose(self): + r"""将哈密顿量分解为不同的形式 + + Notes: + 这是一个内部函数，你不需要直接使用它 + 这是一个比较基础的函数，它负责将输入的 Pauli string 拆分为不同的形式并存储在内部变量中 + """ + self.__pauli_words = [] + self.__pauli_words_r = [] + self.__sites = [] + self.__terms = [] + self.__coefficients = [] + self.__nqubits = 1 + new_pauli_str = [] + for coefficient, pauli_term in self.__pauli_str: + pauli_word_r = '' + site = [] + single_pauli_terms = re.split(r',\s*', pauli_term.upper()) + self.__coefficients.append(float(coefficient)) + self.__terms.append(single_pauli_terms) + for single_pauli_term in single_pauli_terms: + match_I = re.match(r'I', single_pauli_term, flags=re.I) + if match_I: + assert single_pauli_term[0].upper() == 'I', \ + 'The offset is defined with a sole letter "I", i.e. (3.0, "I")' + pauli_word_r += 'I' + site.append('') + else: + match = re.match(r'([XYZ])([0-9]+)', single_pauli_term, flags=re.I) + if match: + pauli_word_r += match.group(1).upper() + assert int(match.group(2)) not in site, 'each Pauli operator should act on different qubit' + site.append(int(match.group(2))) + else: + raise Exception( + 'Operators should be defined with a string composed of Pauli operators followed' + + 'by qubit index on which it act, separated with ",". i.e. "Z0, X1"') + self.__nqubits = max(self.__nqubits, int(match.group(2)) + 1) + self.__pauli_words_r.append(pauli_word_r) + self.__sites.append(site) + new_pauli_str.append([float(coefficient), pauli_term.upper()]) + + for term_index in range(len(self.__pauli_str)): + pauli_word = ['I' for _ in range(self.__nqubits)] + site = self.__sites[term_index] + for site_index in range(len(site)): + if type(site[site_index]) == int: + pauli_word[site[site_index]] = self.__pauli_words_r[term_index][site_index] + self.__pauli_words.append(''.join(pauli_word)) + self.__pauli_str = new_pauli_str + self.__update_flag = False + + def __compress(self): + r""" 对同类项进行合并。 + + Notes: + 这是一个内部函数，你不需要直接使用它 + """ + if self.__update_flag: + self.__decompose() + else: + pass + new_pauli_str = [] + flag_merged = [False for _ in range(self.n_terms)] + for term_idx_1 in range(self.n_terms): + if not flag_merged[term_idx_1]: + for term_idx_2 in range(term_idx_1 + 1, self.n_terms): + if not flag_merged[term_idx_2]: + if self.pauli_words[term_idx_1] == self.pauli_words[term_idx_2]: + self.__coefficients[term_idx_1] += self.__coefficients[term_idx_2] + flag_merged[term_idx_2] = True + else: + pass + if self.__coefficients[term_idx_1] != 0: + new_pauli_str.append([self.__coefficients[term_idx_1], ','.join(self.__terms[term_idx_1])]) + self.__pauli_str = new_pauli_str + self.__update_flag = True + + def decompose_with_sites(self): + r"""将 pauli_str 分解为系数、泡利字符串的简化形式以及它们分别作用的量子比特下标。 + + Returns: + tuple: 包含如下元素的 tuple: + + - coefficients (list): 元素为每一项的系数 + - pauli_words_r (list): 元素为每一项的泡利字符串的简化形式，例如 'Z0, Z1, X3' 这一项的泡利字符串为 'ZZX' + - sites (list): 元素为每一项作用的量子比特下标，例如 'Z0, Z1, X3' 这一项的 site 为 [0, 1, 3] + + """ + if self.__update_flag: + self.__decompose() + return self.coefficients, self.__pauli_words_r, self.__sites + + def decompose_pauli_words(self): + r"""将 pauli_str 分解为系数和泡利字符串。 + + Returns: + tuple: 包含如下元素的 tuple: + + - coefficients(list): 元素为每一项的系数 + - pauli_words(list): 元素为每一项的泡利字符串，例如 'Z0, Z1, X3' 这一项的泡利字符串为 'ZZIX' + """ + if self.__update_flag: + self.__decompose() + else: + pass + return self.coefficients, self.__pauli_words + + def construct_h_matrix(self, qubit_num=None): + r"""构建 Hamiltonian 在 Z 基底下的矩阵。 + + Returns: + np.ndarray: Z 基底下的哈密顿量矩阵形式 + """ + coefs, pauli_words, sites = self.decompose_with_sites() + if qubit_num is None: + qubit_num = 1 + for site in sites: + if type(site[0]) is int: + qubit_num = max(qubit_num, max(site) + 1) + else: + assert qubit_num >= self.n_qubits, "输入的量子数不小于哈密顿量表达式中所对应的量子比特数" + n_qubit = qubit_num + h_matrix = np.zeros([2 ** n_qubit, 2 ** n_qubit], dtype='complex64') + spin_ops = SpinOps(n_qubit, use_sparse=True) + for idx in range(len(coefs)): + op = coefs[idx] * sparse.eye(2 ** n_qubit, dtype='complex64') + for site_idx in range(len(sites[idx])): + if re.match(r'X', pauli_words[idx][site_idx], re.I): + op = op.dot(spin_ops.sigx_p[sites[idx][site_idx]]) + elif re.match(r'Y', pauli_words[idx][site_idx], re.I): + op = op.dot(spin_ops.sigy_p[sites[idx][site_idx]]) + elif re.match(r'Z', pauli_words[idx][site_idx], re.I): + op = op.dot(spin_ops.sigz_p[sites[idx][site_idx]]) + h_matrix += op + return h_matrix + + +class SpinOps: + r"""矩阵表示下的自旋算符，可以用来构建哈密顿量矩阵或者自旋可观测量。 - Args: - state (numpy.ndarray or paddle.Tensor): 输入的量子态，可以支持态矢量和密度矩阵, - 该函数下，列表内每一个量子态对应一张单独的图片 - which_qubits(list or None):若为多量子比特，则给出要展示的量子比特，默认为 None，表示全展示 - show_arrow (bool): 是否展示向量的箭头，默认为 ``False`` - save_gif (bool): 是否存储 gif 动图，默认为 ``False`` - save_pic (bool): 是否存储静态图片，默认为 ``True`` - filename (str): 存储的 gif 动图的名字 - view_angle (list or tuple): 视图的角度， - 第一个元素为关于 xy 平面的夹角 [0-360]，第二个元素为关于 xz 平面的夹角 [0-360], 默认为 ``(30, 45)`` - view_dist (int): 视图的距离，默认为 7 - set_color (str): 若要设置指定的颜色，请查阅 ``cmap`` 表。默认为蓝色 """ - # Check input data - __input_args_dtype_check(show_arrow, save_gif, filename, view_angle, view_dist) - - assert type(state) == paddle.Tensor or type(state) == np.ndarray, \ - 'the type of "state" must be "paddle.Tensor" or "np.ndarray".' - assert type(set_color) == str, \ - 'the type of "set_color" should be "str".' - - n_qubits = int(np.log2(state.shape[0])) + def __init__(self, size: int, use_sparse=False): + r"""SpinOps 的构造函数，用于实例化一个 SpinOps 对象。 - if which_qubits is None: - which_qubits = list(range(n_qubits)) - else: - assert type(which_qubits)==list,'the type of which_qubits should be None or list' - assert 1<=len(which_qubits)<=n_qubits,'展示的量子数量需要小于n_qubits' - for i in range(len(which_qubits)): - assert 0<=which_qubits[i]=2 and state.size==state.shape[0]: - state_vector = state - state = np.outer(state_vector, np.conj(state_vector)) - - #多量子态分解 - if state.shape[0]>2: - rho = paddle.to_tensor(state) - tmp_s = [] - for q in which_qubits: - tmp_s.append(partial_trace_discontiguous(rho,[q])) - state = tmp_s - else: - state = [state] - state_len = len(state) - - # Calc the bloch_vectors - bloch_vector_list = [] - for i in range(state_len): - bloch_vector_tmp = __density_matrix_convert_to_bloch_vector(state[i]) - bloch_vector_list.append(bloch_vector_tmp) + Returns: + list : :math:`S^z_i` 算符组成的列表，其中每一项对应不同的 :math:`i` + """ + return self.__sigz_p - # List must be converted to array for slicing. - bloch_vectors = np.array(bloch_vector_list) + @property + def sigy_p(self): + r""" :math:`Z` 基底下的 :math:`S^y_i` 算符。 - # A update function for animation class - def update(frame): - view_rotating_angle = 5 - new_view_angle = [view_angle[0], view_angle[1] + view_rotating_angle * frame] - __plot_bloch_sphere( - ax, bloch_vectors, show_arrow, clear_plt=True, - view_angle=new_view_angle, view_dist=view_dist, set_color=set_color - ) + Returns: + list : :math:`S^y_i` 算符组成的列表，其中每一项对应不同的 :math:`i` + """ + return self.__sigy_p - # Dynamic update and save - if save_gif: - # Helper function to plot vectors on a sphere. - fig = plt.figure(figsize=(8, 8), dpi=100) - fig.subplots_adjust(left=0, right=1, bottom=0, top=1) - ax = fig.add_subplot(111, projection='3d') + @property + def sigx_p(self): + r""" :math:`Z` 基底下的 :math:`S^x_i` 算符。 - frames_num = 7 - anim = animation.FuncAnimation(fig, update, frames=frames_num, interval=600, repeat=False) - anim.save(filename, dpi=100, writer='pillow') - # close the plt - plt.close(fig) + Returns: + list : :math:`S^x_i` 算符组成的列表，其中每一项对应不同的 :math:`i` + """ + return self.__sigx_p - # Helper function to plot vectors on a sphere. - fig = plt.figure(figsize=(8, 8), dpi=100) - fig.subplots_adjust(left=0, right=1, bottom=0, top=1) - dim = np.ceil(sqrt(len(which_qubits))) - for i in range(1,len(which_qubits)+1): - ax = fig.add_subplot(dim,dim,i,projection='3d') - bloch_vector=np.array([bloch_vectors[i-1]]) - __plot_bloch_sphere( - ax, bloch_vector, show_arrow, clear_plt=True, - view_angle=view_angle, view_dist=view_dist, set_color=set_color - ) - if save_pic: - plt.savefig('n_qubit_state_in_bloch.png',bbox_inches='tight') - plt.show() + def __direct_prod_op(self, spin_op, spin_index): + r"""直积，得到第 n 个自旋（量子比特）上的自旋算符 -def plot_state_in_bloch_sphere( - state, - show_arrow=False, - save_gif=False, - filename=None, - view_angle=None, - view_dist=None, - set_color=None + Args: + spin_op: 单体自旋算符 + spin_index: 标记第 n 个自旋（量子比特） + + Returns: + scipy.sparse or np.ndarray: 直积后的自旋算符，其数据类型取决于 self.__use_sparse + """ + s_p = copy.copy(spin_op) + for i in range(self.size): + if i < spin_index: + s_p = sparse.kron(self.id, s_p) + elif i > spin_index: + s_p = sparse.kron(s_p, self.id) + if self.__sparse: + return s_p + else: + return s_p.toarray() + + +def __input_args_dtype_check( + show_arrow, + save_gif, + filename, + view_angle, + view_dist ): - r"""将输入的量子态展示在 Bloch 球面上 + r""" + 该函数实现对输入默认参数的数据类型检查，保证输入函数中的参数为所允许的数据类型 Args: - state (list(numpy.ndarray or paddle.Tensor)): 输入的量子态列表，可以支持态矢量和密度矩阵 - show_arrow (bool): 是否展示向量的箭头，默认为 ``False`` - save_gif (bool): 是否存储 gif 动图，默认为 ``False`` + show_arrow (bool): 是否展示向量的箭头，默认为 False + save_gif (bool): 是否存储 gif 动图 filename (str): 存储的 gif 动图的名字 view_angle (list or tuple): 视图的角度， - 第一个元素为关于 xy 平面的夹角 [0-360]，第二个元素为关于 xz 平面的夹角 [0-360], 默认为 ``(30, 45)`` + 第一个元素为关于xy平面的夹角[0-360],第二个元素为关于xz平面的夹角[0-360], 默认为 (30, 45) view_dist (int): 视图的距离，默认为 7 - set_color (str): 若要设置指定的颜色，请查阅 ``cmap`` 表。默认为红色到黑色的渐变颜色 """ - # Check input data - __input_args_dtype_check(show_arrow, save_gif, filename, view_angle, view_dist) - - assert type(state) == list or type(state) == paddle.Tensor or type(state) == np.ndarray, \ - 'the type of "state" must be "list" or "paddle.Tensor" or "np.ndarray".' - if type(state) == paddle.Tensor or type(state) == np.ndarray: - state = [state] - state_len = len(state) - assert state_len >= 1, '"state" is NULL.' - for i in range(state_len): - assert type(state[i]) == paddle.Tensor or type(state[i]) == np.ndarray, \ - 'the type of "state[i]" should be "paddle.Tensor" or "numpy.ndarray".' - if set_color is not None: - assert type(set_color) == str, \ - 'the type of "set_color" should be "str".' - - # Assign a value to an empty variable - if filename is None: - filename = 'state_in_bloch_sphere.gif' - if view_angle is None: - view_angle = (30, 45) - if view_dist is None: - view_dist = 7 - # Convert Tensor to numpy - for i in range(state_len): - if type(state[i]) == paddle.Tensor: - state[i] = state[i].numpy() - - # Convert state_vector to density_matrix - for i in range(state_len): - if state[i].size == 2: - state_vector = state[i] - state[i] = np.outer(state_vector, np.conj(state_vector)) + if show_arrow is not None: + assert type(show_arrow) == bool, \ + 'the type of "show_arrow" should be "bool".' + if save_gif is not None: + assert type(save_gif) == bool, \ + 'the type of "save_gif" should be "bool".' + if save_gif: + if filename is not None: + assert type(filename) == str, \ + 'the type of "filename" should be "str".' + other, ext = os.path.splitext(filename) + assert ext == '.gif', 'The suffix of the file name must be "gif".' + # If it does not exist, create a folder + path, file = os.path.split(filename) + if not os.path.exists(path): + os.makedirs(path) + if view_angle is not None: + assert type(view_angle) == list or type(view_angle) == tuple, \ + 'the type of "view_angle" should be "list" or "tuple".' + for i in range(2): + assert type(view_angle[i]) == int, \ + 'the type of "view_angle[0]" and "view_angle[1]" should be "int".' + if view_dist is not None: + assert type(view_dist) == int, \ + 'the type of "view_dist" should be "int".' - # Calc the bloch_vectors - bloch_vector_list = [] - for i in range(state_len): - bloch_vector_tmp = __density_matrix_convert_to_bloch_vector(state[i]) - bloch_vector_list.append(bloch_vector_tmp) - # List must be converted to array for slicing. - bloch_vectors = np.array(bloch_vector_list) +class QuantumFisher: + r"""量子费舍信息及相关量的计算器。 - # A update function for animation class - def update(frame): - view_rotating_angle = 5 - new_view_angle = [view_angle[0], view_angle[1] + view_rotating_angle * frame] - __plot_bloch_sphere( - ax, bloch_vectors, show_arrow, clear_plt=True, - view_angle=new_view_angle, view_dist=view_dist, set_color=set_color - ) + Attributes: + cir (UAnsatz): 需要计算量子费舍信息的参数化量子电路 + """ + def __init__(self, cir): + r"""QuantumFisher 的构造函数，用于实例化一个量子费舍信息的计算器。 - # Dynamic update and save - if save_gif: - # Helper function to plot vectors on a sphere. - fig = plt.figure(figsize=(8, 8), dpi=100) - fig.subplots_adjust(left=0, right=1, bottom=0, top=1) - ax = fig.add_subplot(111, projection='3d') + Args: + cir (UAnsatz): 需要计算量子费舍信息的参数化量子电路 + """ + self.cir = cir - frames_num = 7 - anim = animation.FuncAnimation(fig, update, frames=frames_num, interval=600, repeat=False) - anim.save(filename, dpi=100, writer='pillow') - # close the plt - plt.close(fig) + def get_qfisher_matrix(self): + r"""利用二阶参数平移规则计算量子费舍信息矩阵。 - # Helper function to plot vectors on a sphere. - fig = plt.figure(figsize=(8, 8), dpi=100) - fig.subplots_adjust(left=0, right=1, bottom=0, top=1) - + Returns: + numpy.ndarray: 量子费舍信息矩阵 - ax = fig.add_subplot(111, projection='3d') - __plot_bloch_sphere( - ax, bloch_vectors, show_arrow, clear_plt=True, - view_angle=view_angle, view_dist=view_dist, set_color=set_color - ) + 代码示例: - plt.show() + .. code-block:: python + import paddle + from paddle_quantum.circuit import UAnsatz + from paddle_quantum.utils import QuantumFisher -def plot_rotation_in_bloch_sphere( - init_state, - rotating_angle, - show_arrow=False, - save_gif=False, - filename=None, - view_angle=None, - view_dist=None, - color_scheme=None, -): - r"""在 Bloch 球面上刻画从初始量子态开始的旋转轨迹 + cir = UAnsatz(1) + cir.ry(theta=paddle.to_tensor(0., dtype="float64", stop_gradient=False), + which_qubit=0) + cir.rz(theta=paddle.to_tensor(0., dtype="float64", stop_gradient=False), + which_qubit=0) - Args: - init_state (numpy.ndarray or paddle.Tensor): 输入的初始量子态，可以支持态矢量和密度矩阵 - rotating_angle (list(float)): 旋转角度 ``[theta, phi, lam]`` - show_arrow (bool): 是否展示向量的箭头，默认为 ``False`` - save_gif (bool): 是否存储 gif 动图，默认为 ``False`` - filename (str): 存储的 gif 动图的名字 - view_angle (list or tuple): 视图的角度， - 第一个元素为关于 xy 平面的夹角 [0-360]，第二个元素为关于 xz 平面的夹角 [0-360], 默认为 ``(30, 45)`` - view_dist (int): 视图的距离，默认为 7 - color_scheme (list(str,str,str)): 分别是初始颜色，轨迹颜色，结束颜色。若要设置指定的颜色，请查阅 ``cmap`` 表。默认为红色 - """ - # Check input data - __input_args_dtype_check(show_arrow, save_gif, filename, view_angle, view_dist) + qf = QuantumFisher(cir) + qfim = qf.get_qfisher_matrix() + print(f'The QFIM at {cir.get_param().tolist()} is \n {qfim}.') - assert type(init_state) == paddle.Tensor or type(init_state) == np.ndarray, \ - 'the type of input data should be "paddle.Tensor" or "numpy.ndarray".' - assert type(rotating_angle) == tuple or type(rotating_angle) == list, \ - 'the type of rotating_angle should be "tuple" or "list".' - assert len(rotating_angle) == 3, \ - 'the rotating_angle must include [theta=paddle.Tensor, phi=paddle.Tensor, lam=paddle.Tensor].' - for i in range(3): - assert type(rotating_angle[i]) == paddle.Tensor or type(rotating_angle[i]) == float, \ - 'the rotating_angle must include [theta=paddle.Tensor, phi=paddle.Tensor, lam=paddle.Tensor].' - if color_scheme is not None: - assert type(color_scheme) == list and len(color_scheme) <= 3, \ - 'the type of "color_scheme" should be "list" and ' \ - 'the length of "color_scheme" should be less than or equal to "3".' - for i in range(len(color_scheme)): - assert type(color_scheme[i]) == str, \ - 'the type of "color_scheme[i] should be "str".' + :: - # Assign a value to an empty variable - if filename is None: - filename = 'rotation_in_bloch_sphere.gif' + The QFIM at [0.0, 0.0] is + [[1. 0.] + [0. 0.]]. + """ + # Get the real-time parameters from the UAnsatz class + list_param = self.cir.get_param().tolist() + num_param = len(list_param) + # Initialize a numpy array to record the QFIM + qfim = np.zeros((num_param, num_param)) + # Assign the signs corresponding to the four terms in a QFIM element + list_sign = [[1, 1], [1, -1], [-1, 1], [-1, -1]] + # Run the circuit and record the current state vector + psi = self.cir.run_state_vector().numpy() + # For each QFIM element + for i in range(0, num_param): + for j in range(i, num_param): + # For each term in each element + for sign_i, sign_j in list_sign: + # Shift the parameters by pi/2 * sign + list_param[i] += np.pi / 2 * sign_i + list_param[j] += np.pi / 2 * sign_j + # Update the parameters in the circuit + self.cir.update_param(list_param) + # Run the shifted circuit and record the shifted state vector + psi_shift = self.cir.run_state_vector().numpy() + # Calculate each term as the fidelity with a sign factor + qfim[i][j] += abs(np.vdot( + psi_shift, psi))**2 * sign_i * sign_j * (-0.5) + # De-shift the parameters + list_param[i] -= np.pi / 2 * sign_i + list_param[j] -= np.pi / 2 * sign_j + self.cir.update_param(list_param) + if i != j: + # The QFIM is symmetric + qfim[j][i] = qfim[i][j] + + return qfim + + def get_qfisher_norm(self, direction, step_size=0.01): + r"""利用有限差分计算沿给定方向的量子费舍信息的投影。 - # Assign colors to bloch vectors - color_list = ['orangered', 'lightsalmon', 'darkred'] - if color_scheme is not None: - for i in range(len(color_scheme)): - color_list[i] = color_scheme[i] - set_init_color, set_trac_color, set_end_color = color_list + Args: + direction (list): 要计算量子费舍信息投影的方向 + step_size (float, optional): 有限差分的步长，默认为 0.01 - theta, phi, lam = rotating_angle + Returns: + float: 沿给定方向的量子费舍信息的投影 - # Convert Tensor to numpy - if type(init_state) == paddle.Tensor: - init_state = init_state.numpy() + 代码示例: - # Convert state_vector to density_matrix - if init_state.size == 2: - state_vector = init_state - init_state = np.outer(state_vector, np.conj(state_vector)) + .. code-block:: python - # Rotating angle - def rotating_operation(rotating_angle_each): - gate_matrix = simulator.u_gate_matrix(rotating_angle_each) - return np.matmul(np.matmul(gate_matrix, init_state), gate_matrix.conj().T) + import paddle + from paddle_quantum.circuit import UAnsatz + from paddle_quantum.utils import QuantumFisher - # Rotating angle division - rotating_frame = 50 - rotating_angle_list = [] - state = [] - for i in range(rotating_frame + 1): - angle_each = [theta / rotating_frame * i, phi / rotating_frame * i, lam / rotating_frame * i] - rotating_angle_list.append(angle_each) - state.append(rotating_operation(angle_each)) + cir = UAnsatz(2) + cir.ry(theta=paddle.to_tensor(0., dtype="float64", stop_gradient=False), + which_qubit=0) + cir.ry(theta=paddle.to_tensor(0., dtype="float64", stop_gradient=False), + which_qubit=1) + cir.cnot(control=[0, 1]) + cir.ry(theta=paddle.to_tensor(0., dtype="float64", stop_gradient=False), + which_qubit=0) + cir.ry(theta=paddle.to_tensor(0., dtype="float64", stop_gradient=False), + which_qubit=1) - state_len = len(state) - # Calc the bloch_vectors - bloch_vector_list = [] - for i in range(state_len): - bloch_vector_tmp = __density_matrix_convert_to_bloch_vector(state[i]) - bloch_vector_list.append(bloch_vector_tmp) + qf = QuantumFisher(cir) + v = [1,1,1,1] + qfi_norm = qf.get_qfisher_norm(direction=v) + print(f'The QFI norm along {v} at {cir.get_param().tolist()} is {qfi_norm:.7f}') - # List must be converted to array for slicing. - bloch_vectors = np.array(bloch_vector_list) + :: - # A update function for animation class - def update(frame): - frame = frame + 2 - if frame <= len(bloch_vectors) - 1: - __plot_bloch_sphere( - ax, bloch_vectors[1:frame], show_arrow=show_arrow, clear_plt=True, - rotating_angle_list=rotating_angle_list, - view_angle=view_angle, view_dist=view_dist, set_color=set_trac_color - ) + The QFI norm along [1, 1, 1, 1] at [0.0, 0.0, 0.0, 0.0] is 5.9996250 + """ + # Get the real-time parameters + list_param = self.cir.get_param().tolist() + # Run the circuit and record the current state vector + psi = self.cir.run_state_vector().numpy() + # Check whether the length of the input direction vector is equal to the number of the variational parameters + assert len(list_param) == len( + direction + ), "the length of direction vector should be equal to the number of the parameters" + # Shift the parameters by step_size * direction + array_params_shift = np.array( + list_param) + np.array(direction) * step_size + # Update the parameters in the circuit + self.cir.update_param(array_params_shift.tolist()) + # Run the shifted circuit and record the shifted state vector + psi_shift = self.cir.run_state_vector().numpy() + # Calculate quantum Fisher-Rao norm along the given direction + qfisher_norm = (1 - abs(np.vdot(psi_shift, psi))**2) * 4 / step_size**2 + # De-shift the parameters and update + self.cir.update_param(list_param) + + return qfisher_norm + + def get_eff_qdim(self, num_param_samples=4, tol=None): + r"""计算有效量子维数，即量子费舍信息矩阵的秩在整个参数空间的最大值。 - # The starting and ending bloch vector has to be shown - # show starting vector - __plot_bloch_sphere( - ax, bloch_vectors[:1], show_arrow=True, clear_plt=False, - view_angle=view_angle, view_dist=view_dist, set_color=set_init_color - ) + Args: + num_param_samples (int, optional): 用来估计有效量子维数时所用的参数样本量，默认为 4 + tol (float, optional): 奇异值的最小容差，低于此容差的奇异值认为是 0，默认为 None，其含义同 ``numpy.linalg.matrix_rank()`` - # Show ending vector - if frame == len(bloch_vectors): - __plot_bloch_sphere( - ax, bloch_vectors[frame - 1:frame], show_arrow=True, clear_plt=False, - view_angle=view_angle, view_dist=view_dist, set_color=set_end_color - ) + Returns: + int: 给定量子电路对应的有效量子维数 - if save_gif: - # Helper function to plot vectors on a sphere. - fig = plt.figure(figsize=(8, 8), dpi=100) - fig.subplots_adjust(left=0, right=1, bottom=0, top=1) - ax = fig.add_subplot(111, projection='3d') + 代码示例: - # Dynamic update and save - stop_frames = 15 - frames_num = len(bloch_vectors) - 2 + stop_frames - anim = animation.FuncAnimation(fig, update, frames=frames_num, interval=100, repeat=False) - anim.save(filename, dpi=100, writer='pillow') - # close the plt - plt.close(fig) + .. code-block:: python - # Helper function to plot vectors on a sphere. - fig = plt.figure(figsize=(8, 8), dpi=100) - fig.subplots_adjust(left=0, right=1, bottom=0, top=1) - ax = fig.add_subplot(111, projection='3d') + import paddle + from paddle_quantum.circuit import UAnsatz + from paddle_quantum.utils import QuantumFisher - # Draw the penultimate bloch vector - update(len(bloch_vectors) - 3) - # Draw the last bloch vector - update(len(bloch_vectors) - 2) + cir = UAnsatz(1) + cir.rz(theta=paddle.to_tensor(0., dtype="float64", stop_gradient=False), + which_qubit=0) + cir.ry(theta=paddle.to_tensor(0., dtype="float64", stop_gradient=False), + which_qubit=0) - plt.show() + qf = QuantumFisher(cir) + print(cir) + print(f'The number of parameters of -Rz-Ry- is {len(cir.get_param().tolist())}') + print(f'The effective quantum dimension -Rz-Ry- is {qf.get_eff_qdim()}') + :: -def pauli_basis(n): - r"""生成 n 量子比特的泡利基空间 - Args: - n (int): 量子比特的数量 + --Rz(0.000)----Ry(0.000)-- - Return: - tuple: - basis_str: 泡利基空间的一组基底表示（array形式） - label_str: 泡利基空间对应的一组基底表示（标签形式），形如``[ 'X', 'Y', 'Z', 'I']`` - """ - sigma_x = np.array([[0, 1], [1, 0]], dtype=np.complex128) - sigma_y = np.array([[0, -1j], [1j, 0]], dtype=np.complex128) - sigma_z = np.array([[1, 0], [0, -1]], dtype=np.complex128) - sigma_id = np.array([[1, 0], [0, 1]], dtype=np.complex128) - pauli = [sigma_x, sigma_y, sigma_z, sigma_id] - labels = ['X', 'Y', 'Z', 'I'] + The number of parameters of -Rz-Ry- is 2 + The effective quantum dimension -Rz-Ry- is 1 + """ + # Get the real-time parameters + list_param = self.cir.get_param().tolist() + num_param = len(list_param) + # Generate random parameters + param_samples = 2 * np.pi * np.random.random( + (num_param_samples, num_param)) + # Record the ranks + list_ranks = [] + # Here it has been assumed that the set of points that do not maximize the rank of QFIMs, as singularities, form a null set. + # Thus one can find the maximal rank using a few samples. + for param in param_samples: + # Set the random parameters + self.cir.update_param(param.tolist()) + # Calculate the ranks + list_ranks.append(self.get_qfisher_rank(tol)) + # Recover the original parameters + self.cir.update_param(list_param) + + return max(list_ranks) + + def get_qfisher_rank(self, tol=None): + r"""计算量子费舍信息矩阵的秩。 - num_qubits = n - num = 1 - if num_qubits > 0: - basis_str = pauli[:] - label_str = labels[:] - pauli_basis = pauli[:] - palui_label = labels[:] - while num < num_qubits: - length = len(basis_str) - for i in range(4): - for j in range(length): - basis_str.append(np.kron(basis_str[j], pauli_basis[i])) - label_str.append(label_str[j] + palui_label[i]) - basis_str = basis_str[-1:-4**(num+1)-1:-1] - label_str = label_str[-1:-4**(num+1)-1:-1] - num += 1 - return basis_str, label_str + Args: + tol (float, optional): 奇异值的最小容差，低于此容差的奇异值认为是 0，默认为 None，其含义同 ``numpy.linalg.matrix_rank()`` + Returns: + int: 量子费舍信息矩阵的秩 + """ + qfisher_rank = np.linalg.matrix_rank(self.get_qfisher_matrix(), + tol, + hermitian=True) + return qfisher_rank -def decompose(matrix): - r"""生成 n 量子比特的泡利基空间 - Args: - matrix (numpy.ndarray): 要分解的矩阵 - Return: - pauli_form (list): 返回矩阵分解后的哈密顿量，形如 ``[[1, 'Z0, Z1'], [2, 'I']]`` +class ClassicalFisher: + r"""经典费舍信息及相关量的计算器。 + + Attributes: + model (paddle.nn.Layer): 经典或量子神经网络模型的实例 + num_thetas (int): 参数集合的数量 + num_inputs (int): 输入的样本数量 """ - if np.log2(len(matrix)) % 1 != 0: - print("Please input correct matrix!") - return -1 - basis_space, label_str = pauli_basis(np.log2(len(matrix))) - coefficients = [] # 对应的系数 - pauli_word = [] # 对应的label - pauli_form = [] # 输出pauli_str list形式：[[1, 'Z0, Z1'], [2, 'I']] - for i in range(len(basis_space)): - # 求系数 - a_ij = 1/len(matrix) * np.trace(matrix@basis_space[i]) - if a_ij != 0: - if a_ij.imag != 0: - coefficients.append(a_ij) + def __init__(self, + model, + num_thetas, + num_inputs, + model_type='quantum', + **kwargs): + r"""ClassicalFisher 的构造函数，用于实例化一个经典费舍信息的计算器。 + + Args: + model (paddle.nn.Layer): 经典或量子神经网络模型的实例 + num_thetas (int): 参数集合的数量 + num_inputs (int): 输入的样本数量 + model_type (str, optional): 模型是经典 "classical" 的还是量子 "quantum" 的，默认是量子的 + + Note: + 这里 ``**kwargs`` 包含如下选项: + - size (list): 经典神经网络各层神经元的数量 + - num_qubits (int): 量子神经网络量子比特的数量 + - depth (int): 量子神经网络的深度 + - encoding (str): 量子神经网络中经典数据的编码方式，目前支持 "IQP" 和 "re-uploading" + + Raises: + ValueError: 不被支持的编码方式 + ValueError: 不被支持的模型类别 + """ + self.model = model + self.num_thetas = num_thetas + self.num_inputs = num_inputs + self._model_type = model_type + if self._model_type == 'classical': + layer_dims = kwargs['size'] + self.model_args = [layer_dims] + self.input_size = layer_dims[0] + self.output_size = layer_dims[-1] + self.num_params = sum(layer_dims[i] * layer_dims[i + 1] + for i in range(len(layer_dims) - 1)) + elif self._model_type == 'quantum': + num_qubits = kwargs['num_qubits'] + depth = kwargs['depth'] + # Supported QNN encoding: ‘IQP' and 're-uploading' + encoding = kwargs['encoding'] + self.model_args = [num_qubits, depth, encoding] + self.input_size = num_qubits + # Default dimension of output layer = 1 + self.output_size = 1 + # Determine the number of model parameters for different encoding types + if encoding == 'IQP': + self.num_params = 3 * depth * num_qubits + elif encoding == 're-uploading': + self.num_params = 3 * (depth + 1) * num_qubits else: - coefficients.append(a_ij.real) - pauli_word.append(label_str[i]) - for i in range(len(coefficients)): - pauli_site = [] # 临时存放一个基 - pauli_site.append(coefficients[i]) - word = '' - for j in range(len(pauli_word[0])): - if pauli_word[i] == 'I'*int(np.log2(len(matrix))): - word = 'I' # 和Hamiltonian类似，若全是I就用一个I指代 - break - if pauli_word[i][j] == 'I': - continue # 如果是I就不加数字下标 - if j != 0 and len(word) != 0: - word += ',' - word += pauli_word[i][j] - word += str(j) # 对每一个label加标签，说明是作用在哪个比特 - pauli_site.append(word) # 添加上对应作用的门 - pauli_form.append(pauli_site) + raise ValueError('Non-existent encoding method') + else: + raise ValueError( + 'The model type should be equal to either classical or quantum' + ) - return pauli_form + # Generate random data + np.random.seed(0) + x = np.random.normal(0, 1, size=(num_inputs, self.input_size)) + # Use the same input data for each theta set + self.x = np.tile(x, (num_thetas, 1)) -def plot_density_graph(density_matrix: Union[paddle.Tensor, np.ndarray], - size: Optional[float]=.3) -> plt.Figure: - r"""密度矩阵可视化工具。 - Args: - density_matrix (numpy.ndarray or paddle.Tensor): 多量子比特的量子态的状态向量或者密度矩阵,要求量子数大于1 - size (float): 条宽度，在0到1之间，默认0.3 - Returns: - plt.Figure: 对应的密度矩阵可视化3D直方图 - """ - if not isinstance(density_matrix, (np.ndarray, paddle.Tensor)): - msg = f'Expected density_matrix to be np.ndarray or paddle.Tensor, but got {type(density_matrix)}' - raise TypeError(msg) - if isinstance(density_matrix, paddle.Tensor): - density_matrix = density_matrix.numpy() - if density_matrix.shape[0] != density_matrix.shape[1]: - msg = f'Expected density matrix dim0 equal to dim1, but got dim0={density_matrix.shape[0]}, dim1={density_matrix.shape[1]}' - raise ValueError(msg) + def get_gradient(self, x): + r"""计算输出层关于变分参数的梯度。 - real = density_matrix.real - imag = density_matrix.imag + Args: + x (numpy.ndarray): 输入样本 - figure = plt.figure() - ax_real = figure.add_subplot(121, projection='3d', title="real") - ax_imag = figure.add_subplot(122, projection='3d', title="imag") + Returns: + numpy.ndarray: 输出层关于变分参数的梯度，数组形状为（输入样本数量, 输出层维数, 变分参数数量） + """ + if not paddle.is_tensor(x): + x = paddle.to_tensor(x, stop_gradient=True) + gradvectors = [] + seed = 0 + + pbar = tqdm(desc="running in get_gradient: ", + total=len(x), + ncols=100, + ascii=True) + + for m in range(len(x)): + pbar.update(1) + if m % self.num_inputs == 0: + seed += 1 + paddle.seed(seed) + net = self.model(*self.model_args) + output = net(x[m]) + logoutput = paddle.log(output) + grad = [] + for i in range(self.output_size): + net.clear_gradients() + logoutput[i].backward(retain_graph=True) + grads = [] + for param in net.parameters(): + grads.append(param.grad.reshape((-1, ))) + gr = paddle.concat(grads) + grad.append(gr * paddle.sqrt(output[i])) + jacobian = paddle.concat(grad) + # Jacobian matrix corresponding to each data point + jacobian = paddle.reshape(jacobian, + (self.output_size, self.num_params)) + gradvectors.append(jacobian.detach().numpy()) + + pbar.close() + + return gradvectors + + def get_cfisher(self, gradients): + r"""利用雅可比矩阵计算经典费舍信息矩阵。 - xx, yy = np.meshgrid( - list(range(real.shape[0])), list(range(real.shape[1]))) - xx, yy = xx.ravel(), yy.ravel() - real = real.reshape(-1) - imag = imag.reshape(-1) + Args: + gradients (numpy.ndarray): 输出层关于变分参数的梯度, 数组形状为（输入样本数量, 输出层维数, 变分参数数量） - ax_real.bar3d(xx, yy, np.zeros_like(real), size, size, np.abs(real)) - ax_imag.bar3d(xx, yy, np.zeros_like(imag), size, size, np.abs(imag)) + Returns: + numpy.ndarray: 经典费舍信息矩阵，数组形状为（输入样本数量, 变分参数数量, 变分参数数量） + """ + fishers = np.zeros((len(gradients), self.num_params, self.num_params)) + for i in range(len(gradients)): + grads = gradients[i] + temp_sum = np.zeros( + (self.output_size, self.num_params, self.num_params)) + for j in range(self.output_size): + temp_sum[j] += np.array( + np.outer(grads[j], np.transpose(grads[j]))) + fishers[i] += np.sum(temp_sum, axis=0) - return figure + return fishers -def img_to_density_matrix(img_file): - r"""将图片编码为密度矩阵 - Args: - img_file: 图片文件 + def get_normalized_cfisher(self): + r"""计算归一化的经典费舍信息矩阵。 - Return: - rho:密度矩阵 `` - """ - img_matrix = matplotlib.image.imread(img_file) - - #将图片转为灰度图 - img_matrix = img_matrix.mean(axis=2) - - #填充矩阵,使其变为[2**n,2**n]的矩阵 - length = int(2**np.ceil(np.log2(np.max(img_matrix.shape)))) - img_matrix = np.pad(img_matrix,((0,length-img_matrix.shape[0]),(0,length-img_matrix.shape[1])),'constant') - #trace为1的密度矩阵 - rho = img_matrix@img_matrix.T - rho = rho/np.trace(rho) - return rho + Returns: + numpy.ndarray: 归一化的经典费舍信息矩阵，数组形状为（输入样本数量, 变分参数数量, 变分参数数量） + """ + grads = self.get_gradient(self.x) + fishers = self.get_cfisher(grads) + fisher_trace = np.trace(np.average(fishers, axis=0)) + # Average over input data + fisher = np.average(np.reshape(fishers, + (self.num_thetas, self.num_inputs, + self.num_params, self.num_params)), + axis=1) + normalized_cfisher = self.num_params * fisher / fisher_trace + + return normalized_cfisher, fisher_trace + + def get_eff_dim(self, normalized_cfisher, list_num_samples, gamma=1): + r"""计算经典的有效维数。 + + Args: + normalized_cfisher (numpy.ndarray): 归一化的经典费舍信息矩阵 + list_num_samples (list): 不同样本量构成的列表 + gamma (int, optional): 有效维数定义中包含的一个人为可调参数，默认为 1 + + Returns: + list: 对于不同样本量的有效维数构成的列表 + """ + eff_dims = [] + for n in list_num_samples: + one_plus_F = np.eye( + self.num_params) + normalized_cfisher * gamma * n / ( + 2 * np.pi * np.log(n)) + det = np.linalg.slogdet(one_plus_F)[1] + r = det / 2 + eff_dims.append(2 * (logsumexp(r) - np.log(self.num_thetas)) / + np.log(gamma * n / (2 * np.pi * np.log(n)))) + + return eff_dims diff --git a/requirements.txt b/requirements.txt index 630d7b6..d1c6ce7 100644 --- a/requirements.txt +++ b/requirements.txt @@ -1,6 +1,8 @@ -paddlepaddle>=2.1.1 +paddlepaddle>=2.2.0 scipy networkx>=2.5 matplotlib>=3.3.0 interval -tqdm \ No newline at end of file +tqdm +openfermion +pyscf; platform_system == "Linux" or platform_system == "Darwin" diff --git a/setup.py b/setup.py index 5b6c2d9..c1ed5a2 100644 --- a/setup.py +++ b/setup.py @@ -23,7 +23,7 @@ with open("README.md", "r", encoding="utf-8") as fh: setuptools.setup( name='paddle-quantum', - version='2.1.2', + version='2.1.3', author='Institute for Quantum Computing, Baidu INC.', author_email='quantum@baidu.com', description='Paddle Quantum is a quantum machine learning (QML) toolkit developed based on Baidu PaddlePaddle.', @@ -48,7 +48,16 @@ setuptools.setup( 'paddle_quantum.mbqc.VQSVD.example': ['*.txt'], }, - install_requires=['paddlepaddle>=2.1.2', 'scipy', 'networkx>=2.5', 'matplotlib>=3.3.0', 'interval', 'tqdm'], + install_requires=[ + 'paddlepaddle>=2.2.0', + 'scipy', + 'networkx>=2.5', + 'matplotlib>=3.3.0', + 'interval', + 'tqdm', + 'openfermion', + 'pyscf; platform_system == "Linux" or platform_system == "Darwin"' + ], python_requires='>=3.6, <4', classifiers=[ 'Programming Language :: Python :: 3', diff --git a/test_and_documents/readme.md b/test_and_documents/readme.md deleted file mode 100644 index 6853f8b..0000000 --- a/test_and_documents/readme.md +++ /dev/null @@ -1,11 +0,0 @@ -- 通过在UAnsatz类中添加新的成员函数expand来实现扩展 - - -- 增加utils.plot_density_graph密度矩阵可视化工具。 -``` -Args: -density_matrix (numpy.ndarray or paddle.Tensor): 多量子比特的量子态的状态向量或者密度矩阵,要求量子数大于1 -size (float): 条宽度，在0到1之间，默认0.3 -Returns: -plt.Figure: 对应的密度矩阵可视化3D直方图 -``` \ No newline at end of file diff --git a/test_and_documents/test.py b/test_and_documents/test.py deleted file mode 100644 index 249ba61..0000000 --- a/test_and_documents/test.py +++ /dev/null @@ -1,62 +0,0 @@ -from paddle_quantum.circuit import UAnsatz -import matplotlib.pyplot as plt -from paddle_quantum.utils import plot_density_graph -import numpy as np -import paddle -import unittest - - -#density_matrix -def test_density_matrix(): - cir = UAnsatz(1) - cir.ry(paddle.to_tensor(1,dtype='float64'),0) - state = cir.run_density_matrix() - cir.expand(3) - print(cir.get_state()) - - cir2 = UAnsatz(3) - cir2.ry(paddle.to_tensor(1,dtype='float64'),0) - cir2.run_density_matrix() - print(cir2.get_state()) - -#state_vector -def test_state_vector(): - cir = UAnsatz(1) - cir.ry(paddle.to_tensor(1,dtype='float64'),0) - state = cir.run_state_vector() - cir.expand(3) - print(cir.get_state()) - - cir2 = UAnsatz(3) - cir2.ry(paddle.to_tensor(1,dtype='float64'),0) - cir2.run_state_vector() - print(cir2.get_state()) - - -class TestPlotDensityGraph(unittest.TestCase): - def setUp(self): - self.func = plot_density_graph - self.x_np = (np.random.rand(8, 8) + np.random.rand(8, 8) * 1j)-0.5-0.5j - self.x_tensor = paddle.to_tensor(self.x_np) - - def test_input_type(self): - self.assertRaises(TypeError, self.func, 1) - self.assertRaises(TypeError, self.func, [1, 2, 3]) - - def test_input_shape(self): - x = np.zeros((2, 3)) - self.assertRaises(ValueError, self.func, x) - - def test_ndarray_input_inputs(self): - res = self.func(self.x_np) - res.show() - - def test_tensor_input(self): - res = self.func(self.x_tensor) - res.show() - - -if __name__ == '__main__': - test_density_matrix() - test_state_vector() - unittest.main() \ No newline at end of file diff --git a/test_documents/test.py b/test_documents/test.py deleted file mode 100644 index 38b676c..0000000 --- a/test_documents/test.py +++ /dev/null @@ -1,16 +0,0 @@ -from paddle_quantum.utils import img_to_density_matrix -import paddle -import matplotlib.image -import numpy as np - - -img_file = '/home/aistudio/f1.jpeg' -rho = (img_to_density_matrix(img_file)) - -#半正定 -w,_=np.linalg.eig(rho) -print(all(w>=0)) -#迹为1 -print(np.trace(rho)) -#shape为[2**n,2**n] -print(rho.shape) diff --git a/test_documents/test_construct_h_matrix.py b/test_documents/test_construct_h_matrix.py deleted file mode 100644 index 399de22..0000000 --- a/test_documents/test_construct_h_matrix.py +++ /dev/null @@ -1,6 +0,0 @@ -from paddle_quantum.utils import Hamiltonian - -h = Hamiltonian([(1, 'Z0, Z1')]) - -print(h.construct_h_matrix()) -print(h.construct_h_matrix(4)) diff --git a/tutorial/combinatorial_optimization/DC-QAOA_CN.ipynb b/tutorial/combinatorial_optimization/DC-QAOA_CN.ipynb index d6d48fd..9386cb0 100644 --- a/tutorial/combinatorial_optimization/DC-QAOA_CN.ipynb +++ b/tutorial/combinatorial_optimization/DC-QAOA_CN.ipynb @@ -38,7 +38,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 14, "metadata": { "ExecuteTime": { "end_time": "2021-05-16T03:41:44.449329Z", @@ -50,6 +50,8 @@ "import networkx as nx # networkx的版本 >= 2.5\n", "import matplotlib.pyplot as plt\n", "from itertools import combinations\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\")\n", "\n", "# 将一个图形分割成两个有重合的分离顶点子图\n", "def NaiveLGP(g, k):\n", @@ -103,7 +105,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 15, "metadata": { "ExecuteTime": { "end_time": "2021-05-16T03:41:44.839484Z", @@ -113,7 +115,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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    " ] @@ -127,7 +129,7 @@ "n = 10\n", "G = nx.Graph()\n", "G.add_nodes_from([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n", - "G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 4), (4, 5),\n", + "G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (1, 7),\n", " (5, 6), (6, 7), (7, 8), (8, 9), (9, 0)])\n", " \n", "k = 9 # 设定量子比特的最大数量\n", @@ -149,7 +151,7 @@ " a.margins(0.20)\n", "nx.draw_networkx(G, pos=nx.circular_layout(G), ax=ax[0], **options, node_color=node_color1)\n", "nx.draw_networkx(S[0], pos=nx.circular_layout(S[0]), ax=ax[1], **options, node_color=node_color2)\n", - "nx.draw_networkx(S[1], pos=nx.circular_layout(S[1]), ax=ax[2], **options, node_color=node_color3)" + "nx.draw_networkx(S[1], pos=nx.circular_layout(S[1]), ax=ax[2], **options, node_color=node_color3)\n" ] }, { @@ -170,7 +172,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 16, "metadata": { "ExecuteTime": { "end_time": "2021-05-16T03:41:46.108438Z", @@ -214,7 +216,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 17, "metadata": { "ExecuteTime": { "end_time": "2021-05-16T03:42:41.303385Z", @@ -227,11 +229,11 @@ "output_type": "stream", "text": [ "第一个子图的最大割：\n", - "{'010xxxxxxx': 0.49999449162430293, '101xxxxxxx': 0.49999449162430293, '000xxxxxxx': 2.4202658690211183e-06, '111xxxxxxx': 2.420265869021086e-06, '110xxxxxxx': 1.544054913842632e-06, '011xxxxxxx': 1.5440549138425979e-06, '001xxxxxxx': 1.5440549138425754e-06, '100xxxxxxx': 1.5440549138424998e-06}\n", + "{'01010101xx': 0.07887396513978905, '10010101xx': 0.07887396513978903, '01101010xx': 0.078873965139789, '10101010xx': 0.078873965139789, '10101101xx': 0.040906327139884305, '01010010xx': 0.0409063271398843, '01010110xx': 0.04004434869249364, '10100101xx': 0.04004434869249363, '01011010xx': 0.040044348692493625, '10101001xx': 0.040044348692493625}\n", "第二个子图的最大割：\n", - "{'0x01010101': 0.14011845299520287, '1x10101010': 0.1401184529952028, '1x01010010': 0.04249785377879272, '0x10100101': 0.04249785377879272, '1x01011010': 0.0424978537787927, '0x10101101': 0.0424978537787927, '0x10101001': 0.036328002709709005, '1x01001010': 0.036328002709709, '0x10110101': 0.036328002709709, '1x01010110': 0.03632800270970896}\n", + "{'0xxxxxx101': 0.4556003303152275, '1xxxxxx010': 0.45560033031522745, '1xxxxxx100': 0.0254542520553071, '0xxxxxx011': 0.025454252055307092, '0xxxxxx110': 0.010740876742244158, '1xxxxxx001': 0.010740876742244157, '1xxxxxx000': 0.0022930869455346486, '0xxxxxx111': 0.002293086945534646, '0xxxxxx100': 0.002293086945534642, '1xxxxxx011': 0.002293086945534638}\n", "母图的最大割：\n", - "{'0101010101': 0.14011845299520287, '1010101010': 0.1401184529952028, '0001010101': 2.4202658690211183e-06, '1110101010': 2.420265869021086e-06, '1101010110': 1.544054913842632e-06, '1101001010': 1.544054913842632e-06, '1101011010': 1.544054913842632e-06, '1101010010': 1.544054913842632e-06, '0110110101': 1.5440549138425979e-06, '0110101001': 1.5440549138425979e-06}\n" + "{'0101010101': 0.07887396513978905, '1010101010': 0.078873965139789, '1010100100': 0.0254542520553071, '1010010100': 0.0254542520553071, '1010110100': 0.0254542520553071, '1001010100': 0.0254542520553071, '0101101011': 0.025454252055307092, '0101011011': 0.025454252055307092, '0101001011': 0.025454252055307092, '0110101011': 0.025454252055307092}\n" ] } ], @@ -281,16 +283,16 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "就以上例子来说，对于第一个子图而言，最有可能的几个最大割将包括 {'010xxxxxxx','101xxxxxxx'}，而第二个子图最有可能的最大割将包括 {'1x10101010','0x01010101'}。这些字符串中的 'x' 代表不在这个子图却在母图的顶点。从这个例子中我们看到，分离顶点0和2在第一个子图中可能的最大割，'010xxxxxxx'，中都属于 $S_0$，但它们在第二个子图的最大割，'1x10101010'，中都属于 $S_1$，所以它们无法整合。（虽然因为 $S_0$ 和 $S_1$ 的对称性，我们可以把他们进行反转从而进行整合，但是没有必要这么做。）\n", + "就以上例子来说，对于第一个子图而言，最有可能的几个最大割将包括 {'01010101xx', '10010101xx', '01101010xx', '10101010xx'}，而第二个子图最有可能的最大割将包括 {'0xxxxxx101,'1xxxxxx010'}。这些字符串中的 'x' 代表不在这个子图却在母图的顶点。\n", "\n", - "我们接着尝试整合第一个子图的第一个最大割 '010xxxxxxx' 和第二个子图的第二个最大割 '0x01010101'，此最大割即是'101xxxxxxx' 的对称组。我们发现在这两个字符串所代表的最大割当中，分离顶点0和2都属于 $S_0$，我们也可以从下图第一张和第二张图中看出。所以我们可以整合这两个最大割并得到母图的最大割，'0101010101'，如下图第三张图所示。\n", + "从这个例子中我们看到，分离顶点 0 和 7 在第一个子图中可能的最大割，'01010101xx' 中分别属于 $S_0$ 和 $S_1$，它们在第二个子图的最大割，'0xxxxxx101'，中也分别属于 $S_0$ 和 $S_1$，所以我们可以整合这两个最大割并得到母图的最大割，'0101010101'，如下图第三张图所示。\n", "\n", "以下为图形展示，前两个图为两个子图的最大割实例，最右的图为母图的最大割。红色点和蓝色点分别表示被分在在 $S_0$ 和 $S_1$ 中的顶点，虚线表示被切割的边。" ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 18, "metadata": { "ExecuteTime": { "end_time": "2021-05-16T03:42:41.647686Z", @@ -300,7 +302,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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    " ] @@ -311,8 +313,8 @@ ], "source": [ "# 计算出的两个子图的最大割\n", - "strr1 = '010xxxxxxx'\n", - "strr2 = '0x01010101' \n", + "strr1 = '01010101xx'\n", + "strr2 = '0xxxxxx101' \n", "strr = '0101010101'\n", "\n", "# 图形示例展示\n", @@ -353,7 +355,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 19, "metadata": { "ExecuteTime": { "end_time": "2021-05-16T03:44:13.784486Z", @@ -365,8 +367,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "最有可能的 t 个图形 G 的最大割: {'0101010101': 947, '1010101010': 920, '1001010010': 150, '1001010100': 150, '1001010110': 150, '1101010010': 136, '1101010100': 136, '1101010110': 136, '1101010101': 135, '1001010101': 135}\n", - "量子近似优化分治算法找到的图形 G 的（最有可能的）最大割: 0101010101\n" + "最有可能的 t 个图形 G 的最大割: {'1010101100': 419, '0101010011': 382, '0101011011': 368, '1010100100': 351, '0110101011': 303, '0101001011': 251, '1001010100': 247, '1010101010': 229, '0100101011': 227, '1011010100': 218}\n", + "量子近似优化分治算法找到的图形 G 的（最有可能的）最大割: 1010101100\n" ] } ], @@ -413,7 +415,7 @@ " out_cnt = [(k, int(s * v / cnt_sum)) for (k, v) in out_cnt]\n", "\n", " return out_cnt[0][0], dict(out_cnt)\n", - " \n", + "\n", "# 设定 量子近似优化算法 中的参数\n", "p = 2 # 量子电路的层数\n", "ITR = 100 # 训练迭代的次数\n", @@ -456,7 +458,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 20, "metadata": { "ExecuteTime": { "end_time": "2021-05-16T03:44:54.150187Z", @@ -468,7 +470,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "最有可能的 t 个图形 G 的最大割：{'00101': 549, '10110': 512, '00001': 510, '11110': 501, '01001': 471, '11010': 457}\n" + "最有可能的 t 个图形 G 的最大割：{'01001': 531, '00001': 504, '11110': 501, '10110': 494, '00101': 489, '11010': 481}\n" ] } ], @@ -494,7 +496,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 21, "metadata": { "ExecuteTime": { "end_time": "2021-05-11T07:06:44.690385Z", @@ -522,7 +524,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 26, "metadata": { "ExecuteTime": { "end_time": "2021-05-11T07:16:56.698522Z", @@ -538,29 +540,29 @@ "顶点编号 = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n", "\n", "随机图形 1\n", - "边 = [(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (2, 3), (2, 4), (2, 7), (3, 8), (3, 9), (4, 5), (5, 6), (5, 9), (6, 7), (6, 8)]\n", - "半正定规划找的最大割的上限: 14.773421849579332\n", - "量子近似优化分治算法找到的最大割分类: 0011011000, 最大割 = 14.0\n", + "边 = [(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 8), (1, 2), (1, 4), (1, 5), (1, 6), (1, 8), (1, 9), (2, 3), (2, 8), (3, 9), (4, 5), (4, 6), (5, 7), (5, 8), (6, 8), (7, 8)]\n", + "半正定规划找的最大割的上限: 16.366014900074795\n", + "量子近似优化分治算法找到的最大割分类: 0010100011, 最大割 = 14.0\n", "\n", "随机图形 2\n", - "边 = [(0, 1), (0, 2), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 4), (1, 6), (1, 7), (1, 8), (2, 4), (2, 5), (2, 7), (2, 9), (3, 6), (3, 8), (3, 9), (4, 5), (4, 6), (5, 7), (6, 9), (7, 9)]\n", - "半正定规划找的最大割的上限: 17.637249299053625\n", - "量子近似优化分治算法找到的最大割分类: 1010011010, 最大割 = 15.0\n", + "边 = [(0, 2), (0, 3), (0, 4), (0, 5), (0, 8), (1, 4), (1, 8), (1, 9), (2, 5), (2, 6), (2, 8), (3, 4), (3, 5), (3, 6), (3, 9), (4, 6), (4, 7), (4, 8), (5, 7), (6, 8), (7, 9), (8, 9)]\n", + "半正定规划找的最大割的上限: 17.401823913484183\n", + "量子近似优化分治算法找到的最大割分类: 1100111001, 最大割 = 16.0\n", "\n", "随机图形 3\n", - "边 = [(0, 1), (0, 2), (0, 4), (0, 5), (0, 7), (0, 8), (0, 9), (1, 4), (1, 5), (2, 7), (2, 8), (2, 9), (3, 5), (3, 6), (3, 8), (3, 9), (4, 5), (4, 6), (4, 9), (5, 6), (5, 8), (5, 9), (6, 7), (7, 8), (7, 9)]\n", - "半正定规划找的最大割的上限: 19.048588813917966\n", - "量子近似优化分治算法找到的最大割分类: 0010110100, 最大割 = 17.0\n", + "边 = [(0, 1), (0, 2), (0, 3), (0, 5), (0, 7), (0, 8), (1, 3), (1, 5), (1, 6), (1, 8), (2, 3), (2, 4), (2, 6), (2, 7), (2, 8), (3, 4), (3, 5), (3, 7), (3, 8), (5, 6), (5, 7), (6, 7), (7, 8), (8, 9)]\n", + "半正定规划找的最大割的上限: 17.481389612347442\n", + "量子近似优化分治算法找到的最大割分类: 0111000101, 最大割 = 17.0\n", "\n", "随机图形 4\n", - "边 = [(0, 3), (0, 6), (0, 7), (0, 8), (0, 9), (1, 2), (1, 5), (1, 7), (2, 6), (2, 7), (3, 4), (3, 7), (3, 8), (3, 9), (4, 5), (4, 8), (4, 9), (5, 6), (5, 9), (6, 7), (7, 9), (8, 9)]\n", - "半正定规划找的最大割的上限: 16.551132643953018\n", - "量子近似优化分治算法找到的最大割分类: 1010110100, 最大割 = 16.0\n", + "边 = [(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 4), (1, 5), (1, 7), (2, 3), (2, 4), (2, 6), (2, 7), (2, 8), (2, 9), (3, 6), (3, 8), (3, 9), (4, 5), (5, 6), (5, 7), (5, 9), (6, 9), (8, 9)]\n", + "半正定规划找的最大割的上限: 19.247444317293844\n", + "量子近似优化分治算法找到的最大割分类: 1110010000, 最大割 = 18.0\n", "\n", "随机图形 5\n", - "边 = [(0, 2), (0, 5), (0, 6), (0, 7), (0, 8), (1, 2), (1, 4), (1, 7), (2, 4), (2, 7), (2, 9), (3, 4), (3, 5), (3, 6), (3, 9), (4, 6), (4, 7), (4, 8), (5, 6), (5, 7), (5, 9), (6, 8), (7, 8), (8, 9)]\n", - "半正定规划找的最大割的上限: 18.19997280321202\n", - "量子近似优化分治算法找到的最大割分类: 1100110001, 最大割 = 17.0\n" + "边 = [(0, 3), (0, 5), (0, 6), (0, 7), (1, 3), (1, 5), (1, 7), (1, 8), (2, 7), (2, 9), (3, 4), (3, 6), (3, 7), (3, 8), (3, 9), (4, 6), (4, 7), (4, 8), (4, 9), (5, 7), (5, 8), (5, 9), (6, 7), (6, 9), (8, 9)]\n", + "半正定规划找的最大割的上限: 18.715743968566105\n", + "量子近似优化分治算法找到的最大割分类: 1111110000, 最大割 = 17.0\n" ] } ], @@ -609,7 +611,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 27, "metadata": { "ExecuteTime": { "end_time": "2021-05-11T07:16:56.935061Z", @@ -619,7 +621,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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    " ] @@ -693,6 +695,9 @@ ], "metadata": { "celltoolbar": "Raw Cell Format", + "interpreter": { + "hash": "3b61f83e8397e1c9fcea57a3d9915794102e67724879b24295f8014f41a14d85" + }, "kernelspec": { "display_name": "Python 3", "language": "python", @@ -708,7 +713,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.10" + "version": "3.7.11" }, "toc": { "base_numbering": 1, diff --git a/tutorial/combinatorial_optimization/DC-QAOA_EN.ipynb b/tutorial/combinatorial_optimization/DC-QAOA_EN.ipynb index 53f4c0b..06fca63 100644 --- a/tutorial/combinatorial_optimization/DC-QAOA_EN.ipynb +++ b/tutorial/combinatorial_optimization/DC-QAOA_EN.ipynb @@ -54,7 +54,8 @@ "import networkx as nx # version of networkx >= 2.5\n", "import matplotlib.pyplot as plt\n", "from itertools import combinations\n", - "\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\")\n", "# Partition a graph into two subgraphs\n", "def NaiveLGP(g, k):\n", " E = list(g.edges)\n", @@ -117,7 +118,7 @@ "outputs": [ { "data": { - "image/png": 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FrqqomVlG1Al2nAoz6ilwfiqPOuCgCJ4oY2BtRkT8KyJ2Ao4ADgVel3S4ixmVjpOpFpK0FfBfYFFgg4h4INOA7FsRMSUiTiCVk75c0jWSemYdl1lriIjZEXFvROxAahS5DvCOpMskrZlxeGbWxkhaD3gAHv8JdNwYeByYCuQr3z2TdL7qOWC7CPKXo7CiRcTjEbEjaWv44aSVqgFOqhaez0w1U+5szrmkaikDI+LubCOypuSSqD8Cu5LOso3OOCSzVidpOWAg8FPgWdK5qkd9rsrMyik3gfMP4NSIGDn3+/QmnfU8GOhFOks1EfgrMCSC11s/2rZJ0vbAOcDypPHtyIho9rbKXC+xI4D/AxYDZgAfA8OBByOYVeKQK5aTqWbIdZu+jnQ+6riIcJnOKiFpV+Aa0hv1aRExOeOQzFpdbjLoR8BJpBngwcAtETEty7jMrPbkKow+BvwmIoZnHY8VJknA9qSkallSUnVLU0mVxBq5639A2rrZrcElk0grkIOBwREUc2auqrSZZEqiK9ARmJQ7FNmM56gzqbv0j4ETI+L2MoZoZSJpUWAIsA1wREQ83vzn0hHoTvq9aTOzLFabch+cu5D6VW0EXA5cERHjMg3MzGpCrsroY8DFubOcVgVynw07kJKkpZmbVM2a/zq2B+4lJVDtF3DbelI1x10i+LrUMVeSmj4zJbGpxE0SU0mZ8pfATInnJA7IDZQLPFebAM+Tzh1s5ESqekXE+Ig4nDSAvCXXm6fhTMq3JFaU+J3E18A0Uvf1GRIfSZwksWirBG5WYpE8lGvwuBOwIjAmd75w/YzDM7MqlttWPBoY5kSquuQ+Gx4FtiVtDT8GeFXSIZLaA0hsBtwP9GDBiRRAV2AD4J9So9WrmlKTK1MS6wO3AqsAncn/P30SMAs4OYIRc5+rjsCvSL9MJwM3+3xB7ZC0BDAU2BQ4PCKenvsYiwLXk2buAbrkucUU0u/TcOCkCNyzwaqapKVIZ6oGAv8jbc14KCKaW3nLzNq43PvIP0mrGedlHI4tpNxKVV/SStVisNT58PkQKKr1TD1wcwQ/KWWMlaTmkimJbYAHSFuzmtMkro60p/NMSRuQBtOfAj+JiLHli9SyJGl/4FLgBuBsiEWBp0gHMTs34xZ1wAuk5eu8Hd7NqkluW/PBpBXczqStsTdGRF2WcZlZZcv1dnwUeCAifpV1PFY6uaRqZzhuGPxhVVik4I621VeHV16BO++EQw9t9HA9sGwEE8sYbmZqKpmSWA94BlikZc+MOhjxKBy5OXA6MMKrUbVP0tLAZdBzPfi0C3RbkdSAubnqSdWK9opodv8Ms4o2z4HkQcDmwNWkbTueXDKz+eQq5z4MPAmc4rFTbZLiFWh6K/hDD0HXrvDBB3mTqSnALyK4tFwxZqnWzkwNJ61I5bX66lBfDzfe2PARdYMf7QGDdomI4X4zaBtyh+4PhFGvQLuVaZBIHXccPPccTJ0KI0bkvUVXYDtgn7IHa9ZKcnvn/xERewNbkcoX/0/SjbmzpGZmSOpOOkPzH5xI1SyJtUGrNnXNQQfB+PEwunATmu7AiSUOrWLUTDIlsQ7poFvBrX3DhqXBcX4dp8Gfdi9HbFbJoj3stCN0afR7M3YsnHceDG+6sGt34LRyRWeWpYh4KyKOB1YDXgHukfSYpH3nHEo2s7Yn127hXuAt4HgnUjWtNxQ+H96jB/z2t3DyyQu8z/IljKmi1EwyRcp4C1bnW3DWrK7AIKlZFUqsdvwf0CnfA3/5C9xzD3z11QLvsZHEmqUOzKxSRMQ3EXEhsCqpnPoZpCqAJ0rqkW10Ztaacucr7yJVuv2Ji9XUvCZrEJx7Llx7LXzyyQLv05zz6FWplpKpH1LgvEsLsubOwMYljssq249IZT4XRgdg34UPxayyRcSMiLiVdJbqMFLvtvck/VHSStlGZ2bllqt4fAupKeuAhn2IrCZNhPz9WTfaCPr2hcGDm3Wfmi3W1ZLD9pWuZ6EHWpA1zwaWLGVQVvFKsezckdQ53KxNyG3peQp4SlJv4ATgRUmPAIMj4pks4zOz0stt7b2BNPH8g4hwa5C24TUKrCptvz307g0ffpj+eZFFoH17WHdd2HTTRpe/Ub4Qs1VLK1N5lyBbmDVD8xqRWe0o1WugliYmzJotIt6PiFNIff2eBkZKelrSDyX5dWFWAyS1A64BlgL2j4jpGYdkrSSCT4AnyLM6ddVVsNpq0KdP+rriCrj/fth110a3mQT8sdyxZqWWPujqyLNdq4VZs4CvyxqlVZovS3CPWaS942ZtVkRMBIZIGkqqcDkI+GPun6+JiPFZxmdmxcm1S7iUVIhm94iYmnFI1vr+SNrePV/rofr69DXH5MmpAvKXjUdWs4C7yxphhmppZephaNzrpwVZM6T/Hi+WNUqrNKOAyfkeaN8eOndOf8779zymkn7/zNq8iJgVEaMiYhtgf9I51HclXSJptYzDM7MWyCVSFwObAHtGxJSMQ7JsPAJ8BMxs6qJzzinYY+r3EYUrAla7WkqmLiKtTs2nvh4+/3zuVxNZ83Tgmgg849K23EaBLaJnnpl+V844I705TJ2avpfHJ0DBovtmbVVEPB8RhwAbkj5Qn5F0t6TtcoM0M6ts5wE7kFakJmYdjGUjgtlAX9LurSYTqgbqgPtIY/SapVppDSAhUr+DYmc+pwLrR/BO6aKyaiAxFPgpTZTWb8IU4MQImu5GZWZzmnweBpxEeu38Cbjd5y/MKo+kM4F+wHYRUYot8VblJFYC/gksTSqZXsDsgHZ1wE3AcRHUdNXHmkmmACR2Av4KdG3hU6cAN0QwsPRRWaWTWA54GViCJnop5DEDGAN8zyuaZs2XO8y+O+lc1TrAMODKiFhwVzczKztJp5AmGbeNiM+yjscqh0R34BDgdFJS1YVUgyGAqTCrAzw1CbbZH3gsIn9Z9VpSU8kUgMRhwBU0P6GqA0YDP6j1zNkKk9gA+BepiElztr9OBz4jJVLjyhmbWS2TtCFppeoHpG23QyKiZkvomlU6SccBp5BWpD7KOh6rTLkdYVuQ+g0uSdrh9Tm8eS+s9RRpa+grWcbYWmoumQKQ2BMYCSHQIgUum0pahbgKGOREyiRWBx5i7vJ1nlWqWbOh/VRSoZK9I1z90awUJC0DDASOAf4DDAYeiVr8kDKrUJKOBM4mJVLvZR2PVSdJZwHLR8QxWcfSGmoymQKQ6AIjL4DNj4JV2wHTcg+1Jx2euxS4PIKxmQVpFSc307IDcGruz2mkpWvB7M5w5yzYa5uIri9kGadZrZLUhbSFZBDptTcEuNnlmM3KS9IhwIXADhHxZtbxWPWStByp2W/viJiQdTzlVrPJFICkO4C/Q8xZbegIfAO8U8slGq00JJYAViT1VZgAfAB6Ejg+Ih7PNDizGper9teXlFRtStq+fVlEuKebWYlJ2p80ydw3Il7NOh6rfpJuBZ6KiEuyjqXcajaZktSTVBN/lYjwViwrCUlnACtFxLFZx2LWVkhaB/gZcBCp8ePgiHg506DMaoSkPYFrgV0j4r8Zh2M1QtI2wDXAOhHRqA9sLamlPlMN7Qs85kTKSuxW4ABJxZRRN7MiRMTrub33q5NaYPxN0mhJe+YqA5pZAxId0pGHpq7RzsBwYC8nUlZiT5COSuyUdSDlVssfQv2AkVkHYbUldyD3TWDnrGMxa2si4quI+D2wCjACOAd4XdLAXA8rszZNYl2JqyQmkarOTpaYIfG0xA8kOsy9VtuRxkn7RcSzWcVstSlXPGgYcFzWsZRbTW7zk7Q0acC7QkRMyToeqy2Sjgc2j4gfZR2LWVuWO1e1Delc1TbA1cClEfFJpoGZtbJcNdqRwPqk8+Ed8lw2iVSA6xTQG8A9QL+IGN1qgVqbImkR4ANg44j4MOt4yqVWV6YOBO53ImVlcgewp6RuWQdi1pZF8nhE/ADYnNTS4BVJN0v6bsbhmbUKie8Cz5MKtXQlfyIFqY/iYjDrMrjoEWCAEykrp4iYDNxIanlRs2o1meoH3JJ1EFabctXE/g3slXUsZpZExNsRcSKwKqkP3F2S/iVpP0ntMw7PrCwkVgMeAXrR7DFd+y7ws/YQa5cxNLM5LgOOlNQ560DKpeaSKUkrA2sDf886FqtpI0lJu5lVkIgYHxEXAasBQ0k9496SdFKuyqtZLbmKtOL0rUmT5v+aORMuaVScukNn4PcSy7VWoNY25XqWvUTaNVaTai6ZAg4G7oqI6VkHYjXtL8AOkhbLOhAzaywiZkbE7RGxBdAf2AJ4T9KfJPXONjqzhSfRG9iSBmO5Hj3mfi27LNTXwx13FLzNT8sbpRlQ44UoajGZ6o+r+FmZRcRE4GFg/6xjMbOmRcQzEXEQsDEwC/iPpDslbZUrYmFWjY4Hmvz93X9/GDcO/vWvvA93AU6ct8KfWZncBywvadOsAymHmkqmJK0HLAHkf9swKy1v9TOrIhHxYUScCvQGHgOuB/4t6WD3jrMq1B9o8hzKgAFwww1N3qM9qXiLWdlExCzgCmp0daqmSqNLOg/oEhE/zzoWq32SugCfAutFxNis4zGzlskVptiTVFp9VeBS4OqI+CbTwMyaQaKOVL0vr5VWgnffhdVXh/ffL3ibCcDhEdxd8gDN5iFpKVLT9dUi4qus4ymlmlmZym3VcKNeazURMRW4G/hhxqGYWREiYlZE3BMR2wP7AhsA70q6VNIamQZntmBNjuEOPRSeeKLJRArSNkFv87Oyi4gvgL8CR2QdS6nVTDIFbEZqRvdi1oFYm3ILaauFmVWxiHghIg4F1iPN1j8l6V5JO/hclVWoSU09eNhhcP31C7xHAF6JtdZyKXCspFrKP2oqmeoPjIxa2rdo1eBRYCVJq2cdiJktvIgYGxG/AlYG7if1SHlB0oBa7pNiVekRUkGVRrbYAlZYockqfnN0Ap4tcVxmhTxLSt53yzqQUqqJZCq37/2HuFGvtbKImAncgQtRmNWUiKiLiCtJK1W/BA4B3pf069zef7OsXQxMy/fAgAEwahRMntzk82cCIyOaXuEyK5XcgkfNlUmviQIUkvoCf4iI72Ydi7U9krYAhgPremXUrHZJWh84idQS4U5gSES8mmlQ1qZJvA6sXeTT64DvR/C/EoZk1iRJXYEPge9HxLtZx1MKNbEyRdri51Upy8ozpH4dG2UdiJmVT0T8LyKOAtYCPgIekfSQpN18rsoyMhCoL+J5dcDdTqSstUVEPXAdcGzGoZRM1a9M5cpTjwU2jIiPs47H2iZJvwc6RMRpWcdiZq0jd4aqH6m0ekdgCHBjbrBg1iokDgWupIky6Q3UAf8Gdo1gRtkCMytA0qqk38GVauH9shZWpnYHXnIiZRkbCRxcaxVqzKywiJgWEdcBfYATgL2BDySdK2m5LGOztiOCG4EDgcm5r0KmA1OB23EiZRnKbe97Fjg461hKoRYGfv3wFj/LWET8j1ROeausYzGz1hXJ6IjYE9gGWAJ4TdL1kvpkG521BRHcDyxNSurfIK0+TYDxABNJZdQvBdaN4AgnUlYBhgHH18IW6are5iepJ2nf+qq11k3Zqo+kM4DvRMTArGMxs2xJWhw4GjgeeAsYDNwXEbMzDczaBInVgGVg+yfhn32AMRFMzTgss2/ldvK8BRwSEc9kHc/CqPZk6lDghxGxV9axmElahbRsvXxEeNbPzJDUkbQFaxCwKPBn4LqIaLpotVkJSIqIqPqZf6tNkn4ObJRrmF61qn2bX3/SWRWzzEXEe6RZlr5Zx2JmlSEiZkTESGAz4AhgB1K/qgslfSfb6MzMMjUc2FPS0lkHsjCqNpnKNU3cErg361jM5nELKck3M/tW7lzVExGxPymx6gi8JOlWSd/PODwzs1YXEV8Do4Ajs45lYVTtNj9JA4GtI8IDV6sYkpYhHf5dISLqso7HzCqXpF7Aj4ETgU+BPwF3R8TMTAOzmuFtflbpJG0C/IVU/2BW1vEUo2pXpvAWP6tAEfE56dzUnlnHYmaVLSImRMRgYA3gYtK5qrclnZxLtMzMalpEvEDqF1u146aqTKYkrQysDfw961jM8vBWPzNrtoiYGRF3RcRWwA+B7wHvSRqSa25pZlbLhgHHZR1EsaoymSI1+borIqZnHYhZHn8BdpC0WNaBmFl1iYhnI6IfsBEwDXhW0ihJ29RCPxYzszzuADaStFbWgRSjKpIpic4Si0m0z33LjXqtYkXEBOARYD8kIXVDWpTUU8HMbIEi4qOIOB3oDYwmVb16TtIhkjqV4t8h0SH32dq5FPczMytGREwDrgUGAkhIYhGJHhIVP4lUsYM7iVUkLpaYQOrk/RkwQ5r+CZyyMvzvv9lGaFbYMfDkvXAu6Xd3IvA5MAPpZaRDkDx4MbMFiojJETEMWAs4h1T16l1JZ+QaA7eIRC+JEyU+AKaTPlvrJCZIXCSxckl/ADOzZulyBfQ9XJrxd2AG8A3wFTBDYrTEblJl5i0VV81PYingZmAbUrKXZwZu2gzoPBO4Ajg1gqqs/mE1KC1R3xqw5kzo1jH/VZNyf/6KiKGtFZqZ1QZJfYCTgH2AW4EhETGm6efQAbgIOBqYDXTPc9k0IIDHgEMi+Kp0UVsWXM3PqoHEDsD1UL88dGkHebc0TwKmAEdFcH/rRti0ikqmcjNiTwFLkjeJaqQOeBLYMwKfn7JsSZuRtvd1p3mrvnXACOAEKumFaGZVQdKypG0xxwDPAYOB0dHg/SS3je8BYHOgWzNuPR34Atgigo9KGrS1KidTVukkDiKNhbo28yn1wM8iuLp8UbVMxSRTEosBLwIrwrdno5qjDrgPODiCyvhhrO2RVgf+A/Rs4TOnAH8g4rzSB2VmbYGkrsCPSKtVs4AhwMiImJo7b3AnsDvNH6wAzAQ+AjaJYHwp47XW42TKKpnEjqQxfEvemyAlVP0iuKf0UbVcJe09/DWwLA0SqX/8A+rrYdKk9PXGG42e1w3YA+jbKlGa5XclsEij7y62GIwaBZMnw/vvQ79+Da/oDvyKVO7fzKzFIqI+Iq4G1gdOJZVXf1/S2fDyD4FdaTBYOe44eO45mDoVRozIe9sOwPLAL8savJm1SbnzTzeTJ5G68UYYOxYmTIAxY+DIIxs9vStwvdSsXWxlVxHJlEQX4CjIX1Ho+OOhR4/0tfbaeW/RHfh5+SI0a4LUG9iSfK+nYcNg+nRYZhk45BC4/HJYd91GdyBXwcbMrFiRPBQRuwE7AivANzeR53zU2LFw3nkwfHiTt+wM/NTV/sysDHYl/9lNzj8feveGXr1g773Te9UmmzS6rB2wX3lDbJ6KSKaAAxfy+QK2lVixFMGYtdBAyFO6s1s32H9/+PWvYcoUePJJuPdeOPTQhld2Bo6hROWOzcwi4jWI38G2eQs0/eUvcM898NWCS0yIChmwmFlNOQ3oke+B115L89AAEelrtdUaXdYDOL2M8TVbpSRTh1LgPyikDPWLL+CJJ2C77QreYzawdxliM1uQfuRbVV1zTZg5E956a+73XnoJ1luv0H22KkdwZtZm7Q1a2LPEPUif0WZmJZFb7d6mqWuGDUvz0GPGwKefwgMP5L1sHYklyxFjS1RKMrVMoQdOPx1WXRVWWAGuugr++tf0z3l0gez/g1qbtGje7y6yCEycOP/3JkxI+1Xz8++vmZXSUqTPxoVV8DPazKwIi0HTVbiPOy4Nl7beOh09nzYt72XTqYCxU6UkUwWr9z37bDq7P3063HBD2im1xx55LxWV8/NY25L/927yZOjZoLhfz56pkkpL7mNmVpyWVMZtjfuYmUEz31Nmz07j/hVXhGOPLXhZ5mOnzAPIaXZjwIgCrbxSs8FvShWQWQtMzPvdN9+EDh1g9dXnfm+jjeDVV/NdHfj318xK6ysWMPvbgvuYmZXK1zSvnyyQhlJ5zkwBdKQCxk6VkkyNIvWLmk+vXrDLLtC5M7RvD/37w7bbwoMP5r1HAA+XOU6zfP5G6skyv7q6tDb929+mYhRbbgn77JNqfjbWCXi6zHGaWdvyMETj9ybSZ+qcz9Z5/57HFOCucgZpZm1LBPVA3pnlpZaCgw6C7t2hXbuUB/TrB6NH573VZ7mvTFVKMnU9eWLp2DGVQ/ziC/jySzjhBNh33/nP88/j1QheK3OcZvkModDs78CB0LUrjBsHt9yS1qlfa/RrOhO4hYiC+//MzFpCUi/QzvBax3yPn3lm6jF1xhmpwOjUqel7ebQDbipnrGbWJl0ANBr3RKSh0scfwzffwEUXwUknpZoJDUwBLoxgYYvsLDRFZB4DABI3AP0pbm/2ZODHEdxR2qjMmkl6EehT5LPrgM2JeKV0AZlZWyRpVeBE4DDgIXjgVdj9dPI1FV+wmcANETRumWlVQVJERP7DEWYZylX0Gwf0XNC1BdQDy0Q0TshaW6WsTAH8mjwZajNMA14D7i5pNGYtM5A8W1WboQ64y4mUmRVLyTaSRgHPklbK+0REP9j9AmAMxZ2dmgScU8JQzcwAiGAaaeKn2LHTLyshkYIKSqYi+ADYhfTm3dzlsqnAB8BuEcwoV2xmCxTxNKkXS0veFOqAp8CzvmbWcpI6SjqElEANBx4FekfEaRHxIUDus3EX4EPS5GNzzCYV1ukbwYelj9zMDCK4nrTdr6Vjp6siGFKWoIpQMdv85pBYh3Sgf3HStoQ8y9OzZkP7acATwP6VkpmaIe0I3BXQXoUbUU8jTRjcBBxL5D8gbmaWj6TFgaOB44G3gMHAfRExu/Bz6EUqJLEFqeBNhzyXBekcwpekScoxJQ7dWpm3+Vk1kDgKuASmdoQu+d6bICVR7YAzI7i49aJbsIpLpgAk2gF9gVNJHZLnDD7bwaxOcGs9/HDriI55K4GYZUrqdCuctREMWie98Kfz7e8vs4HLgcuI+CjLMM2sukhaC/gZ0A+4FxgSES+27B6sD5xEOqM8k/SeJKAz8DhwIfBoBAUTM6seTqasWkjHrQwdXoc/fQXtF4dvd5x1BMYDFwHXRWRfCr2hikym5iWxFLA80A2YAF98AEu/Auzf0g8Rs9YiaTjwSsDtwDKkmeDxwLtElKLvi5m1AZIE7AgMAjYDrgQui4hPF+6+dAd6A71Iq1GfRPDlwkVrlcbJlFULSacCG0AMAFYBliBN9HwNvFvJEzwVn0zlI+l3QKeIODXrWMwaktQFGAusHxFjs47HzKqPpM6k1aOTSDOzg4GbIqI+y7isujiZsmogqT1py3K/iPh31vG0VMUUoGihW4CDJVVr/Fbbdgf+60TKzFpK0tKSziYVVzoIOB1YLyKudiJlZjVqN+ArUjGdqlOVyUhE/A/4Btg661jM8ugPjMw6CDOrHpLWl3QtqYz5CsBOEbFbRDwY1biFxMys+Y4DhlXre11VJlM5I0mDVrOKIaknqQzxXVnHYmaVTVI7SbtL+jvwMPA+sGZEHB0RLrBkZjVP0mrA94Dbso6lWFV5ZgpAUm/gOWCF8IF+qxCSDiMVR9kn61jMrDJJ6kbqS3cSqVrtYODWiGhuHyizZvGZKat0ki4CZkfEaVnHUqxCtdwrXkS8L+lNYGfg/qzjMcvpD1yXdRBmVnkkLU/aznI08DQwEPhntW5tMTNbGLmJpcNJK1NVq5q3+UEqRNEv6yDMIB0cBzYH/pp1LGZWOSRtIulG4FVSKfItI2LviPiHEykza8MOBp6JiPeyDmRhVHsydQewZy6zNcvagcD9ETEl60DMLFuS2kvaV9JjwD3AK8CqEXF8RLyVcXhW4yTaSywOSyPROet4zBrK9dA7HhiWdSwLq6qTqYj4HPg3sFfWsZiRVkldxc+sDZPUQ9KJpKp8ZwCXk5KoCyPim2yjs1omIYnNJe4A6oFP4T2AOonXJQ6X6JptlGbf2hzoCTyUdSALq2oLUMwhaQCwnw/8W5bmKYiyfETMyDgcM2tlklYGTgCOAB4lFZV42tv4rDVIbADcSSqr35X8k+WTc3+eDQyOwL+blhlJNwEvRsTFWceysGohmeoJfASsEhFfZx2PtU2SfgH0johjso7FzFqPpC2AQUBfUvGZodW+/9+qi8S2pEJc3YHmVO6rA24ABjqhsizkzpiPAVarhbF7VW/zA4iIiaT+HPtlHYu1ad7iZ9ZGSOog6YeSngZuBp4iTaac7ETKWpPEuqREahGal0gBzCnNf1a54jJbgKOAu2ohkYIaSKZy3MDXMiNpPWBx4ImsYzGz8pG0qKSfA++QtvT9EVgjIobkJvbMWtvVpBWp+ay8Mtx/P3z9NXz6KQwdCu3bz3dJd+AXEiu1UpxmQJqMAo6hBgpPzFErydQDwMa5Hh5mra0fqeHm7KwDMbPSk7SapEuAd4GNSY25t4mIURExK+PwrI2SWAPYhDwrUpddBuPGwXLLQZ8+sN12MHBg41uQep2ZtaY9gY8j4sWsAymVmkimImIqcDdwUMahWBuTK+3Zj9TzzMxqhJLtJN0NPANMATaMiEMi4vlsozMD4ESgfb4HVlkFbr8dpk2Dzz+HBx+E9dZrdFln4FiJTmWO02xex1FDq1JQI8lUjhv4WhY2A2YANTPDYtaWSeok6VDgP8BVpLK9vSPijIj4ONvozOZzINAx3wNDhsDBB0PXrrD88rD77imhKmDzMsVnNh9Ja8G3lSdrRi0lU48CK0taI+tArE3pD9zi8sdm1U3SEpJ+SWrMMwD4NbBORFzuRtxWoXoWeuDxx9NK1MSJ8Mkn8PzzcPfdBe+zRDmCM8tjIHBtREzLOpBSqplkKiJmArfh1SlrJblDlAfhLX5mVUvS2pKuAN4GVgd2j4i+EXG/z0FahctbvU9Kq1CjRkH37rDEErDYYnDBBQXvUzNjQatckhYhVZG8MutYSq3WXkC3AP1z51jMym174KOIeDPrQMys+XLnoXaW9ADwGPA5sHZE/DgiXs44PLPmmpTvm4svnqr5XXopTJ+eKvqNGAF77JH3HgHURHlqq3g/Ah6LiA+zDqTUai2ZeoZ0oLJPxnFY29Afr0qZVQ1JXSQdCbwMDAbuAlaOiLMj4vNsozNrsQeAmQ2/+dVX8O67cOyxqRx6r14wYAC8nH+aoAPw7zLHaW1cbpGj5gpPzFFTyVTu3IoLUVjZSeoC7EvaWmpmFUzSMpLOAT4A9gdOBjaIiGtz1WDNqtGfgOn5HthvP9htN/jiC3j7bZgxAwYNanTZDOC6COrKHKfZNqRiKaOzDqQcVGvn5iWtD/yNNNvo/e5WFpJ+AJwYETtkHYuZ5SdpQ2AQcyc+/hwRr2calFkJSfwX2KjIp9cDfSLwVnUrK0m3AU9ExNCsYymHmlqZAoiI/wHjga0yDsVqWz9gZNZBmNn8JLWTtKek0aSJtbeA1SPiGCdSVoOOgWJWlmbVA9c7kbJyk7QcsDNwQ9axlEvNJVM5I0nnWcxKTlJPYFfSeQszqwCSuksaCLwOnAOMAFaJiN9HxFfZRmdWHhE8AxxCWmVqppnT4KF2sGjNVVWzinQ0cFtETMg6kHKpuW1+AJJWAZ4Flo+IGVnHY7VF0mHAARGxd9axmLV1klYEjgeOAv5FKizxL/d+s7ZEYjvSBF8noEeBy+acD7wCOj0NM4YAO3nF1spFUkfgfWDX3M6xmtQh6wDKISLek/QWaVnxgazjsZrTjxperjarBpK+SzoPtTtwE7B5RLydbVRm2YjgMYllgb2A00lVjaeTSp93IG0F/DNwdQSfw3QkdQYelrS9XztWJvsCb9dyIgU1ujIFIOl40ofrj7KOxWqHpKVIZzBWiIgpWcdj1pZIag/sQ0qiVgKGAtdExPgs4zKrNBJLAkuT2sV8A3wUwazG1+knwK+A7SLig9aN0mqdpH8Cl0XE7VnHUk61nEwtA4whbfVz2U8ridyZjK0i4pCsYzFrK3LnFH8MnEhqsDsYGBURjXrsmFnLSDoB+Bkpofok63isNkjaAHiIVF27po/c1GoBCnINGP8N7CUhiUUkFpNq92e20pPoLLGERMfct9yo16yVSOot6U/Ae8AWQP+I2CIibnciZVYauXLVVwGjcxPRZqUwELiq1hMpqOFkKjn2aXj4YtKhy6+Bz4AZEi9IHCTRKdv4rBJJrCTxB4lvSPvMPwGmSTM/g1/0gcefyzZCs9qlZCtJdwL/AWYBG0fEQRHxTMbhmdWkiLgQuJV0hmqJrOOx6iapF3AwKUmveTW5zU9iQ+A2iJVgdjdon++yScBs4OcRXNOqAVpFkliMdJB9R0CkveYNTJsJnWcC1wMnRuTvPm9mLZOr+rQ/cDKwOOmw/HURMSnTwMzaCEkC/gD0JVX5G59tRFatcltHt46Ig7KOpTXUXDKVKw96P9CNNCBekDrgkgjOKGtgVtEklgOeBpaDZq1Y1gH/BfpGtKS/h5nNS9JiwE9I5c3fJZ2Hui8iGh2WN7PyyiVUQ4DNgF08mWFNkpYFvg8sCswAPn8b/rUGvAT8NCIezzK81lJTyZTE+qQB8SItfGod8KsIhpQ8KKt4EouQthOtSsvaBdQDjwH/F8HscsRmVqskrUE69N4fuA8YEhEvZBuVmeUSqiuBtYDdXcTL5pN+P7YBfk5qQTSddGwogJgB7S+HuqNhky4RH2cYaauptTNTw4Hu+R446CB47TWYPBnefhu23nq+h7sB50v44GXbdAqpzPJ8idTaa8Po0TB+PLz1Fuy7b6PndQW2JvVRMLMFyJ2H2kHSvcCTwHhg/Yg4zImUWWXINbw+BvgAuFtSl4xDskoh9QAeJe0A2xPoAvQkLWL0AHp2hO4DYdEu8BZpu1/Nq5lkSmIdYH3ybO3r2xcuuACOOAJ69IBtt4V33210iyBtNbE2RKIDqdzyfB8W7dvDPffAfffB4ovD0UfDTTfBGms0usUiwGmtE61ZdZLUWdIA4AXgMtJKVO+IODMixmYbnZk1FBGzSe0IxgN3SHLBrrZOWoS0+2tz0tin4FGaDtCRNK46H+ms1gkwOzWzzU/iStILv9E2rSefhGuvheHDF3ibL4Fl8zW2s9oksS9wA2lG5VvrrQfPPJOS7zkeegj+/W84q/HbQj2wcQRjyhqsWZXJNbk+hlQi9xXSeaiHcgM1M6twucIwd5LOwxzslgRtmPR30va+lq5U1gFHEnFr6YOqDDWzMgUcQJ5Eql07+O53Yaml0latjz6CoUOhS/5fhc7AxmWO0yrLITRIpAqRYP318z7UAdinhDGZVTVJ60m6GngTWBnYOSJ2iYi/OZEyqx65HkE/JK1EXCcpb3lkq3HS94AtaZhIdeoE11wD778PEyfCiy/Cbrs1fHY34GKkWso55lNLP1jPfN9cZpn0//qAA2CbbaBPH9h4YzjzzLz3mA0sWcYYrfIsn++bY8bAuHFw6qnQoQPsvDNstx1065b3Hh2BZcsZpFmly52H2k3SQ8AjwEfAWhFxVET8L+PwzKxIETEN2A9YAbhSNTwotoJOIZ0Tn1+HDmmVYrvtoFevNLi+/XZYeeWGV/YktZ2pSbX0gsi7d7M+V7R66FD47DP46iv4059gjz0K3sezLm1L3tfAzJmp4MT//V/6vTnllPT+8HHhujQtqQJoVjMkdZV0NPAqcAFwC+k81G8jYly20ZlZKeQq+u0FrANckqv4Z22BtDhp903j8VJdHZxzDnzwAUTA/ffDe+/Bpps2vLI7cGr5g81GLSVTU/J9c/z4lDTPezSsiWNiAr4ucVxW2b4o9MArr8D228OSS6ZV61VXhWefzXvpLODzMsVnVpEkLSfpXFLFr71IfaL6RMR1uZlsM6shETEZ2IPUV+hCJ1RtRh+gee/pSy8Na64Jr77a8BGRfm9qUi0lU3+H/L1+RoyAE05I56YWXRQGDUpV2vJoB7xYvhCtAo0CJud7YIMNoHNn6No1rUwttxxcd13ee0wl/f6Z1TxJfSRdD7wGLE7qcr9XRDwatVLRyMzyiogJwK7ALsA5GYdjrWNRmqjc960OHeDmm+H669NZicbyH5SoAbWUTF1MqqrWyLnnwnPPwZtvwuuvp/Nxv/tdo8umA1dHMLXMcVplua3QA4ceCp9+ms5O7bRTOjc1fXreSz+O4LmyRWiWMUntJO0t6R+ksuavA6tFxHER8WbG4ZlZK4qIr0nNWg+QdEbW8VjZTSO1DypMghtvTIOk448vdFXNVoKspdLoIlWOWr24O8yYBf/ZKGLzRmuTVtukd26D7xwInYrZsjAFOCGCEaWOyyxrSn1FDgd+Ruo3Mxi4I1fhy8zaMEnLA48BwyJiSMbhWLlIm5D+Py9S8Jrhw6F371SQYGrBNYlPiFix9AFmr2ZWpiII4GgKrE4t4Nl1cP9bsMU9krYudWxWmXKNRM+DbXeE2ZObPE2X33TgXdKBe7OaIek7ki4E3gd2AI4ANouIkU6kzAwg13B7J+Bnkn6adTxWNi+SJtPyu/xyWGcd2GuvphKpqcDVpQ+tMtRMMgUQwT9oeUI1BfR32Hd9UunH2yVdLKlxCUirGZL6AM8BG8DYDaDLlqAJFDh3l8c04FNgJ28NtVohaTNJtwIvkUr+fy8i9o+IJ3weyswaiogPgb7AmZIGZB2PlUF67/8j+Qq9rbQSHHNM6jv02WcwaVL66t8/352uLG+g2amZbX7zktiDtFogCjdknZp7/DLg5xFpEC1pSeBSUvWSARHx77IHbK0m1839DFLlsZ8DN84ZJEqsCjwILEcq45lv299M0orU88C+EXzTGnGblYukDsC+wCBS37VLgGsjYmKWcZlZ9ZC0NvAoMCgiCp5Ftiol9QLGUlwRiRnAg0TsXdqgKkdNJlMAEp2BA4DTgDVJA+Ag9ZGaThowXBnBZ/mfrwOBocAI4Dcu9Vv9JK0PXAd8CRwVEY26RuXO3m1L6ofQl7kHL9uRekndBgyO4OVWCtusLJQ+HI8ETgQ+Jp2HuiciavaQsJmVj6QNgIeBYyLi7ozDsVKT9gNuIl/z3sJmk1rQbEREzbaQqdlkal4SKwBLA52Ab4B3IxZcVUTSMsDlpGRsQET8p6yBWlnkZt5/TtrGeQZp1n2Bv/gSi5M6vncHJgIfRuQvo25WLSStSkqgDiOtxA6JiPwd1MzMWkCpWMHfgMMj4m9Zx2MlJh0BDKN5CdUM0uT1tkS8Xda4MtYmkqmFkWtK1580a3s58LuIyF8g2yqOpLWA60l7fX8cER9kHJJZq8u9j21N2sq3LXANcGm+1Vkzs4UhaXPgXuDgiHg063isxKQdgSHAakBn0o6vedWRdvPcA5xIxLhWjS8DTqaaKVcC9GrSmYIBEeFtXhVMUntSOedfAmcDl0dEc4tLmNUESZ2AA0lJVE/SB+D1EdH4ILGZWYlI2g64E/hBRDwx9/t0BX4I/Ii0Y6gd8BVwO3BjBJMyCNeKkQp5nQzsSKpPMJO0EnUNMJyIr7ILrnU5mWqB3Ozu4cCFpEHJBT5fUHkkrUY6GxXAERHxTrYRmbUuSYsDPwWOI/XfGwzc7wkFM2stknYhnbHZE+Jt4CzSOU1o3LNoCimxGgn8JgKvmlvVcDJVBEkrkTLvRUmrVK9nG5EBSGoHHAucA/wO+LMHj9aW5La1ngQcTNpiMSQi/ptlTGbWdknaC1YfAa/OhE6Lkc6uN2Um6YzyThH8t+wBmpWAk6ki5VapjgbOAy4ABkfErGyjarsk9QauJRWLGBARY7KNyKx15N6LdiJt5fsuqZfHZRGRt1KpmVlrkVgW6t+ATr0aH60pKEgJ1fcieKt80ZmVhpOphSRpFVL59I6k6jV+4bei3EDyKOD3wEXAxd56aW2BpC5AP1IS1Z60le/miGhJ03Izs7KReAzYgjRGaonZwLvAmhF4oGoVrV3WAVS7iHiPdPjuNuBpSSfmtptZmUlakVSC9Rhgh4jwGTareZKWlnQ28D7pIPfPgfUj4honUmZWKSTWAr5HnkRq7bVh9GgYPx7eegv23bfR09sBywLblDlMs4XmQX8JRMTsiLiENPtyEPBobsXKykDJAOAF4Elg84j4X8ZhmZWVpPUlXQuMIVUV3TEido+Ivzenb5qZWSs7kdTsfj7t28M998B998Hii8PRR8NNN8EaazR6fnfSZJFZRfM2vxLLleQeBJwO/Bq40gOd0pG0LHAVsDLpbNR/s43IrHxyq9y7kd5T1gMuA66IiC8zDczMrAkSAiYD3Ro+tt568Mwz0KPH3O899BD8+99w1lmNbjUNWCaCCeWL1mzheGWqxCJiVkRcRGqM+WPgIUnfyTisqpdbjeoHvAS8DHzPiZTVKkndJB0DvEqqTHkjsEpEnOdEysyqQA9acE5KgvXXz/vQdGC5EsVkVhaNll+tNCLidUlbAqcBL0g6HRixoFUqiW6kylxLk/7/fA08EcGn5Y65nHKzVFuQOmYvAkwCXgdeWNDhUklLAZcD6wJ7RsRzZQ7XbMFSBcnNSS0SpgGfAaOJmF78LbU8cDzwE+ApUqn/x7y6bWZVpjupzHmjhGrMGBg3Dk49FQYPhh12gO22g3/8I+99ZpNndavqSHnHdkRU9djOEm/zawWSNgSuBz4Bjo6IsY2vYS3gZ8AA0htQe0C5v3cGHiZVq3u8mirbSPQCDgNOBRbLfbsdMCv35yek0vK3RlDX+PnaDxhGmpk/KyKmtkbcZnmlbby7kiZJvg/MIL1Wg/Q7DXAFMIyID5t/W21C2sr3f8DNwCWuDGpm1UqiK2nSNG899A02gKFD02rU88/DF1/AtGlw1FENr5wSsNVoeOlF4A3SmdExVbNCn3r/NWtshwfkVcvJVCuR1BH4FWmm+WRgZEREbsXmt8AppNmKQsviQeoQ/jTwgwimlD/qhSOxNXA/6c2jexOXTgamkpr0vZyeq8WBS0l9cw6PiKfKHK5Z06QlgL8Da5JWVwuZRnq9nkLEZYVvp/bAXqQkahVgKHBNRHxTspjNzDIiMZZmbtF78km4/nq46qqGj8yqgxWOhM9XBdYC1s79OZNcYpX7mpNovRMRM0r0IxQvtW1p8diOiIof21ljTqZaWW4G+gbgTeh2LEz5DXAoTScb85pKetPYMoKKLYMssSPwV5q/PD/nDWU70PKkxqN3AL+MiEYrVmatKiX3/yFV0evUzGfVAb8j4vfz30o9gCNIs5VfkPpDjaqIAYCZWYlInAr8hjzjgA02gDffhHbtYOBAOO64VC59+vybpKcDV0Zw4vz3lUjb5eYkVnO+1gZWBD5knlUs5iZbX7bKlukU32UUObbDLS6qjpOpDEjqDJwNpxwHf+gMHTq38Bb1wMMR7FOG8BaaxOrAizQ9e1/A5Omw1mcw9rCIeKzUsZm1WPpgfBbYkOYnUnPUAz8iYpSklYETSInUaGBwRDxd0ljNzCqExBLAx0CXho9deGHa0texI/zrX3DCCfDOO41uMRXYIIK3m//vVGfS2ex5V7Hm/D2YfxVrztfbsRBnXfMEcQJwPs1PpOaoBx4moiLHdlaYk6mMSHSCmV9Bh/kSjkmT5r+ua1e47DI48UQaqge+G8Fr5YyzGBLXkvYHz7dXeuWV08+yxRZpb/Sdd8JJJ8GsWfNeNX0WzLgoovsvWjFks8KknYC7aTg50KlT+oXu2zc1S3nnHTjjDHjwwfkuq4dPu8MTkQ4fjwCGRsQHrRS9mVlmJC4jjQdaWkRiKmnSeO/SxCEBSzF/cjXn7ysBH9F4y+AYYFyLVrOkTsA4oFejxxZbDK69FnbZBb78Mn1e3HJLw6vqge8SUXFjOyvM1fyy8wPo0OgFOm/fhe7d4bPP4I478j6/I3AScHR5wiuORE+gH3kOnV52Wargs9xysOii8PDDaXl/6NB5r+rUHjr9VOLXEXjbk1WCU8k3w9ihA3z0USpD9eGHsMcecPvtaf/KB3Nzpdmw7LEw9jLoHRGTGt3HzKx2/YzUI+97QNdmPmca8C5pLFESuYRoXO7rX/M+ppQAzVnNWotUefiI3N/bS5o3uZrz97cjYlqef9W+FGo7NGxY2se4zDLQpw/cfz+89BK8Nl/eVJFjO2uaV6YyIvEfYJOmrjnsMDj7bFhttYKX1ANLRzC5xOEVTeI4UnW+RoPP116DU06Bv/0t/fOFF0LPnnDMMY1uMwk4IoK7yhut2QJIKwBvk2ebSl4vvQTnnAOjRn37rYDZgr8SsW9ZYjQzq2ASXYDbSKvzC9r6NpnUS3KPSmjUK2lJ8p/NWplUjXi+RGsaDO0EGzS6Ubdu8M03qXzhW7lCrTfcAJ98klao5lcPLE1ExYztrGlu2pudDRd0wYAB6bXWhBmkF3Yl2YECb5ZDhsDBB6eti8svD7vv3mhH1Bw9gC3LF6JZs21KmiVdsKWXhjXXhFdfne/bSu+zm5c+NDOzyhfBVNKKzYHAP0hb+OpJZ5hinn9+lrQlcLtKSKQAIuLLiHgiIq6NiNMiYp+IWIs0TtmDVCzrM2Az4HfKl0hB+myYOXNuIgVp8m299fJdXYljO2uCt/llIJ2XajqRXWmltHvoyCObvFWQGoZWksULPfD443D00TBxYtohdd11cPfdBe+zdBliM2upXhTokzKfDh3g5ptTbd8xY/JdUUQxFjOz2pDrj/k34G8SvUk99ZYkjYW+Av4ewRvZRdgyueqrc1ak7gXmnJeqJ9/4bpFF0uBnXhMmzH+2Y57bU3ljO2uCV6ayMXNBFxx6KDzxBLz/flNXje8FWz0iKSrlCx7YIV+kUlqFGjUqnQVbYol0FvOCCwr+cO61YJVgGjC7ySskuPHGtBf++OMLXVW6SlFmZlUsgvcjGBbBORGcHcEl1ZRINaHw2G7y5HSuYV49ezauOjbX1JJFZWXnZCoDEcyGppewDzssTXI3bdF6eHK1iFClfMEew4BZDSNdfPFUze/SS9OY8+uvYcSIdGY/j+mAq51ZJfiE1K2+sGuvTQeK998/bePIb1ypAzMzswoSUXhs9+abaQfD6qvP/d5GGzXaFp7TCfi0DBFamTiZys51FJit3mILWGGFglX85vV2BO+WOK6FNZw8Z0y++grefReOPRbat4devdKZsJdfznuP2cDIMsdp1hxPQxPNsS+/HNZZB/baC6YWnEicAlxehtjMzKyyjCDf2K6uLm3N+e1vUzGKLbeEffZJuxoae5uIShvbWROcTGXnUgpsHxowIL3mJjddx2USqWpeRYngBeD9fI/ttx/stht88QW8/TbMmAGDBuW9zVMRXpmyCpBmGv9EvoRqpZVSKco+fVIPg0mT0lf//g2vbA8scJ3ZzMyqXsGxHQMHpgpc48al/lLHHtuwLDpU6NjOmubS6BmSeBTYhuIKgUwAloloZqWxViTxI+AKWt79G9Is/n4R/L20UZkVKZXG/ZDm90iZ1zTgNiIGlDYoMzOrSNJoYFsWYmxH/h5WVqG8MpWtHwHjSZVbWqIe2LcSE6mckcBDNLU9Kr864AYnUlZRIr4kleuta+EzZ5LOXJ1Y8pjMzKxSHcpCjO2cSFUfJ1MZimAsaWXqC1JfgeaoA/pF8M9yxbWwcgU2+gOP0vyqfFOAO4ATyhWXWdEi7gB+RvMnCKaRVrO2JaIi+qWYmVkriCh6bEfEP8sVlpWPk6mM5cqBbgSMIpXCzDf7PSP32JOkZnb3tF6Excmtmu0NnEvqIZGv/mfkvv8pcApwRETjSoBmFSHiGmBP4CVSUpWvdN+U3GM3AJsQ8UnrBWhmZhUhosVjOyIqfmxn+fnMVAWRWAL4MWlL0ZKkg+sTgQeAP0fwdobhFU2iA6lB3yBgNaAbadD5Gulw/yO51Syz6iBtAJwMbAf0JFVvGkc6K3gzEQWbh5iZWRsiNTm2I6Iqx3Y2l5MpMzMzMzOzInibn5mZmZmZWRGcTJmZmZmZmRXByZSZmZmZmVkRnEyZmZmZmZkVwcmUmZmZmZlZEZxMmZmZmZmZFcHJlJmZmZmZWRGcTJmZmZmZmRXByZSZmZmZmVkRnEyZmZmZmZkVwcmUmZmZmZlZEZxMmZmZmZmZFcHJlJmZmZmZWRGcTJmZmZmZmRXByZSZmZmZmVkRnEyZmZmZmZkVwcmUmZmZmZlZEZxMmZmZmZmZFcHJlJmZmZmZWRGcTJmZmZmZmRXByZSZmZmZmVkRnEyZmZmZmZkVwcmUmZmZmZlZEZxMmZmZmZmZFcHJlJmZmZmZWRGcTJmZmZmZmRXByZSZmZmZmVkRnEyZmZmZmZkV4f8B/cKouf7+nE8AAAAASUVORK5CYII=\n", + "image/png": 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\n", 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    " ] @@ -131,7 +132,7 @@ "n = 10\n", "G = nx.Graph()\n", "G.add_nodes_from([0,1,2,3,4,5,6,7,8,9])\n", - "G.add_edges_from([(0,1),(1,2),(2,3),(3,4),(4,5),(5,6),(6,7),(7,8),(8,9),(9,0)])\n", + "G.add_edges_from([(0,1),(1,2),(2,3),(3,4),(4,5),(1, 7),(5,6),(6,7),(7,8),(8,9),(9,0)])\n", " \n", "k = 9 # Set qubit (vertex) limit\n", "S = NaiveLGP(G,k) # Partition G into two subgrahs once\n", @@ -217,7 +218,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2021-05-11T06:52:48.693469Z", @@ -230,11 +231,11 @@ "output_type": "stream", "text": [ "Max cut for the first partitioned subgraph: \n", - "{'010xxxxxxx': 0.49999449162430293, '101xxxxxxx': 0.49999449162430293, '111xxxxxxx': 2.420265869021529e-06, '000xxxxxxx': 2.42026586902126e-06, '001xxxxxxx': 1.5440549138418965e-06, '011xxxxxxx': 1.544054913841822e-06, '100xxxxxxx': 1.544054913841805e-06, '110xxxxxxx': 1.5440549138414785e-06}\n", + "{'01010101xx': 0.07887396513978905, '10010101xx': 0.07887396513978903, '01101010xx': 0.078873965139789, '10101010xx': 0.078873965139789, '10101101xx': 0.040906327139884305, '01010010xx': 0.0409063271398843, '01010110xx': 0.04004434869249364, '10100101xx': 0.04004434869249363, '01011010xx': 0.040044348692493625, '10101001xx': 0.040044348692493625}\n", "Max cut for the second partitioned subgraph: \n", - "{'1x10101010': 0.14011845299520345, '0x01010101': 0.14011845299520342, '1x01010010': 0.04249785377879293, '0x10101101': 0.04249785377879292, '1x01011010': 0.0424978537787929, '0x10100101': 0.042497853778792886, '0x10101001': 0.036328002709709185, '1x01010110': 0.03632800270970918, '0x10110101': 0.03632800270970918, '1x01001010': 0.036328002709709165}\n", + "{'0xxxxxx101': 0.4556003303152275, '1xxxxxx010': 0.45560033031522745, '1xxxxxx100': 0.0254542520553071, '0xxxxxx011': 0.025454252055307092, '0xxxxxx110': 0.010740876742244158, '1xxxxxx001': 0.010740876742244157, '1xxxxxx000': 0.0022930869455346486, '0xxxxxx111': 0.002293086945534646, '0xxxxxx100': 0.002293086945534642, '1xxxxxx011': 0.002293086945534638}\n", "Combined max cut for the original graph: \n", - "{'1010101010': 0.14011845299520345, '0101010101': 0.14011845299520342, '1110101010': 2.420265869021529e-06, '0001010101': 2.42026586902126e-06, '0010110101': 1.5440549138418965e-06, '0010101001': 1.5440549138418965e-06, '0010100101': 1.5440549138418965e-06, '0010101101': 1.5440549138418965e-06, '0110110101': 1.544054913841822e-06, '0110101001': 1.544054913841822e-06}\n" + "{'0101010101': 0.07887396513978905, '1010101010': 0.078873965139789, '1010100100': 0.0254542520553071, '1010010100': 0.0254542520553071, '1010110100': 0.0254542520553071, '1001010100': 0.0254542520553071, '0101101011': 0.025454252055307092, '0101011011': 0.025454252055307092, '0101001011': 0.025454252055307092, '0110101011': 0.025454252055307092}\n" ] } ], @@ -282,14 +283,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The top several possible max cuts for the first subgraph include {'010xxxxxxx','101xxxxxxx'} and those for the second subgraph include {'1x10101010','0x01010101'}, where 'x' indicates those missing nodes in the subgraph. Shared nodes $0$ and $2$ are all '0's in the first possibility of the first subgraph, i.e. '010xxxxxxx', while they are all '1's in the first possibility of the second subgraph, i.e. '1x10101010', so they cannot combine. (Note that although we can flip 0s and 1s in this situation by symmetry, it is not necessary). We then try to combine '010xxxxxxx' (first possibility of the first subgraph) and '0x01010101' (second possibility of the second subgraph). It is clear that the shared nodes $0$ and $2$ are all '0's in both subgraphs as shown below in the left and middle figure, so we combine these two max cuts and get '0101010101' for the original cycle of six as shown below in the right.\n", + "The top several possible max cuts for the first subgraph include {'01010101xx', '10010101xx', '01101010xx', '10101010xx'} and those for the second subgraph include {'0xxxxxx101,'1xxxxxx010'}, where 'x' indicates those missing nodes in the subgraph. From this example we see that the possible maximal cuts of separated vertices 0 and 7 in the first subgraph, '01010101xx', belong to $S_0$ and $S_1$, respectively. And they also belong to $S_0$ and $S_1$, respectively, in the maximal cut of the second subgraph, '0xxxxxx101'. so we can integrate these two maximal cuts and get the maximal cut of the original graph, ' 0101010101', as shown in the third diagram below.\n", "\n", "Graph illustration is shown below. The left and middle subgraphs are subgraphs with approximate max cuts, where red and blue nodes represent $S_0$ and $S_1$ and dashed lines represent cuts." ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2021-05-11T06:52:49.021611Z", @@ -299,7 +300,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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    " ] @@ -310,8 +311,8 @@ ], "source": [ "# Computed max cut for two subgraphs\n", - "strr1 = '010xxxxxxx'\n", - "strr2 = '0x01010101' \n", + "strr1 = '01010101xx'\n", + "strr2 = '0xxxxxx101' \n", "strr = '0101010101'\n", "\n", "# Show graph illustration\n", @@ -352,7 +353,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2021-05-11T06:54:04.788730Z", @@ -364,8 +365,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "First t possible approximate maxcut for graph G: {'1010101010': 938, '0101010101': 878, '0110101001': 160, '0110101011': 160, '1001010110': 152, '1001010100': 152, '1001010010': 145, '1101010010': 137, '1101010110': 137, '1101010100': 137}\n", - "Max cut found by DC-QAOA algorithms: 1010101010\n" + "First t possible approximate maxcut for graph G: {'0101011011': 408, '0101010011': 393, '1010101100': 386, '1010100100': 350, '1001010100': 257, '0101010101': 250, '1011010100': 248, '0101001011': 244, '0110101011': 235, '0100101011': 225}\n", + "Max cut found by DC-QAOA algorithms: 0101011011\n" ] } ], @@ -461,7 +462,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2021-05-11T06:54:45.016920Z", @@ -473,7 +474,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "First t possible approximate maxcut for graph G: {'00001': 532, '00101': 501, '11110': 496, '01001': 496, '10110': 492, '11010': 483}\n" + "First t possible approximate maxcut for graph G: {'11010': 535, '01001': 515, '00001': 495, '11110': 495, '10110': 488, '00101': 472}\n" ] } ], @@ -499,7 +500,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2021-05-11T06:54:47.679276Z", @@ -527,7 +528,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 15, "metadata": { "ExecuteTime": { "end_time": "2021-05-11T07:02:35.277145Z", @@ -543,29 +544,29 @@ "Node = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n", "\n", "Random graph 1\n", - "Edges = [(0, 2), (0, 6), (0, 7), (0, 8), (1, 3), (1, 5), (1, 6), (1, 8), (1, 9), (2, 3), (2, 4), (2, 6), (2, 8), (2, 9), (3, 4), (3, 6), (3, 7), (3, 8), (3, 9), (4, 9), (5, 8), (7, 9), (8, 9)]\n", - "SDP upper bound: 17.750789460578076\n", - "DC-QAOA node partition: 1001011001, max cut = 17.0\n", + "Edges = [(0, 1), (0, 5), (0, 6), (0, 7), (1, 3), (1, 4), (1, 6), (1, 8), (1, 9), (2, 3), (2, 4), (2, 6), (2, 8), (3, 5), (3, 6), (3, 8), (4, 5), (4, 7), (4, 8), (5, 8), (5, 9), (6, 7), (6, 8), (6, 9), (7, 8), (7, 9)]\n", + "SDP upper bound: 21.03787674994891\n", + "DC-QAOA node partition: 1001100011, max cut = 21.0\n", "\n", "Random graph 2\n", - "Edges = [(0, 1), (0, 3), (0, 6), (1, 2), (1, 3), (2, 5), (2, 6), (2, 7), (3, 5), (3, 6), (3, 8), (3, 9), (4, 6), (4, 7), (4, 8), (4, 9), (5, 7), (5, 8), (6, 7), (6, 8), (7, 9)]\n", - "SDP upper bound: 16.64755118085844\n", - "DC-QAOA node partition: 1100111001, max cut = 15.0\n", + "Edges = [(0, 1), (0, 2), (0, 4), (0, 8), (0, 9), (1, 2), (1, 3), (1, 5), (1, 6), (1, 7), (1, 8), (2, 3), (2, 6), (2, 8), (3, 8), (4, 8), (4, 9), (5, 9), (6, 8), (6, 9)]\n", + "SDP upper bound: 16.028382190698274\n", + "DC-QAOA node partition: 1011011100, max cut = 14.0\n", "\n", "Random graph 3\n", - "Edges = [(0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (2, 3), (2, 4), (2, 6), (2, 7), (2, 8), (4, 5), (4, 7), (4, 9), (5, 7), (5, 8), (5, 9), (6, 7), (7, 8), (8, 9)]\n", - "SDP upper bound: 19.402766322145684\n", - "DC-QAOA node partition: 1101100010, max cut = 18.0\n", + "Edges = [(0, 2), (0, 5), (0, 6), (0, 7), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 9), (2, 3), (2, 5), (2, 6), (2, 9), (3, 4), (3, 6), (3, 7), (4, 6), (4, 7), (4, 8), (5, 6), (5, 7), (6, 7)]\n", + "SDP upper bound: 17.0971057189657\n", + "DC-QAOA node partition: 0010111100, max cut = 15.0\n", "\n", "Random graph 4\n", - "Edges = [(0, 1), (0, 2), (0, 5), (0, 6), (0, 7), (0, 9), (1, 5), (1, 6), (1, 7), (1, 9), (2, 3), (2, 6), (2, 8), (3, 5), (3, 6), (3, 8), (3, 9), (4, 5), (4, 6), (4, 7), (4, 9), (5, 6), (5, 7), (5, 8), (6, 7), (6, 8), (7, 8)]\n", - "SDP upper bound: 20.999869854784496\n", - "DC-QAOA node partition: 0010011011, max cut = 18.0\n", + "Edges = [(0, 1), (0, 2), (0, 3), (0, 4), (0, 6), (0, 7), (0, 8), (0, 9), (1, 7), (1, 8), (1, 9), (2, 3), (2, 6), (2, 7), (2, 9), (3, 4), (3, 5), (3, 7), (3, 8), (3, 9), (4, 7), (4, 8), (5, 6), (5, 8), (5, 9), (6, 7), (6, 9), (7, 8), (7, 9)]\n", + "SDP upper bound: 20.153931079390457\n", + "DC-QAOA node partition: 1111101000, max cut = 17.0\n", "\n", "Random graph 5\n", - "Edges = [(0, 1), (0, 4), (0, 7), (1, 2), (1, 3), (1, 6), (1, 7), (1, 8), (1, 9), (2, 4), (2, 7), (2, 9), (3, 7), (3, 9), (4, 5), (4, 6), (4, 8), (5, 6), (5, 7), (5, 8), (6, 7), (6, 8), (6, 9), (7, 9), (8, 9)]\n", - "SDP upper bound: 19.454398132157152\n", - "DC-QAOA node partition: 1011011001, max cut = 18.0\n" + "Edges = [(0, 1), (0, 2), (0, 6), (1, 2), (1, 4), (1, 5), (1, 7), (1, 8), (2, 3), (2, 4), (2, 5), (2, 6), (2, 8), (2, 9), (3, 6), (3, 7), (3, 8), (4, 7), (4, 9), (5, 7), (5, 8), (6, 7), (6, 9), (7, 9), (8, 9)]\n", + "SDP upper bound: 18.82486962324589\n", + "DC-QAOA node partition: 1010000110, max cut = 18.0\n" ] } ], @@ -612,7 +613,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 16, "metadata": { "ExecuteTime": { "end_time": "2021-05-11T07:02:35.547590Z", @@ -622,7 +623,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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    " ] @@ -698,6 +699,9 @@ ], "metadata": { "celltoolbar": "Raw Cell Format", + "interpreter": { + "hash": "3b61f83e8397e1c9fcea57a3d9915794102e67724879b24295f8014f41a14d85" + }, "kernelspec": { "display_name": "Python 3", "language": "python", @@ -713,7 +717,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.10" + "version": "3.7.11" }, "toc": { "base_numbering": 1, diff --git a/tutorial/combinatorial_optimization/MAXCUT_CN.ipynb b/tutorial/combinatorial_optimization/MAXCUT_CN.ipynb index 6c70d42..a73ce5f 100644 --- a/tutorial/combinatorial_optimization/MAXCUT_CN.ipynb +++ b/tutorial/combinatorial_optimization/MAXCUT_CN.ipynb @@ -136,7 +136,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:11:08.078417Z", @@ -153,7 +153,10 @@ "# 加载额外需要用到的包\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", - "import networkx as nx" + "import networkx as nx\n", + "\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\")" ] }, { @@ -165,7 +168,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:11:08.411878Z", @@ -175,7 +178,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
    " ] @@ -190,7 +193,7 @@ "G = nx.Graph()\n", "V = range(n)\n", "G.add_nodes_from(V)\n", - "E = [(0, 1), (1, 2), (2, 3), (3, 0)]\n", + "E = [(0, 1), (1, 2), (2, 3), (3, 0), (1, 3)]\n", "G.add_edges_from(E)\n", "\n", "# 将生成的图 G 打印出来\n", @@ -221,7 +224,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:11:08.426170Z", @@ -233,7 +236,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "[[-1.0, 'z0,z1'], [-1.0, 'z1,z2'], [-1.0, 'z2,z3'], [-1.0, 'z3,z0']]\n" + "[[-1.0, 'z0,z1'], [-1.0, 'z1,z2'], [-1.0, 'z2,z3'], [-1.0, 'z3,z0'], [-1.0, 'z1,z3']]\n" ] } ], @@ -261,7 +264,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:11:08.792299Z", @@ -273,8 +276,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "[-4. 0. 0. 0. 0. 4. 0. 0. 0. 0. 4. 0. 0. 0. 0. -4.]\n", - "H_max: 4.0\n" + "[-5. 1. -1. 1. 1. 3. 1. -1. -1. 1. 3. 1. 1. -1. 1. -5.]\n", + "H_max: 3.0\n" ] } ], @@ -319,7 +322,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:11:10.245237Z", @@ -373,7 +376,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:11:11.218109Z", @@ -419,7 +422,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:11:12.968989Z", @@ -443,7 +446,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:11:54.550338Z", @@ -455,32 +458,32 @@ "name": "stdout", "output_type": "stream", "text": [ - "iter: 10 loss: -3.8886\n", - "iter: 20 loss: -3.9134\n", - "iter: 30 loss: -3.9659\n", - "iter: 40 loss: -3.9906\n", - "iter: 50 loss: -3.9979\n", - "iter: 60 loss: -3.9993\n", - "iter: 70 loss: -3.9998\n", - "iter: 80 loss: -3.9999\n", - "iter: 90 loss: -4.0000\n", - "iter: 100 loss: -4.0000\n", - "iter: 110 loss: -4.0000\n", - "iter: 120 loss: -4.0000\n", + "iter: 10 loss: -1.8359\n", + "iter: 20 loss: -2.5392\n", + "iter: 30 loss: -2.7250\n", + "iter: 40 loss: -2.8061\n", + "iter: 50 loss: -2.8748\n", + "iter: 60 loss: -2.9134\n", + "iter: 70 loss: -2.9302\n", + "iter: 80 loss: -2.9321\n", + "iter: 90 loss: -2.9321\n", + "iter: 100 loss: -2.9325\n", + "iter: 110 loss: -2.9327\n", + "iter: 120 loss: -2.9328\n", "\n", "训练后的电路：\n", - "--H----*-----------------*--------------------------------------------------X----Rz(3.140)----X----Rx(0.824)----*-----------------*--------------------------------------------------X----Rz(0.737)----X----Rx(2.506)----*-----------------*--------------------------------------------------X----Rz(4.999)----X----Rx(4.854)----*-----------------*--------------------------------------------------X----Rz(0.465)----X----Rx(1.900)--\n", - " | | | | | | | | | | | | | | | | \n", - "--H----X----Rz(3.140)----X----*-----------------*---------------------------|-----------------|----Rx(0.824)----X----Rz(0.737)----X----*-----------------*---------------------------|-----------------|----Rx(2.506)----X----Rz(4.999)----X----*-----------------*---------------------------|-----------------|----Rx(4.854)----X----Rz(0.465)----X----*-----------------*---------------------------|-----------------|----Rx(1.900)--\n", - " | | | | | | | | | | | | | | | | \n", - "--H---------------------------X----Rz(3.140)----X----*-----------------*----|-----------------|----Rx(0.824)---------------------------X----Rz(0.737)----X----*-----------------*----|-----------------|----Rx(2.506)---------------------------X----Rz(4.999)----X----*-----------------*----|-----------------|----Rx(4.854)---------------------------X----Rz(0.465)----X----*-----------------*----|-----------------|----Rx(1.900)--\n", - " | | | | | | | | | | | | | | | | \n", - "--H--------------------------------------------------X----Rz(3.140)----X----*-----------------*----Rx(0.824)--------------------------------------------------X----Rz(0.737)----X----*-----------------*----Rx(2.506)--------------------------------------------------X----Rz(4.999)----X----*-----------------*----Rx(4.854)--------------------------------------------------X----Rz(0.465)----X----*-----------------*----Rx(1.900)--\n", - " \n", + "--H----*-----------------*--------------------------------------------------x----Rz(2.379)----x----Rx(2.503)-----------------------------------*-----------------*--------------------------------------------------x----Rz(1.230)----x----Rx(0.792)-----------------------------------*-----------------*--------------------------------------------------x----Rz(4.375)----x----Rx(5.180)-----------------------------------*-----------------*--------------------------------------------------x----Rz(0.711)----x----Rx(2.353)---------------------------------\n", + " | | | | | | | | | | | | | | | | \n", + "--H----x----Rz(2.379)----x----*-----------------*---------------------------|-----------------|--------*---------------------*----Rx(2.503)----x----Rz(1.230)----x----*-----------------*---------------------------|-----------------|--------*---------------------*----Rx(0.792)----x----Rz(4.375)----x----*-----------------*---------------------------|-----------------|--------*---------------------*----Rx(5.180)----x----Rz(0.711)----x----*-----------------*---------------------------|-----------------|--------*---------------------*----Rx(2.353)--\n", + " | | | | | | | | | | | | | | | | | | | | | | | | \n", + "--H---------------------------x----Rz(2.379)----x----*-----------------*----|-----------------|--------|---------------------|----Rx(2.503)---------------------------x----Rz(1.230)----x----*-----------------*----|-----------------|--------|---------------------|----Rx(0.792)---------------------------x----Rz(4.375)----x----*-----------------*----|-----------------|--------|---------------------|----Rx(5.180)---------------------------x----Rz(0.711)----x----*-----------------*----|-----------------|--------|---------------------|----Rx(2.353)--\n", + " | | | | | | | | | | | | | | | | | | | | | | | | \n", + "--H--------------------------------------------------x----Rz(2.379)----x----*-----------------*--------x--------Rz(2.379)----x----Rx(2.503)--------------------------------------------------x----Rz(1.230)----x----*-----------------*--------x--------Rz(1.230)----x----Rx(0.792)--------------------------------------------------x----Rz(4.375)----x----*-----------------*--------x--------Rz(4.375)----x----Rx(5.180)--------------------------------------------------x----Rz(0.711)----x----*-----------------*--------x--------Rz(0.711)----x----Rx(2.353)--\n", + " \n", "优化后的参数 gamma:\n", - " [3.14046713 0.73681226 4.99897226 0.46481489]\n", + " [2.37918879 1.22914743 4.37582352 0.71142941]\n", "优化后的参数 beta:\n", - " [0.82379898 2.50618308 4.85422542 1.90024859]\n" + " [2.50287593 0.79179726 5.17941547 2.35294027]\n" ] } ], @@ -529,7 +532,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 20, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:11:55.548009Z", @@ -539,7 +542,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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    " ] @@ -569,7 +572,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 21, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:11:55.906817Z", @@ -586,7 +589,7 @@ }, { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
    " ] @@ -603,10 +606,15 @@ "# 在图上画出上面得到的比特串对应的割\n", "node_cut = [\"blue\" if cut_bitstring[v] == \"1\" else \"red\" for v in V]\n", "\n", - "edge_cut = [\n", - " \"solid\" if cut_bitstring[u] == cut_bitstring[v] else \"dashed\"\n", - " for (u, v) in E\n", - " ]\n", + "edge_cut = []\n", + "for u in range(n):\n", + " for v in range(u+1,n):\n", + " if (u, v) in E or (v, u) in E:\n", + " if cut_bitstring[u] == cut_bitstring[v]:\n", + " edge_cut.append(\"solid\")\n", + " else:\n", + " edge_cut.append(\"dashed\")\n", + "\n", "nx.draw(\n", " G,\n", " pos,\n", @@ -640,6 +648,9 @@ } ], "metadata": { + "interpreter": { + "hash": "3b61f83e8397e1c9fcea57a3d9915794102e67724879b24295f8014f41a14d85" + }, "kernelspec": { "display_name": "Python 3", "language": "python", @@ -655,7 +666,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.10" + "version": "3.7.11" }, "toc": { "base_numbering": 1, diff --git a/tutorial/combinatorial_optimization/MAXCUT_EN.ipynb b/tutorial/combinatorial_optimization/MAXCUT_EN.ipynb index ddebe3a..dc81947 100644 --- a/tutorial/combinatorial_optimization/MAXCUT_EN.ipynb +++ b/tutorial/combinatorial_optimization/MAXCUT_EN.ipynb @@ -139,7 +139,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:07:40.001750Z", @@ -157,7 +157,10 @@ "import numpy as np\n", "from numpy import pi as PI\n", "import matplotlib.pyplot as plt\n", - "import networkx as nx" + "import networkx as nx\n", + "\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\")" ] }, { @@ -169,7 +172,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:07:40.192343Z", @@ -179,7 +182,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
    " ] @@ -194,7 +197,7 @@ "G = nx.Graph()\n", "V = range(n)\n", "G.add_nodes_from(V)\n", - "E = [(0, 1), (1, 2), (2, 3), (3, 0)]\n", + "E = [(0, 1), (1, 2), (2, 3), (3, 0), (1, 3)]\n", "G.add_edges_from(E)\n", "\n", "# Print out the generated graph G\n", @@ -225,7 +228,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:07:40.206426Z", @@ -237,7 +240,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "[[-1.0, 'z0,z1'], [-1.0, 'z1,z2'], [-1.0, 'z2,z3'], [-1.0, 'z3,z0']]\n" + "[[-1.0, 'z0,z1'], [-1.0, 'z1,z2'], [-1.0, 'z2,z3'], [-1.0, 'z3,z0'], [-1.0, 'z1,z3']]\n" ] } ], @@ -265,7 +268,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:07:40.501135Z", @@ -277,8 +280,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "[-4. 0. 0. 0. 0. 4. 0. 0. 0. 0. 4. 0. 0. 0. 0. -4.]\n", - "H_max: 4.0\n" + "[-5. 1. -1. 1. 1. 3. 1. -1. -1. 1. 3. 1. 1. -1. 1. -5.]\n", + "H_max: 3.0\n" ] } ], @@ -322,7 +325,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:07:41.987233Z", @@ -381,7 +384,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:07:43.856891Z", @@ -424,7 +427,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:07:44.907375Z", @@ -460,32 +463,32 @@ "name": "stdout", "output_type": "stream", "text": [ - "iter: 10 loss: -3.8886\n", - "iter: 20 loss: -3.9134\n", - "iter: 30 loss: -3.9659\n", - "iter: 40 loss: -3.9906\n", - "iter: 50 loss: -3.9979\n", - "iter: 60 loss: -3.9993\n", - "iter: 70 loss: -3.9998\n", - "iter: 80 loss: -3.9999\n", - "iter: 90 loss: -4.0000\n", - "iter: 100 loss: -4.0000\n", - "iter: 110 loss: -4.0000\n", - "iter: 120 loss: -4.0000\n", + "iter: 10 loss: -1.8359\n", + "iter: 20 loss: -2.5392\n", + "iter: 30 loss: -2.7250\n", + "iter: 40 loss: -2.8061\n", + "iter: 50 loss: -2.8748\n", + "iter: 60 loss: -2.9134\n", + "iter: 70 loss: -2.9302\n", + "iter: 80 loss: -2.9321\n", + "iter: 90 loss: -2.9321\n", + "iter: 100 loss: -2.9325\n", + "iter: 110 loss: -2.9327\n", + "iter: 120 loss: -2.9328\n", "\n", "The trained circuit:\n", - "--H----*-----------------*--------------------------------------------------X----Rz(3.140)----X----Rx(0.824)----*-----------------*--------------------------------------------------X----Rz(0.737)----X----Rx(2.506)----*-----------------*--------------------------------------------------X----Rz(4.999)----X----Rx(4.854)----*-----------------*--------------------------------------------------X----Rz(0.465)----X----Rx(1.900)--\n", - " | | | | | | | | | | | | | | | | \n", - "--H----X----Rz(3.140)----X----*-----------------*---------------------------|-----------------|----Rx(0.824)----X----Rz(0.737)----X----*-----------------*---------------------------|-----------------|----Rx(2.506)----X----Rz(4.999)----X----*-----------------*---------------------------|-----------------|----Rx(4.854)----X----Rz(0.465)----X----*-----------------*---------------------------|-----------------|----Rx(1.900)--\n", - " | | | | | | | | | | | | | | | | \n", - "--H---------------------------X----Rz(3.140)----X----*-----------------*----|-----------------|----Rx(0.824)---------------------------X----Rz(0.737)----X----*-----------------*----|-----------------|----Rx(2.506)---------------------------X----Rz(4.999)----X----*-----------------*----|-----------------|----Rx(4.854)---------------------------X----Rz(0.465)----X----*-----------------*----|-----------------|----Rx(1.900)--\n", - " | | | | | | | | | | | | | | | | \n", - "--H--------------------------------------------------X----Rz(3.140)----X----*-----------------*----Rx(0.824)--------------------------------------------------X----Rz(0.737)----X----*-----------------*----Rx(2.506)--------------------------------------------------X----Rz(4.999)----X----*-----------------*----Rx(4.854)--------------------------------------------------X----Rz(0.465)----X----*-----------------*----Rx(1.900)--\n", - " \n", + "--H----*-----------------*--------------------------------------------------x----Rz(2.379)----x----Rx(2.503)-----------------------------------*-----------------*--------------------------------------------------x----Rz(1.230)----x----Rx(0.792)-----------------------------------*-----------------*--------------------------------------------------x----Rz(4.375)----x----Rx(5.180)-----------------------------------*-----------------*--------------------------------------------------x----Rz(0.711)----x----Rx(2.353)---------------------------------\n", + " | | | | | | | | | | | | | | | | \n", + "--H----x----Rz(2.379)----x----*-----------------*---------------------------|-----------------|--------*---------------------*----Rx(2.503)----x----Rz(1.230)----x----*-----------------*---------------------------|-----------------|--------*---------------------*----Rx(0.792)----x----Rz(4.375)----x----*-----------------*---------------------------|-----------------|--------*---------------------*----Rx(5.180)----x----Rz(0.711)----x----*-----------------*---------------------------|-----------------|--------*---------------------*----Rx(2.353)--\n", + " | | | | | | | | | | | | | | | | | | | | | | | | \n", + "--H---------------------------x----Rz(2.379)----x----*-----------------*----|-----------------|--------|---------------------|----Rx(2.503)---------------------------x----Rz(1.230)----x----*-----------------*----|-----------------|--------|---------------------|----Rx(0.792)---------------------------x----Rz(4.375)----x----*-----------------*----|-----------------|--------|---------------------|----Rx(5.180)---------------------------x----Rz(0.711)----x----*-----------------*----|-----------------|--------|---------------------|----Rx(2.353)--\n", + " | | | | | | | | | | | | | | | | | | | | | | | | \n", + "--H--------------------------------------------------x----Rz(2.379)----x----*-----------------*--------x--------Rz(2.379)----x----Rx(2.503)--------------------------------------------------x----Rz(1.230)----x----*-----------------*--------x--------Rz(1.230)----x----Rx(0.792)--------------------------------------------------x----Rz(4.375)----x----*-----------------*--------x--------Rz(4.375)----x----Rx(5.180)--------------------------------------------------x----Rz(0.711)----x----*-----------------*--------x--------Rz(0.711)----x----Rx(2.353)--\n", + " \n", "Optimized parameters gamma:\n", - " [3.14046713 0.73681226 4.99897226 0.46481489]\n", + " [2.37918879 1.22914743 4.37582352 0.71142941]\n", "Optimized parameters beta:\n", - " [0.82379898 2.50618308 4.85422542 1.90024859]\n" + " [2.50287593 0.79179726 5.17941547 2.35294027]\n" ] } ], @@ -545,7 +548,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
    " ] @@ -587,12 +590,12 @@ "name": "stdout", "output_type": "stream", "text": [ - "The bit string form of the cut found: 1010\n" + "The bit string form of the cut found: 0101\n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
    " ] @@ -609,10 +612,14 @@ "# Draw the cut corresponding to the bit string obtained above on the graph\n", "node_cut = [\"blue\" if cut_bitstring[v] == \"1\" else \"red\" for v in V]\n", "\n", - "edge_cut = [\n", - " \"solid\" if cut_bitstring[u] == cut_bitstring[v] else \"dashed\"\n", - " for (u, v) in E\n", - " ]\n", + "edge_cut = []\n", + "for u in range(n):\n", + " for v in range(u+1,n):\n", + " if (u, v) in E or (v, u) in E:\n", + " if cut_bitstring[u] == cut_bitstring[v]:\n", + " edge_cut.append(\"solid\")\n", + " else:\n", + " edge_cut.append(\"dashed\")\n", "nx.draw(\n", " G,\n", " pos,\n", @@ -646,6 +653,9 @@ } ], "metadata": { + "interpreter": { + "hash": "3b61f83e8397e1c9fcea57a3d9915794102e67724879b24295f8014f41a14d85" + }, "kernelspec": { "display_name": "Python 3", "language": "python", @@ -661,7 +671,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.3" + "version": "3.7.11" }, "toc": { "base_numbering": 1, diff --git a/tutorial/combinatorial_optimization/realStockData_12.csv b/tutorial/combinatorial_optimization/realStockData_12.csv index 75359e7..291eb65 100644 --- a/tutorial/combinatorial_optimization/realStockData_12.csv +++ b/tutorial/combinatorial_optimization/realStockData_12.csv @@ -1,37 +1,37 @@ -closePrice0,closePrice1,closePrice2,closePrice3,closePrice4,closePrice5,closePrice6,closePrice7,closePrice8,closePrice9,closePrice10,closePrice11 -16.87,32.56,5.4,3.71,5.72,7.62,3.7,6.94,5.43,3.46,8.22,4.56 -17.18,32.05,5.48,3.75,5.75,7.56,3.7,6.89,5.37,3.45,8.14,4.54 -17.07,31.51,5.46,3.73,5.74,7.68,3.68,6.91,5.37,3.41,8.1,4.55 -17.15,31.76,5.49,3.79,5.81,7.75,3.7,6.97,5.42,3.5,8.16,4.58 -16.66,31.68,5.39,3.72,5.69,7.79,3.63,6.85,5.29,3.42,7.93,4.48 -16.79,32.2,5.47,3.77,5.79,7.84,3.66,6.94,5.41,3.46,8.02,4.56 -16.69,31.46,5.46,3.76,5.77,7.82,3.63,7.01,5.42,3.48,8,4.53 -16.99,31.68,5.53,3.74,5.8,7.8,3.63,7.03,5.39,3.47,8.03,4.53 -16.76,31.39,5.5,3.78,5.89,7.92,3.66,7.04,5.45,3.48,8.05,4.56 -16.52,30.49,5.47,3.71,5.78,7.96,3.63,7.01,5.43,3.45,7.95,4.47 -16.33,30.53,5.39,3.61,5.7,7.93,3.6,6.99,5.35,3.4,7.92,4.42 -16.39,30.46,5.35,3.58,5.69,7.87,3.59,6.95,5.26,3.41,7.93,4.38 -16.45,29.87,5.37,3.61,5.75,7.86,3.63,6.96,5.54,3.42,7.99,4.35 -16,29.21,5.24,3.53,5.7,7.82,3.6,6.87,6.09,3.32,7.9,4.32 -16.09,30.11,5.26,3.5,5.71,7.9,3.61,6.87,6.7,3.33,8.01,4.34 -15.54,28.98,5.08,3.42,5.54,7.7,3.54,6.58,7.37,3.23,7.73,4.13 -13.99,26.63,4.57,3.08,4.99,6.93,3.19,5.92,8.11,2.91,6.96,3.72 -14.6,27.62,4.44,2.95,4.89,6.91,3.27,5.78,8.1,2.96,7.01,3.51 -14.63,27.64,4.5,3.04,4.94,7.18,3.27,5.89,8.91,3.02,7.06,3.61 -14.77,27.9,4.56,3.05,5.08,7.31,3.31,5.94,9.8,3.06,7.08,3.88 -14.62,27.5,4.52,3.05,5.39,7.35,3.3,5.93,10.78,3.05,7.07,3.87 -14.5,28.67,4.59,3.13,5.35,7.53,3.32,6.06,11.86,3.13,7.15,3.9 -14.79,29.08,4.66,3.12,5.23,7.47,3.33,6.16,10.67,3.15,7.17,3.91 -14.77,29.08,4.67,3.14,5.26,7.48,3.38,6.18,11.36,3.17,7.21,3.95 -14.65,29.95,4.66,3.11,5.19,7.35,3.36,6.15,10.56,3.14,7.19,3.94 -15.03,30.8,4.72,3.07,5.18,7.33,3.34,6.11,9.56,3.15,7.29,3.96 -15.37,30.42,4.84,3.23,5.31,7.46,3.39,6.35,9.15,3.18,7.41,4.04 -15.2,29.7,4.81,3.3,5.33,7.47,3.39,6.34,9.11,3.17,7.4,4.06 -15.24,29.65,4.84,3.31,5.31,7.39,3.37,6.26,8.89,3.12,7.34,3.99 -15.59,29.85,4.88,3.3,5.38,7.47,3.42,6.44,8.36,3.15,7.42,4.04 -15.58,29.25,4.89,3.33,5.39,7.48,3.43,6.46,8.68,3.16,7.52,4.03 -15.23,28.9,4.82,3.31,5.41,8.06,3.37,6.41,8.77,3.12,7.41,3.97 -15.04,29.33,4.74,3.22,5.28,8.02,3.32,6.32,9.65,3.06,7.31,3.9 -14.99,30.11,4.84,3.31,5.3,8.01,3.36,6.32,9.11,3.13,7.51,3.9 -15.11,29.67,4.79,3.25,5.38,8.11,3.37,6.42,8.41,3.15,7.5,3.88 +closePrice0,closePrice1,closePrice2,closePrice3,closePrice4,closePrice5,closePrice6,closePrice7,closePrice8,closePrice9,closePrice10,closePrice11 +16.87,32.56,5.4,3.71,5.72,7.62,3.7,6.94,5.43,3.46,8.22,4.56 +17.18,32.05,5.48,3.75,5.75,7.56,3.7,6.89,5.37,3.45,8.14,4.54 +17.07,31.51,5.46,3.73,5.74,7.68,3.68,6.91,5.37,3.41,8.1,4.55 +17.15,31.76,5.49,3.79,5.81,7.75,3.7,6.97,5.42,3.5,8.16,4.58 +16.66,31.68,5.39,3.72,5.69,7.79,3.63,6.85,5.29,3.42,7.93,4.48 +16.79,32.2,5.47,3.77,5.79,7.84,3.66,6.94,5.41,3.46,8.02,4.56 +16.69,31.46,5.46,3.76,5.77,7.82,3.63,7.01,5.42,3.48,8,4.53 +16.99,31.68,5.53,3.74,5.8,7.8,3.63,7.03,5.39,3.47,8.03,4.53 +16.76,31.39,5.5,3.78,5.89,7.92,3.66,7.04,5.45,3.48,8.05,4.56 +16.52,30.49,5.47,3.71,5.78,7.96,3.63,7.01,5.43,3.45,7.95,4.47 +16.33,30.53,5.39,3.61,5.7,7.93,3.6,6.99,5.35,3.4,7.92,4.42 +16.39,30.46,5.35,3.58,5.69,7.87,3.59,6.95,5.26,3.41,7.93,4.38 +16.45,29.87,5.37,3.61,5.75,7.86,3.63,6.96,5.54,3.42,7.99,4.35 +16,29.21,5.24,3.53,5.7,7.82,3.6,6.87,6.09,3.32,7.9,4.32 +16.09,30.11,5.26,3.5,5.71,7.9,3.61,6.87,6.7,3.33,8.01,4.34 +15.54,28.98,5.08,3.42,5.54,7.7,3.54,6.58,7.37,3.23,7.73,4.13 +13.99,26.63,4.57,3.08,4.99,6.93,3.19,5.92,8.11,2.91,6.96,3.72 +14.6,27.62,4.44,2.95,4.89,6.91,3.27,5.78,8.1,2.96,7.01,3.51 +14.63,27.64,4.5,3.04,4.94,7.18,3.27,5.89,8.91,3.02,7.06,3.61 +14.77,27.9,4.56,3.05,5.08,7.31,3.31,5.94,9.8,3.06,7.08,3.88 +14.62,27.5,4.52,3.05,5.39,7.35,3.3,5.93,10.78,3.05,7.07,3.87 +14.5,28.67,4.59,3.13,5.35,7.53,3.32,6.06,11.86,3.13,7.15,3.9 +14.79,29.08,4.66,3.12,5.23,7.47,3.33,6.16,10.67,3.15,7.17,3.91 +14.77,29.08,4.67,3.14,5.26,7.48,3.38,6.18,11.36,3.17,7.21,3.95 +14.65,29.95,4.66,3.11,5.19,7.35,3.36,6.15,10.56,3.14,7.19,3.94 +15.03,30.8,4.72,3.07,5.18,7.33,3.34,6.11,9.56,3.15,7.29,3.96 +15.37,30.42,4.84,3.23,5.31,7.46,3.39,6.35,9.15,3.18,7.41,4.04 +15.2,29.7,4.81,3.3,5.33,7.47,3.39,6.34,9.11,3.17,7.4,4.06 +15.24,29.65,4.84,3.31,5.31,7.39,3.37,6.26,8.89,3.12,7.34,3.99 +15.59,29.85,4.88,3.3,5.38,7.47,3.42,6.44,8.36,3.15,7.42,4.04 +15.58,29.25,4.89,3.33,5.39,7.48,3.43,6.46,8.68,3.16,7.52,4.03 +15.23,28.9,4.82,3.31,5.41,8.06,3.37,6.41,8.77,3.12,7.41,3.97 +15.04,29.33,4.74,3.22,5.28,8.02,3.32,6.32,9.65,3.06,7.31,3.9 +14.99,30.11,4.84,3.31,5.3,8.01,3.36,6.32,9.11,3.13,7.51,3.9 +15.11,29.67,4.79,3.25,5.38,8.11,3.37,6.42,8.41,3.15,7.5,3.88 14.5,29.59,4.63,3.12,5.12,7.87,3.3,6.15,8.4,3.08,7.18,3.76 \ No newline at end of file diff --git a/tutorial/locc/LOCCNET_Tutorial_CN.ipynb b/tutorial/locc/LOCCNET_Tutorial_CN.ipynb index c3ff73b..462d613 100644 --- a/tutorial/locc/LOCCNET_Tutorial_CN.ipynb +++ b/tutorial/locc/LOCCNET_Tutorial_CN.ipynb @@ -91,7 +91,7 @@ "source": [ "在 `__init__()` 函数中，我们需要初始化所有的参与方、量子态以及 QNN 的参数。\n", "\n", - "- `self.add_new_party(qubits_number, party_name=None)` 是用于添加一个新的参与方的函数，第一个参数代表该参与方有几个量子比特；第二个参数是可选参数，代表着参与者的名字。在协议中，我们可以选择是用过名字来指定参与方，也可以选择用编号来指定。如果我们希望使用名字，那么只需要在 `add_new_party` 函数中给 `party_name` 命名；如果希望使用编号，那么我们就不用给第二个参数赋值，第一个参与方会自动编号为 0，每增加一个参与方，其编号都会加一，同时该函数会将所添加的 party 的 ID 返回，其值根据定义会是 `int` 或者 `str`。\n", + "- `self.add_new_party(qubits_number, party_name=None)` 是用于添加一个新的参与方的函数，第一个参数代表该参与方有几个量子比特；第二个参数是可选参数，代表着参与者的名字。在协议中，我们可以选择使用名字来指定参与方，也可以选择用编号来指定。如果我们希望使用名字，那么只需要在 `add_new_party` 函数中给 `party_name` 命名；如果希望使用编号，那么我们就不用给第二个参数赋值，第一个参与方会自动编号为 0，每增加一个参与方，其编号都会加一，同时该函数会将所添加的 party 的 ID 返回，其值根据定义会是 `int` 或者 `str`。\n", "\n", "- `self.set_init_state(state, which_qubits)` 是用于设置协议的初始态的函数。第一个参数 `state` 是量子态，必须是密度矩阵的形式；第二个参数 `which_qubits` 是定位量子比特（哪一参与方的第几个量子比特，如 `(\"Alice\", 0)`）。需要说明的是，我们必须初始化所有的量子比特，否则程序将出现错误。" ] @@ -100,7 +100,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "在 `forward()` 函数中，我们需要定义协议的流程。如果我们想要训练一个模型，那么需要定义损失函数，并设置为 `forward()` 的返回值，这样才能不断更新参数使得损失函数最小化。如果我们仅仅是想要验证某个协议的结果，我们就做上述的事情，只需要把协议的流程定义清除，就可以把我们感兴趣的值设为返回值。在 `forward()` 函数中，我们主要做两件事情--量子操作和测量，我们为他们提供了相应的函数：\n", + "在 `forward()` 函数中，我们需要定义协议的流程。如果我们想要训练一个模型，那么需要定义损失函数，并设置为 `forward()` 的返回值，这样才能不断更新参数使得损失函数最小化。如果我们仅仅是想要验证某个协议的结果，我们就做上述的事情，只需要把协议的流程定义清楚，就可以把我们感兴趣的值设为返回值。在 `forward()` 函数中，我们主要做两件事情--量子操作和测量，我们为他们提供了相应的函数：\n", "\n", "- `self.create_ansatz(party_id)` 是为某一参与方创建本地量子电路的函数。所以参数 `party_id` 用来指定参与方。举个例子 `cir1 = self.create_ansatz(\"Alice\")` 为 Alice 创建了电路。之后，我们可以在电路中添加不同的操作比如 X 门， CNOT 门等，也可以在添加门之后通过 `run()` 函数来运行电路，得到运行后的结果，如 `status_out = cir1.run(status)`。\n", "\n", @@ -141,7 +141,7 @@ "\n", "[1] Chitambar, Eric, et al. \"Everything you always wanted to know about LOCC (but were afraid to ask).\" [Communications in Mathematical Physics 328.1 (2014): 303-326.](https://link.springer.com/article/10.1007/s00220-014-1953-9)\n", "\n", - "[2] Zhao, Xuanqiang, et al. \"LOCCNet: a machine learning framework for distributed quantum information processing.\" [arXiv:2101.12190 (2021).](https://arxiv.org/abs/2101.12190)\n", + "[2] Zhao, Xuanqiang, et al. \"Practical distributed quantum information processing with LOCCNet.\" [npj Quantum Information 7, 159 (2021).](https://www.nature.com/articles/s41534-021-00496-x)\n", "\n", "[3] Bennett, Charles H., et al. \"Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels.\" [Physical Review Letters 70.13 (1993): 1895.](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.70.1895)\n", "\n", diff --git a/tutorial/locc/LOCCNET_Tutorial_EN.ipynb b/tutorial/locc/LOCCNET_Tutorial_EN.ipynb index 4df609b..b439701 100644 --- a/tutorial/locc/LOCCNET_Tutorial_EN.ipynb +++ b/tutorial/locc/LOCCNET_Tutorial_EN.ipynb @@ -133,7 +133,7 @@ "\n", "[1] Chitambar, Eric, et al. \"Everything you always wanted to know about LOCC (but were afraid to ask).\" [Communications in Mathematical Physics 328.1 (2014): 303-326.](https://link.springer.com/article/10.1007/s00220-014-1953-9)\n", "\n", - "[2] Zhao, Xuanqiang, et al. \"LOCCNet: a machine learning framework for distributed quantum information processing.\" [arXiv:2101.12190 (2021).](https://arxiv.org/abs/2101.12190)\n", + "[2] Zhao, Xuanqiang, et al. \"Practical distributed quantum information processing with LOCCNet.\" [npj Quantum Information 7, 159 (2021).](https://www.nature.com/articles/s41534-021-00496-x)\n", "\n", "[3] Bennett, Charles H., et al. \"Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels.\" [Physical Review Letters 70.13 (1993): 1895.](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.70.1895)\n", "\n", @@ -167,7 +167,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.9" + "version": "3.7.10" }, "toc": { "base_numbering": 1, diff --git a/tutorial/machine_learning/QClassifier_CN.ipynb b/tutorial/machine_learning/QClassifier_CN.ipynb index c848865..577da6f 100644 --- a/tutorial/machine_learning/QClassifier_CN.ipynb +++ b/tutorial/machine_learning/QClassifier_CN.ipynb @@ -15,7 +15,7 @@ "source": [ "## 概览\n", "\n", - "本教程我们将讨论量子分类器（quantum classifier）的原理，以及如何利用量子神经网络（quantum neural network, QNN）来完成**两分类**任务。这类方法早期工作的主要代表是 Mitarai et al.(2018) 的量子电路学习 [(Quantum Circuit Learning, QCL)](https://arxiv.org/abs/1803.00745) [1], Farhi & Neven (2018) [2] 和 Schuld et al.(2018) 的中心电路量子分类器 [Circuit-Centric Quantum Classifiers](https://arxiv.org/abs/1804.00633) [3]。这里我们以第一类的 QCL 框架应用于监督学习（Supervised learning）为例进行介绍，通常我们需要先将经典数据编码成量子数据，然后通过训练量子神经网络的参数，最终得到一个最优的分类器。" + "本教程我们将讨论量子分类器（quantum classifier）的原理，以及如何利用量子神经网络（quantum neural network, QNN）来完成**二分类**任务。这类方法早期工作的主要代表是 Mitarai et al.(2018) 的量子电路学习 [(Quantum Circuit Learning, QCL)](https://arxiv.org/abs/1803.00745) [1], Farhi & Neven (2018) [2] 和 Schuld et al.(2018) 的中心电路量子分类器 [Circuit-Centric Quantum Classifiers](https://arxiv.org/abs/1804.00633) [3]。这里我们以第一类的 QCL 框架应用于监督学习（Supervised learning）为例进行介绍，通常我们需要先将经典数据编码成量子数据，然后通过训练量子神经网络的参数，最终得到一个最优的分类器。" ] }, { @@ -40,7 +40,7 @@ "\n", "这里我们给出实现量子电路学习 (QCL) 框架下量子分类器的一个流程。\n", "\n", - "1. 将经典数据编码$x^k$为量子数据$\\lvert \\psi_{\\rm in}\\rangle^k$。本教材采用角度编码。关于编码方式的具体操作，见[量子态编码经典数据](./DataEncoding_EN.ipynb)。用户也可以尝试其他编码，如振幅编码，体验不同编码方式学习效率的区别。\n", + "1. 将经典数据编码$x^k$为量子数据$\\lvert \\psi_{\\rm in}\\rangle^k$。本教程采用角度编码。关于编码方式的具体操作，见[量子态编码经典数据](./DataEncoding_CN.ipynb)。用户也可以尝试其他编码，如振幅编码，体验不同编码方式对分类器学习效率的影响。\n", "2. 构建可调参数量子电路，对应幺正变换(unitary gate)$U(\\theta)$。\n", "3. 对每一个量子数据$\\lvert\\psi_{\\rm in}\\rangle^k$，通过参数化量子电路$U(\\theta)$，得到输出态$\\lvert \\psi_{\\rm out}\\rangle^k = U(\\theta)\\lvert \\psi_{\\rm in} \\rangle^k$。\n", "4. 对每一个量子数据得到的输出量子态$\\lvert \\psi_{\\rm out}\\rangle^k$，通过测量与数据后处理，得到标签 $\\tilde{y}^{k}$。\n", @@ -69,9 +69,18 @@ "start_time": "2021-03-02T09:15:03.413324Z" } }, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Users\\yeruilin\\Anaconda3\\envs\\paddle_quantum_env\\lib\\site-packages\\matplotlib_inline\\config.py:66: DeprecationWarning: InlineBackend._figure_formats_changed is deprecated in traitlets 4.1: use @observe and @unobserve instead.\n", + " def _figure_formats_changed(self, name, old, new):\n" + ] + } + ], "source": [ - "# 导入numpy与paddle\n", + "# 导入 numpy 与 paddle\n", "import numpy as np\n", "import paddle\n", "\n", @@ -79,8 +88,8 @@ "from paddle_quantum.circuit import UAnsatz\n", "# 一些用到的函数\n", "from numpy import pi as PI\n", - "from paddle import matmul, transpose # paddle矩阵乘法与转置\n", - "from paddle_quantum.utils import pauli_str_to_matrix,dagger # 得到N量子比特泡利矩阵,复共轭\n", + "from paddle import matmul, transpose, reshape # paddle 矩阵乘法与转置\n", + "from paddle_quantum.utils import pauli_str_to_matrix,dagger # 得到 N 量子比特泡利矩阵,复共轭\n", "\n", "# 作图与计算时间\n", "from matplotlib import pyplot as plt\n", @@ -100,18 +109,19 @@ "metadata": {}, "outputs": [], "source": [ - "# 训练参数设置\n", + "# 数据集参数设置\n", "Ntrain = 200 # 规定训练集大小\n", "Ntest = 100 # 规定测试集大小\n", - "gap = 0.5 # 设定决策边界的宽度\n", + "boundary_gap = 0.5 # 设置决策边界的宽度\n", + "seed_data = 2 # 固定随机种子\n", + "# 训练参数设置\n", "N = 4 # 所需的量子比特数量\n", "DEPTH = 1 # 采用的电路深度\n", "BATCH = 20 # 训练时 batch 的大小\n", - "EPOCH = int(200 * BATCH / Ntrain) \n", + "EPOCH = int(200 * BATCH / Ntrain)\n", " # 训练 epoch 轮数，使得总迭代次数 EPOCH * (Ntrain / BATCH) 在200左右\n", "LR = 0.01 # 设置学习速率\n", - "seed_paras = 19 # 设置随机种子用以初始化各种参数\n", - "seed_data = 2 # 固定生成数据集所需要的随机种子" + "seed_paras = 19 # 设置随机种子用以初始化各种参数" ] }, { @@ -120,7 +130,7 @@ "source": [ "### 数据集的生成\n", "\n", - "对于监督学习来说，我们绕不开的一个问题就是——采用的数据集是什么样的？在这个教程中我们按照论文 [1] 里所提及方法生成简单的圆形决策边界二分数据集 $\\{(x^{k}, y^{k})\\}$。其中数据点 $x^{k}\\in \\mathbb{R}^{2}$，标签 $y^{k} \\in \\{0,1\\}$。\n", + "对于监督学习来说，我们绕不开的一个问题就是——采用什么样的数据集呢？在这个教程中我们按照论文 [1] 里所提及方法生成简单的圆形决策边界二分数据集 $\\{(x^{k}, y^{k})\\}$。其中数据点 $x^{k}\\in \\mathbb{R}^{2}$，标签 $y^{k} \\in \\{0,1\\}$。\n", "\n", " \n", "
    图 2：生成的数据集和对应的决策边界
    \n", @@ -137,7 +147,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2021-03-02T09:15:04.631031Z", @@ -183,7 +193,7 @@ " print(\"训练集的维度大小 x {} 和 y {}\".format(np.shape(train_x[0:Ntrain]), np.shape(train_y[0:Ntrain])))\n", " print(\"测试集的维度大小 x {} 和 y {}\".format(np.shape(train_x[Ntrain:]), np.shape(train_y[Ntrain:])), \"\\n\")\n", "\n", - " return train_x[0:Ntrain], train_y[0:Ntrain], train_x[Ntrain:], train_y[Ntrain:]\n" + " return train_x[0:Ntrain], train_y[0:Ntrain], train_x[Ntrain:], train_y[Ntrain:]" ] }, { @@ -195,7 +205,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ @@ -225,7 +235,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2021-03-02T09:15:06.422981Z", @@ -245,7 +255,7 @@ }, { "data": { - "image/png": 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", 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", 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", 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VuQVS2UNju3K6cWauLJa0HHgc+AjwHHAv8OnsLScl/THwexFxiaRNwMcj4lOSzgK+C2wA3grcDrwtIl4f9Z2uLLZa8m3uEq6crq0iK4s3APsi4smIeAW4HtjYt85GYGf6/Cbgw5KUzr8+Il6OiKeAfennmTWPb3OXqHN9iQ2URyA4BXg28/q5dN7AddKb3f8SWDPhewGQtFXSoqTFAwcO5JBsswZoYll7netLbKDGVBZHxI6ImI+I+bVr11adHLPiNbWsvc71JTZQHoFgP3Ba5vWp6byB60g6DvhN4OCE77Wua2KuOA917pswSlPv29xheVQWH0dSWfxhkpP4vcAfRsSezDpfBt6ZqSz+txHxSUm/A/wvjlQW3wGc6cpi+5U699gt2rJlg2+YIyX1EGZTKqyyOC3zvxS4FXgUuDEi9ki6UtKF6WrfBNZI2gd8FdiWvncPcCPwCPB/gC+PCwLWMU3NFefBZe1WEo81ZPXW5Vxxl6+GrBAea8iaqcu5Ype1W0kcCKzeBrVA+bVfg8OHu1F57L4JVgIHAqu3/lzxmjXJ48GDzWpSaTaBqhrIORBY/WVzxSecAK+8cvTyulQed7WZq+Wiym4jDgTWLHUbvqB38pfgs59tXuevaTjQFarKBnIOBNYsdao8zmbh4NjWTXW5UslDU3s5N8igcfpGzc+TAwHO6DRKnYYvGJSF69eWgda63J+jJMuXTzc/T50PBM7oNMywJpVQfjSf5CTflmaudSuSa6HXh3SlHTY/T50PBM7oNFB/k0qoJpqPO8m3aaC1OhXJtdTc3HTz89T5QOCMTgtUFc0HFVNJyWPbOn/VqUiupS644Mjh01PWJu58IHBGpwWqiuaDiqmuuy65Kmlb5y/3ci7UwgLs3Hl0ewMJtmwpZxN3fqwhD+fSAr41ojVcWYewxxoawhmdFnCxhTVc1UXUnQ8E4OFcGs/R3Bqu6iJqBwJrB0dza7CqL2pnCgSSVku6TdLe9HHVgHXOlvRDSXskPSjpU5ll10p6StL96XT2LOkxK5V7IlpOqr6onamyWNKfAoci4ipJ24BVEXFZ3zpvAyIi9kp6K3Af8I6I+IWka4H/HRE3TfO9vjGNVc6tDKyBiqos3gjsTJ/vBC7qXyEiHo+IvenzfwReANbO+L1m1XJPRGuRWQPBSRHxfPr8J8BJo1aWtAFYATyRmb09LTK6WtLxM6bHrBxVN/Mwy9HYQCDpdkkPD5g2ZteLpIxpaDmTpJOB64DPR0TvZrOXA28H/iWwGrhsyNuRtFXSoqTFAwcOjP9lZkWqupmHWY7GBoKIODcifnfAdDPw0/QE3zvRvzDoMyT9BvB94IqIuCfz2c9H4mXg28CGEenYERHzETG/dq1LlqxiVTfzMMvRrEVDu4Et6fMtwM39K0haAXwP+E5/pXAmiIikfuHhGdNjVo6qm3lYq5XdIG3WVkNrgBuBdcDTwCcj4pCkeeCSiPiipM+Q5Pb3ZN76uYi4X9KdJBXHAu5P33N43Pe61ZCZtVWRDdKGtRrq/FhD4ywsJA1BnnkmKf7dvt2ZPjMrTpHjDnmsoSXwTWtawh2/rEGqaJDmQDCCm4q3gKO5NUwVDdIcCEZwU/EWcDS3hqmiQZoDwQhuKl5zkxT5tCmau4irE6pokOZAMIKbitfYpEU+bYnmLuLqlLIH03UgGMFNxWts0iKftkRzF3FZgdx81Jpp2bKjb/DaIyXZqKw2tAGe5veaDTGs+ehxVSTGbGbr1g1ubD2oyGfz5uad+PtN83vNpuSiIWumthT5TKprv9dK5UBgzdS1Cpyu/V4rlesIctCGImgzaz8PMdEnrybZbtVnZk3XyUCQ58nbrfrMrOk6GQjyPHm3qeOqmXVTJwNBnifvtnRcNbPu6mQgyPPk7VZ9ZtZ0MwUCSasl3SZpb/q4ash6r0u6P512Z+afLulHkvZJuiG9rWXh8jx5u1WfmTXdrFcE24A7IuJM4I709SAvRcTZ6XRhZv6fAFdHxG8BPwe+MGN6JpL3ybvsAaLMzPI06z2LHwM+EBHPpzeivzsifnvAeocj4oS+eQIOAG+JiNckvQ/4ekScN+5769aPwMysCYrqR3BSRDyfPv8JcNKQ9d4kaVHSPZIuSuetAX4REa+lr58DTpkxPWZmNqWxg85Juh14y4BFRzW2jIiQNOzyYi4i9ks6A7hT0kPAL6dJqKStwFaAdW6SY2aWm7GBICLOHbZM0k8lnZwpGnphyGfsTx+flHQ38C7gb4A3SzouvSo4Fdg/Ih07gB2QFA2NS7eZmU1m1qKh3cCW9PkW4Ob+FSStknR8+vxE4P3AI5FUTtwFXDzq/WZmVqxZA8FVwEck7QXOTV8jaV7SNek67wAWJT1AcuK/KiIeSZddBnxV0j6SOoNvzpgeMzOb0kyBICIORsSHI+LMiDg3Ig6l8xcj4ovp87+PiHdGxL9IH7+Zef+TEbEhIn4rIj4RES/P9nOqMckAdr7vuJnVle9QNqPeAHa9sYt6A9jBkf4Ek6xjZlaVzgwxUVSOfJIB7DxCqZnVWSeuCIrMkU8ygJ1HKDWzOuvEFUGROfJJBrDzCKVm7dWG+r9OBIIic+TjBrBbWIDDh499n0coNWu+ttyhsBOBoMgc+agB7HoHycGDR79nzRqPUGrWBm2p/+vEzev76wggyZEXfTJevz7JIfSbm0tGKTWzZlu2LLkS6CcloxHXTadvXl/VPQNcSWzWbm2p/+tEIIBq7hnQloPEzAab9iZXS61YLrpCujOBoAq+jaVZu01T2rDUiuUyKqQ7UUdQpYWFpOLomWeSK4Ht211JbNZFS60zzLOucVgdgQOBmVkJllqxnGeFdKcri9ukDZ1XzLpoqXWGZdQ1OhA0SFs6r5h10VLrDMuoa3QgaJC2dF4x66KlNmMvo/m76wgapGmdV8ysXgqpI5C0WtJtkvamj6sGrPNBSfdnpn+SdFG67FpJT2WWnT1LetrO/RLMrAizFg1tA+6IiDOBO9LXR4mIuyLi7Ig4G/gQ8CLwfzOr/Ofe8oi4f8b0tJr7JZhZEWYNBBuBnenzncBFY9a/GPhBRLw4Zj0boKqhMsys3WYNBCdFxPPp858AJ41ZfxPw3b552yU9KOlqScfPmJ7Wq2KoDDNrt7F3KJN0O/CWAYuOaqsSESFpaM2zpJOBdwK3ZmZfThJAVgA7gMuAK4e8fyuwFWCdC8XNzHIz9oogIs6NiN8dMN0M/DQ9wfdO9C+M+KhPAt+LiFczn/18JF4Gvg1sGJGOHRExHxHza9eunfT3mZktWVc6cM5aNLQb2JI+3wLcPGLdT9NXLJQJIiKpX3h4xvSYmU1s1Im+Sx04Zw0EVwEfkbQXODd9jaR5Sdf0VpK0HjgN+H9971+Q9BDwEHAi8N9mTI+N0JXcjdkkxp3ou9SB0x3KxuiNHvr007B8Obz+etJap2mjiFZ1lzazuho3qmcbO3B60LklyOYYIAkC0MxLxC7lbswmMeoOggsLSSAYpKi2KlVesfuKYIRhOYaeJt17uI25G7NZDPt/r1kDL710bMYJiruKLuuK3VcESzDu3sJNuvewh6cwS/Ry3k8/nWSEsno99wcFgeXLiwsCW7ZUe8XuQDDCUscJryMPT2F2bHFvxJFg0Oupf+jQ4Pe+8cZ0QWCSop5eenrFzv1Ky2xGROOmc845J8qwa1fEypURyeFy9LRyZbK8SXbtipibi5CSx6al32xWc3OD/89zc9OtM86gc8egc8aw71rKd04CWIwB59TKT+pLmcoKBBFHTp4QsXz5kZ1T1UnUJ3OzpZMGn3ClI+tMehIfZdJgMiw9RWU2HQhaII8DtGoOZFalSU/Qsx6nkwScUelZvryY/4YDQQvkccmaVfZJuQ2BzJqtrGNwmoBT5n/CgaAFJs1lTKKKk3LegcxsKcrIAE3z/yozQzYsELgfQYOM6wlZ1WdNyn0ZrEt6oxI880zSwrAOoxG4H0EL5NkEdFSvyqK4L4N1SZPuHeJA0CB53qGsipPyoEAmwQUXFPedZjaeA0HD5JXLGHd1UcS4J5s3Jz0os705I2DnzmaN29QGHonWjjKo4qDuU1cri/M2rJKqyIrkulQYd7kZaxtbb3V5f04DtxoqXlsOxiJP1nm2fFqqNp4Ip1GXYJyXru/PaQwLBC4aykmb7mZUZEVyHSqMuz4k97T7t+7FSG3cn6Vv80HRYdIJ+ASwB3gDmB+x3vnAY8A+YFtm/unAj9L5NwArJvneOl4RtCmXVeRvqUPurQ5XJVWaZv/WYX+N07b9WeQ2p4iiIeAdwG8Ddw8LBMBy4AngDGAF8ABwVrrsRmBT+vyvgC9N8r11DARtOhiL/vNXXYTWpqC9FNPs3yZsqyakcRpF/p5CAsGvPmR0IHgfcGvm9eXpJOBnwHGD1hs11TEQtO1grPpkXaQm5HKLNun+bUIGp237s8htPiwQlFFHcArwbOb1c+m8NcAvIuK1vvmN1Lbx/pvUGWZaefbHaKpJ928d6nTGadv+rGKbjw0Ekm6X9PCAaWNxyRqYjq2SFiUtHjhwoMyvnkjbDsa2a3Ogy1NTMjht2p9VbPPjxq0QEefO+B37gdMyr09N5x0E3izpuPSqoDd/WDp2ADsgGWtoxjQVYvPmZh+AZv16x3Pdxsxpsyq2+dhAkIN7gTMlnU5yot8E/GFSFqa7gIuB64EtwM0lpMfMpuAMTvnK3uYz1RFI+rik50gqer8v6dZ0/lsl3QKQ5vYvBW4FHgVujIg96UdcBnxV0j6SOoNvzpIeMzObnoehNjPrCA9DbWZmAzkQmJl1nAOBmVnHNbKOQNIBYMCNFidyIkmP5rpxuqZT13RBfdPmdE2vrmlbarrmImJt/8xGBoJZSFocVFlSNadrOnVNF9Q3bU7X9OqatrzT5aIhM7OOcyAwM+u4LgaCHVUnYAinazp1TRfUN21O1/TqmrZc09W5OgIzMztaF68IzMwsw4HAzKzjWhkIJH1C0h5Jb0ga2sRK0vmSHpO0T9K2zPzTJf0onX+DpBU5pWu1pNsk7U0fVw1Y54OS7s9M/yTponTZtZKeyiw7u6x0peu9nvnu3Zn5VW6vsyX9MN3fD0r6VGZZrttr2PGSWX58+vv3pdtjfWbZ5en8xySdN0s6lpCur0p6JN0+d0iayywbuE9LTNvnJB3IpOGLmWVb0n2/V9KWktN1dSZNj0v6RWZZYdtM0rckvSDp4SHLJenP03Q/KOndmWVL316DblvW9ImK7qU8Qbr+FNiWPt8G/MmY9VcDh4CV6etrgYsL2F4TpQs4PGR+ZdsLeBtwZvr8rcDzwJvz3l6jjpfMOn8M/FX6fBNwQ/r8rHT944HT089ZXmK6Ppg5hr7US9eofVpi2j4H/MWA964GnkwfV6XPV5WVrr71vwJ8q6Rt9q+BdwMPD1l+AfADklv9vhf4UR7bq5VXBBHxaEQ8Nma1DcC+iHgyIl4huSfCRkkCPgTclK63E7gop6RtTD9v0s+9GPhBRLyY0/cPM226fqXq7RURj0fE3vT5PwIvAMf0nMzBwONlRHpvAj6cbp+NwPUR8XJEPAXsSz+vlHRFxF2ZY+gekptAlWGSbTbMecBtEXEoIn4O3AacX1G6Pg18N6fvHiki/o4k8zfMRuA7kbiH5OZeJzPj9mplIJhQFfdSPikink+f/wQ4acz6mzj2ANyeXhJeLen4ktP1JiW3C72nV1xFjbaXpA0kObwnMrPz2l7DjpeB66Tb45ck22eS9xaZrqwvkOQoewbt07xMmrY/SPfRTZJ6dzOsxTZLi9FOB+7MzC5ym40zLO0zba8y7lBWCEm3A28ZsOiKiKjsTmej0pV9EREhaWjb3TTKv5Pkhj49l5OcEFeQtCO+DLiyxHTNRcR+SWcAd0p6iORkt2Q5b6/rgC0R8UY6e8nbq40kfQaYB34/M/uYfRoRTwz+hEL8LfDdiHhZ0r8nuaL6UInfP84m4KaIeD0zr+ptlrvGBoKoyb2Up0mXpJ9KOjkink9PXC+M+KhPAt+LiFczn93LHb8s6dvAfyozXRGxP318UtLdwLuAv6Hi7SXpN4Dvk2QC7sl89pK31wDDjpdB6zwn6TjgN0mOp0neW2S6kHQuSXD9/Yh4uTd/yD7N66Q2Nm0RcTDz8hqSeqHeez/Q9967y0pXxibgy9kZBW+zcYalfabt1eWioV/dS1lJK5dNwO5Ial5691KGfO+lvDv9vEk+95hyyfRk2CuXvwgY2LKgiHRJWtUrWpF0IvB+4JGqt1e6775HUm56U9+yPLfXwONlRHovBu5Mt89uYJOSVkWnA2cC/zBDWqZKl6R3Af8TuDAiXsjMH7hPc0rXpGk7OfPyQpLb2UJyJfzRNI2rgI9y9NVxoelK0/Z2korXH2bmFb3NxtkN/Lu09dB7gV+mGZ7ZtldRtd9VTsDHScrIXgZ+Ctyazn8rcEtmvQuAx0mi+RWZ+WeQ/FH3AX8NHJ9TutYAdwB7gduB1en8eeCazHrrSSL8sr733wk8RHJC2wWcUFa6gH+VfvcD6eMX6rC9gM8ArwL3Z6azi9heg44XkqKmC9Pnb0p//750e5yRee8V6fseAz6W8/E+Ll23p/+D3vbZPW6flpi2/w7sSdNwF/D2zHv/KN2W+4DPl5mu9PXXgav63lfoNiPJ/D2fHtPPkdTpXAJcki4X8I003Q+RaRU5y/byEBNmZh3X5aIhMzPDgcDMrPMcCMzMOs6BwMys4xwIzMw6zoHAzKzjHAjMzDru/wPTby8hcT1iEgAAAABJRU5ErkJggg==", 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    " ] @@ -284,12 +294,6 @@ } ], "source": [ - "# 数据集参数设置\n", - "Ntrain = 200 # 规定训练集大小\n", - "Ntest = 100 # 规定测试集大小\n", - "boundary_gap = 0.5 # 设置决策边界的宽度\n", - "seed_data = 2 # 固定随机种子\n", - "\n", "# 生成自己的数据集\n", "train_x, train_y, test_x, test_y = circle_data_point_generator(Ntrain, Ntest, boundary_gap, seed_data)\n", "\n", @@ -434,7 +438,7 @@ }, "outputs": [], "source": [ - "# 构建绕Y轴，绕Z轴旋转theta角度矩阵\n", + "# 构建绕 Y 轴，绕 Z 轴旋转 theta 角度矩阵\n", "def Ry(theta):\n", " \"\"\"\n", " :param theta: 参数\n", @@ -466,20 +470,20 @@ " zero_state = np.array([[1, 0]])\n", " # 角度编码\n", " for i in range(n_qubits):\n", - " # 对偶数编号量子态作用Rz(arccos(x0^2)) Ry(arcsin(x0))\n", + " # 对偶数编号量子态作用 Rz(arccos(x0^2)) Ry(arcsin(x0))\n", " if i % 2 == 0:\n", " state_tmp=np.dot(zero_state, Ry(np.arcsin(data[sam][0])).T)\n", " state_tmp=np.dot(state_tmp, Rz(np.arccos(data[sam][0] ** 2)).T)\n", " res_state=np.kron(res_state, state_tmp)\n", - " # 对奇数编号量子态作用Rz(arccos(x1^2)) Ry(arcsin(x1))\n", + " # 对奇数编号量子态作用 Rz(arccos(x1^2)) Ry(arcsin(x1))\n", " elif i % 2 == 1:\n", " state_tmp=np.dot(zero_state, Ry(np.arcsin(data[sam][1])).T)\n", " state_tmp=np.dot(state_tmp, Rz(np.arccos(data[sam][1] ** 2)).T)\n", " res_state=np.kron(res_state, state_tmp)\n", " res.append(res_state)\n", - "\n", " res = np.array(res)\n", - " return res.astype(\"complex128\")\n" + "\n", + " return res.astype(\"complex128\")" ] }, { @@ -573,7 +577,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2021-03-02T09:15:06.795398Z", @@ -592,7 +596,7 @@ " \"\"\"\n", " # 初始化网络\n", " cir = UAnsatz(n)\n", - " \n", + "\n", " # 先搭建广义的旋转层\n", " for i in range(n):\n", " cir.rz(theta[i][0], i)\n", @@ -699,7 +703,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2021-03-02T09:15:07.667491Z", @@ -716,12 +720,13 @@ " :return: 局部可观测量: Z \\otimes I \\otimes ...\\otimes I\n", " \"\"\"\n", " Ob = pauli_str_to_matrix([[1.0, 'z0']], n)\n", + "\n", " return Ob" ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 9, "metadata": {}, "outputs": [], "source": [ @@ -735,7 +740,6 @@ " super(Opt_Classifier, self).__init__()\n", " self.n = n\n", " self.depth = depth\n", - " \n", " # 初始化参数列表 theta，并用 [0, 2*pi] 的均匀分布来填充初始值\n", " self.theta = self.create_parameter(\n", " shape=[n, depth + 3], # 此处使用量子电路有初始一层广义旋转门，故+3\n", @@ -759,22 +763,22 @@ " \"\"\"\n", " # 将 Numpy array 转换成 tensor\n", " Ob = paddle.to_tensor(Observable(self.n))\n", - " label_pp = paddle.to_tensor(label)\n", + " label_pp = reshape(paddle.to_tensor(label), [-1, 1])\n", "\n", " # 按照随机初始化的参数 theta \n", " cir = cir_Classifier(self.theta, n=self.n, depth=self.depth)\n", " Utheta = cir.U\n", - " \n", + "\n", " # 因为 Utheta是学习到的，我们这里用行向量运算来提速而不会影响训练效果\n", " state_out = matmul(state_in, Utheta) # [-1, 1, 2 ** n]形式，第一个参数在此教程中为BATCH\n", - " \n", + "\n", " # 测量得到泡利 Z 算符的期望值 -- shape [-1,1,1]\n", " E_Z = matmul(matmul(state_out, Ob), transpose(paddle.conj(state_out), perm=[0, 2, 1]))\n", - " \n", + "\n", " # 映射 处理成标签的估计值 \n", " state_predict = paddle.real(E_Z)[:, 0] * 0.5 + 0.5 + self.bias # 计算每一个y^{i,k}与真实值得平方差\n", " loss = paddle.mean((state_predict - label_pp) ** 2) # 对BATCH个得到的平方差取平均，得到L_i：shape:[1,1]\n", - " \n", + "\n", " # 计算交叉验证正确率\n", " is_correct = (paddle.abs(state_predict - label_pp) < 0.5).nonzero().shape[0]\n", " acc = is_correct / label.shape[0]\n", @@ -842,7 +846,7 @@ "metadata": {}, "outputs": [], "source": [ - "def QClassifier(Ntrain, Ntest, gap, N, DEPTH, EPOCH, LR, BATCH, seed_paras, seed_data,):\n", + "def QClassifier(Ntrain, Ntest, gap, N, DEPTH, EPOCH, LR, BATCH, seed_paras, seed_data):\n", " \"\"\"\n", " 量子二分类器\n", " 输入参数：\n", @@ -861,7 +865,7 @@ " train_x, train_y, test_x, test_y = circle_data_point_generator(Ntrain=Ntrain, Ntest=Ntest, boundary_gap=gap, seed_data=seed_data)\n", " # 读取训练集的维度\n", " N_train = train_x.shape[0]\n", - " \n", + "\n", " paddle.seed(seed_paras)\n", " # 初始化寄存器存储正确率 acc 等信息\n", " summary_iter, summary_test_acc = [], []\n", @@ -904,7 +908,7 @@ " loss.backward()\n", " opt.minimize(loss)\n", " opt.clear_grad()\n", - " \n", + "\n", " # 得到训练后电路\n", " print(\"训练后的电路：\")\n", " print(cir)\n", @@ -960,7 +964,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "主程序段总共运行了 7.24103569984436 秒\n" + "主程序段总共运行了 6.890974283218384 秒\n" ] } ], @@ -998,6 +1002,379 @@ "通过打印训练结果可以看到不断优化后分类器在测试集和数据集的正确率都达到了 $100\\%$。" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 研究不同的编码方式\n", + "\n", + "监督学习的编码方式对分类结果有很大影响 [4]。在量桨中，我们集成了常用的编码方式，包括振幅编码、角度编码、IQP编码等。 用户可以用内置的 ``SimpleDataset`` 类实例对简单分类数据（不需要降维的数据）进行编码；也可以用内置的 ``VisionDataset`` 类实例对图片数据进行编码。编码的方法都是调用类对象的 ``encode`` 方法。" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "(100, 4)\n" + ] + } + ], + "source": [ + "# 使用前面构建的圆形数据集研究编码\n", + "from paddle_quantum.dataset import *\n", + "\n", + "# 用两个量子比特编码二维数据\n", + "quantum_train_x = SimpleDataset(2).encode(train_x, 'angle_encoding', 2)\n", + "quantum_test_x = SimpleDataset(2).encode(test_x, 'angle_encoding', 2)\n", + "\n", + "print(type(quantum_test_x)) # ndarray\n", + "print(quantum_test_x.shape) # (100, 4)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "这里我们对上面的分类器进行化简，之后的所有分类都采用这个分类器。" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [], + "source": [ + "# 简化的分类器\n", + "def QClassifier2(quantum_train_x, train_y,quantum_test_x,test_y, N, DEPTH, EPOCH, LR, BATCH):\n", + " \"\"\"\n", + " 量子二分类分类器\n", + " 输入：\n", + " quantum_train_x # 训练特征\n", + " train_y # 训练标签\n", + " quantum_test_x # 测试特征\n", + " test_y # 测试标签\n", + " N # 使用的量子比特数目\n", + " DEPTH # 分类器电路的深度\n", + " EPOCH # 迭代次数\n", + " LR # 学习率\n", + " BATCH # 一个批量的大小\n", + " \"\"\"\n", + " Ntrain = len(quantum_train_x)\n", + " \n", + " paddle.seed(1)\n", + "\n", + " net = Opt_Classifier(n=N, depth=DEPTH)\n", + "\n", + " # 测试准确率列表\n", + " summary_iter, summary_test_acc = [], []\n", + "\n", + " # 这里用 Adam，但是也可以是 SGD 或者 RMSprop\n", + " opt = paddle.optimizer.Adam(learning_rate=LR, parameters=net.parameters())\n", + "\n", + " # 进行优化\n", + " for ep in range(EPOCH):\n", + " for itr in range(Ntrain // BATCH):\n", + " # 导入数据\n", + " input_state = quantum_train_x[itr * BATCH:(itr + 1) * BATCH] # paddle.tensor类型\n", + " input_state = reshape(input_state, [-1, 1, 2 ** N])\n", + " label = train_y[itr * BATCH:(itr + 1) * BATCH]\n", + " test_input_state = reshape(quantum_test_x, [-1, 1, 2 ** N])\n", + "\n", + " loss, train_acc, state_predict_useless, cir = net(state_in=input_state, label=label)\n", + "\n", + " if itr % 5 == 0:\n", + " # 获取测试准确率\n", + " loss_useless, test_acc, state_predict_useless, t_cir = net(state_in=test_input_state, label=test_y)\n", + " print(\"epoch:\", ep, \"iter:\", itr,\n", + " \"loss: %.4f\" % loss.numpy(),\n", + " \"train acc: %.4f\" % train_acc,\n", + " \"test acc: %.4f\" % test_acc)\n", + " summary_test_acc.append(test_acc)\n", + "\n", + " loss.backward()\n", + " opt.minimize(loss)\n", + " opt.clear_grad()\n", + "\n", + " return summary_test_acc" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "现在可以开始用不同编码方式对上面产生的圆形数据进行编码。这里我们采用五种编码方法：振幅编码、角度编码、泡利旋转编码、IQP编码、复杂纠缠编码。然后我们绘制出测试精度曲线以便分析。" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Encoding method: amplitude_encoding\n", + "epoch: 0 iter: 0 loss: 0.3066 train acc: 0.4000 test acc: 0.5400\n", + "epoch: 0 iter: 5 loss: 0.2378 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 10 loss: 0.2308 train acc: 0.8000 test acc: 0.6700\n", + "epoch: 0 iter: 15 loss: 0.2230 train acc: 0.8000 test acc: 0.6100\n", + "Encoding method: angle_encoding\n", + "epoch: 0 iter: 0 loss: 0.2949 train acc: 0.5000 test acc: 0.3600\n", + "epoch: 0 iter: 5 loss: 0.1770 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 10 loss: 0.1654 train acc: 0.8000 test acc: 0.7000\n", + "epoch: 0 iter: 15 loss: 0.1966 train acc: 0.7000 test acc: 0.5800\n", + "Encoding method: pauli_rotation_encoding\n", + "epoch: 0 iter: 0 loss: 0.2433 train acc: 0.6000 test acc: 0.7000\n", + "epoch: 0 iter: 5 loss: 0.2142 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 10 loss: 0.2148 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 15 loss: 0.2019 train acc: 0.8000 test acc: 0.7600\n", + "Encoding method: IQP_encoding\n", + "epoch: 0 iter: 0 loss: 0.2760 train acc: 0.6000 test acc: 0.4200\n", + "epoch: 0 iter: 5 loss: 0.1916 train acc: 0.6000 test acc: 0.6200\n", + "epoch: 0 iter: 10 loss: 0.1355 train acc: 0.9000 test acc: 0.7300\n", + "epoch: 0 iter: 15 loss: 0.1289 train acc: 0.9000 test acc: 0.6700\n", + "Encoding method: complex_entangled_encoding\n", + "epoch: 0 iter: 0 loss: 0.3274 train acc: 0.3000 test acc: 0.2900\n", + "epoch: 0 iter: 5 loss: 0.2120 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 10 loss: 0.2237 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 15 loss: 0.2095 train acc: 0.8000 test acc: 0.7200\n" + ] + } + ], + "source": [ + "# 测试不同编码方式\n", + "encoding_list = ['amplitude_encoding', 'angle_encoding', 'pauli_rotation_encoding', 'IQP_encoding', 'complex_entangled_encoding']\n", + "num_qubit = 2 # 这里需要小心，如果量子比特数目取 1，可能会报错，因为有 CNOT 门\n", + "dimension = 2\n", + "acc_list = []\n", + "\n", + "for i in range(len(encoding_list)):\n", + " encoding = encoding_list[i]\n", + " print(\"Encoding method:\", encoding)\n", + " # 用 SimpleDataset 类来编码数据，这里数据维度为 2，编码量子比特数目也是 2\n", + " quantum_train_x= SimpleDataset(dimension).encode(train_x, encoding, num_qubit)\n", + " quantum_test_x= SimpleDataset(dimension).encode(test_x, encoding, num_qubit)\n", + " quantum_train_x = paddle.to_tensor(quantum_train_x)\n", + " quantum_test_x = paddle.to_tensor(quantum_test_x)\n", + "\n", + " acc = QClassifier2(\n", + " quantum_train_x, # 训练特征\n", + " train_y, # 训练标签\n", + " quantum_test_x, # 测试特征\n", + " test_y, # 测试标签\n", + " N = num_qubit, # 使用的量子比特数目\n", + " DEPTH = 1, # 分类器电路的深度\n", + " EPOCH = 1, # 迭代次数\n", + " LR = 0.1, # 学习率\n", + " BATCH = 10, # 一个批量的大小\n", + " )\n", + " acc_list.append(acc)" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# 绘制五种编码方法的训练曲线\n", + "x=[2*i for i in range(len(acc_list[0]))]\n", + "for i in range(len(encoding_list)):\n", + " plt.plot(x,acc_list[i])\n", + "plt.legend(encoding_list)\n", + "plt.title(\"Benchmarking different encoding methods\")\n", + "plt.xlabel(\"Iteration\")\n", + "plt.ylabel(\"Test accuracy\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 用内置的 MNIST 和 Iris 数据集实现量子分类\n", + "\n", + "量桨将常用的分类数据集进行了编码，用户可以使用 `paddle_quantum.dataset` 模块获取编码的量子电路或者量子态。目前集成了4个数据集，包括 MNIST, FashionMNIST, Iris 和 BreastCancer。下面展示如何用这些内置数据集快速实现量子监督学习。\n", + "\n", + "我们从 Iris 数据集开始。Iris 数据集包括三种类别，每种类别有50个样本。数据集中只有四个特征，是比较简单且容易编码的数据集。" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "epoch: 0 iter: 0 loss: 0.3543 train acc: 0.0000 test acc: 0.0000\n", + "epoch: 0 iter: 5 loss: 0.2697 train acc: 0.5000 test acc: 0.5000\n", + "epoch: 0 iter: 10 loss: 0.2139 train acc: 1.0000 test acc: 0.9000\n", + "epoch: 0 iter: 15 loss: 0.1989 train acc: 0.7500 test acc: 0.9000\n", + "epoch: 1 iter: 0 loss: 0.0859 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 1 iter: 5 loss: 0.0432 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 1 iter: 10 loss: 0.0432 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 1 iter: 15 loss: 0.0531 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 2 iter: 0 loss: 0.0374 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 2 iter: 5 loss: 0.0356 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 2 iter: 10 loss: 0.0377 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 2 iter: 15 loss: 0.0440 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 3 iter: 0 loss: 0.0317 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 3 iter: 5 loss: 0.0344 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 3 iter: 10 loss: 0.0384 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 3 iter: 15 loss: 0.0412 train acc: 1.0000 test acc: 1.0000\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Iris 数据集二分类\n", + "\n", + "test_rate=0.2\n", + "num_qubit=4\n", + "\n", + "# 获取 Iris 数据集的量子态\n", + "iris =Iris (encoding='angle_encoding', num_qubits=num_qubit, test_rate=test_rate,classes=[0, 1], return_state=True)\n", + "\n", + "quantum_train_x, train_y = iris.train_x, iris.train_y\n", + "quantum_test_x, test_y = iris.test_x, iris.test_y\n", + "testing_data_num = len(test_y)\n", + "training_data_num = len(train_y)\n", + "\n", + "acc = QClassifier2(\n", + " quantum_train_x, # 训练特征\n", + " train_y, # 训练标签\n", + " quantum_test_x, # 测试特征\n", + " test_y, # 测试标签\n", + " N = num_qubit, # 使用的量子比特数目\n", + " DEPTH = 1, # 分类器电路的深度\n", + " EPOCH = 4, # 迭代次数\n", + " LR = 0.1, # 学习率\n", + " BATCH = 4, # 一个批量的大小\n", + " )\n", + "plt.plot(acc)\n", + "plt.title(\"Classify Iris 0&1 using angle encoding\")\n", + "plt.xlabel(\"Iteration\")\n", + "plt.ylabel(\"Testing accuracy\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "第二个例子为 MNIST 数据集。 MNIST 是手写数字数据集，有 0-9 十个类别（每一类训练集中有 6000 个样本，测试集中有 1000 个样本）。所有的图片都是 $28\\times28$ 的灰度图，所以需要使用 ``resize`` 或 ``PCA`` 降维到目标维度 ``target_dimension`` 。" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "epoch: 0 iter: 0 loss: 0.3237 train acc: 0.3250 test acc: 0.5450\n", + "epoch: 0 iter: 5 loss: 0.2124 train acc: 0.7500 test acc: 0.6500\n", + "epoch: 0 iter: 10 loss: 0.2294 train acc: 0.6500 test acc: 0.6850\n", + "epoch: 1 iter: 0 loss: 0.1970 train acc: 0.7250 test acc: 0.7850\n", + "epoch: 1 iter: 5 loss: 0.1521 train acc: 0.8500 test acc: 0.8150\n", + "epoch: 1 iter: 10 loss: 0.1726 train acc: 0.7750 test acc: 0.8900\n", + "epoch: 2 iter: 0 loss: 0.1742 train acc: 0.7250 test acc: 0.8650\n", + "epoch: 2 iter: 5 loss: 0.1167 train acc: 0.9000 test acc: 0.8900\n", + "epoch: 2 iter: 10 loss: 0.1654 train acc: 0.8000 test acc: 0.8950\n", + "epoch: 3 iter: 0 loss: 0.1609 train acc: 0.8000 test acc: 0.8850\n", + "epoch: 3 iter: 5 loss: 0.1148 train acc: 0.9250 test acc: 0.8850\n", + "epoch: 3 iter: 10 loss: 0.1649 train acc: 0.8000 test acc: 0.8750\n", + "epoch: 4 iter: 0 loss: 0.1629 train acc: 0.8250 test acc: 0.8750\n", + "epoch: 4 iter: 5 loss: 0.1112 train acc: 0.9000 test acc: 0.8700\n", + "epoch: 4 iter: 10 loss: 0.1630 train acc: 0.8500 test acc: 0.8850\n" + ] + }, + { + "data": { + "image/png": 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qM3y1a04kzTaz7KjLPEG4puabD+fw6icbSUttxfdPH8oV4weS0ghPeK8s2sCPn1lA4fYSjhrYPUwCQQLI6pZOVtegFLDv2PXxU7SjhPdXFPPe8k3MWl7Eyk07Aejevg1HD+rOsYO6M35QBv27pycsBtf4eYJwzcbcNZv50t9mcsX4Aawp2sVrn25kVFYXfnf+SIb2imW8+sTbtKOE22Ys5Ln56xjWqyO/u2AkI/t2SXZYFGzZzazlRcxcton3lm9iw7agNNOnSzuOCRPGsYMy6NU5LcmRugNVXmF1vkjyBOGajUv/8QEL127jnR9MIL1NCjM+WsvPn13E9j2lfHfCYL5z0mDatE5OfbuZ8d95a/n5swvZWVLONScP5tsnDkpaPDUxM1Zs2hlURy3bxKwVRWzZVQrAQZ3TEhJzRoe2HHNwd29Ij5PS8gpe+2QDT+bkkZaawr1fPbJO+/EE4ZqFD1cWc9H9s7h10qF864SDP5tftKOE259bxH/nrWVoz4789oKRHJHVpUFjW7tlN7dOX8AbiwsZ3S8o0Qzp2ThKNLGoqDAWrdvGrLDtoiLO5wUD1hTvYn7+VsorjLatW5E9oCvHhndejfCG9JgtL9zB1Jw8np6Tz6Yde+nVKY1LxvXj2lMG16mq0BOEa/LMjMkPvM/KTTt566YJtGuz/9Xna59s4NbpH7Nx+x6+cdxAbjhtaNT14qmiwnjswzX89oVPKa8wbjpjKJcdO6BRtok0BpEN6e8t28Sn64Nh0ju2bc1RB3fjmEEZjB/cnUN6eEN6pF17y3h+wXqezFlDzqrNtG4lTjm0B5PH9uOEQzLr9X2rKUE0mwGDXPM2c3kRH6ws5udnH1btSf+UQ3sydmA37njhU/7+zkpeWriBO84fwbGDMhIS08pNO/nh0/P5cGUx4wd35zdfGkm/7ukJOVZz0TEtlVMO7ckph/YEgtLfrBVFn1V1vfrJRiBoSD8mbBMZPzho4G9pDelmxoKCrTyZk8eMeWvZXlLGwRntufnMYZw3pg89Oia+rchLEK7RMzPOu3cmG7bu4Y2bTqJt69pLBbOWF3HztPmsLtrFJeP6ccukYXSK09PGZeUVPPjuSu56ZQltWrfiJ18YzoXZfVvcCSwRCrbsDtpElhft15B+7KDuHDs4SBo9OzXfhvStu0p5Zl4BT+Tk8cm6baSltmLSiIOYPLYfYwd0jfv3zKuYXJP2xqcbuWJKDr85bwSXjOsX83a795Zz16tLePCdFWR2bMuvzh3BqcN71iuWRWu38cOn57OgYCunD+/JL849vFmfrJLJzFheuJNZyzfx3rIiZq0oYuvuoCF9UGZ7xofPdfTq3C7ux24l6NUpjcyObRsk8VdUGO+vLOLJnDxe+Hg9e8sqGNGnMxePzeLsI3rH7eImGk8QrskyM75497ts213GazeeSGodGjI/ytvCD5+ez6frt3P2qN787IvD6d6h7QHto6SsnLtfX8a9by6nS3oqPz/7cCaN6OWlhgZU2ZA+M0wYH64sZndpzH171klaaiv6dk0na58HGD9/nqW+J+4N2/bw1Ox8pubmsbpoF53SWnPu6D5clJ3F4X06x+ld1MwThGuyXvx4PVc9Ops7LxzFBUf2rX2Dauwtq+C+t5bz19eX0qFta247+zDOHtU7phP87NWb+eHT81m2cQfnjenDT74wnK7t29Q5Fhcfe8sqWFCwlW1hqSKeyiqMdVt3k1e8K+wKJegXa/uefbtC6dwu9fMHILum0zdMIlld29Gna7uo1aFl5RW8sbiQJ3PW8MbiQsorjKMP7sbksf2YeHivBr/91xOEa5IqKowz//wOpRUVvPy9E+JyG+SSDdv5wVPzmZe3hZOH9eCX5x5O7y7Rqyh2lpRx58uLmTJzFQd1SuNX541gwtAe9Y7BNV1b9+lMMaJTxbAvrb3lFZ+tK0HPjmmfPz3fNZ09ZeVMn1PAxu0lZHZsy4VH9uWi7CwGZCSvyxhPEK5JmvHRWq59fC5/uWQ0Z4/qHbf9llcYU2au4s6XFpPSStwyaRiXjO23z22V7ywt5JZpC8jfvJuvHdOfH0wcRoe2ftOfq15FhbFxewl5m3expmj/HnnXb9uDgJOH9eDisf2YMDSzUTz74QnCNTll5RWc/qe3SW3ViheuOz4h98SvKdrFLdPn896yIo4a2I07zh9Jt/Q2/Or5RUzNzefgjPbccf5Ixg3sFvdju5anpKycvWUVjW7sDn8OwjU5/523lhWFO7nvq0cm7IGpft3TefQbRzE1N49f/u8TJv7pbTqmpbJ5117+76RBXHfKEO8OwsVN29YpMd2i3Zh4gnCNTml5BX9+bSmH9+nEGYfV77bU2kji4rH9OGloD26bsZD12/Yw5YqxDXYHiXONmScI1+g8NTufNcW7+OflYxvsNtKendLq3NmZc81V8ltInItQUlbOX19byuh+XThpaGayw3GuRfME4RqVJz7MY+3WPdx42lB/CM25JPME4RqN3XvLufuNZRw1sBvjB3dPdjjOtXgJTRCSJkpaLGmZpJujLO8n6Q1JcyXNlzQpnD9A0m5J88Kf+xIZp2scHn1/NYXbS7jxdC89ONcYJKyRWlIKcA9wGpAP5EiaYWaLIlb7MTDVzO6VNBx4HhgQLltuZkckKj7XuOwsKePet5Zz/JAMf+7AuUYikSWIccAyM1thZnuBJ4BzqqxjQKfwdWdgbQLjcY3YlJmrKN65lxtPH5rsUJxzoUQmiD5AXsR0fjgv0m3AVyXlE5QerolYNjCsenpL0vEJjNMl2bY9pTzw9gpOGdajwYcKdc5VL9mN1JcAU8ysLzAJ+JekVsA6oJ+ZjQZuAP4tqVPVjSVdKSlXUm5hYWGDBu7i5x/vrGTr7lKuP+2QZIfinIuQyARRAGRFTPcN50X6BjAVwMxmAWlAhpmVmFlROH82sBzY7+xhZg+YWbaZZWdm+j3zTdHmnXv5x7srOfPwXv70snONTCITRA4wRNJASW2AycCMKuusAU4BkHQoQYIolJQZNnIj6WBgCLAigbG6JHngnRXs3FvmpQfnGqGE3cVkZmWSrgZeAlKAh8xsoaTbgVwzmwHcCPxd0vUEDdaXm5lJOgG4XVIpUAFcZWbFiYrVJUfh9hKmvLeKs0f15pCeHZMdjnOuioT2xWRmzxM0PkfO+2nE60XA+CjbPQ08ncjYXPLd99ZySsrKue6UIckOxTkXRbIbqV0LtX7rHh59fzXnj+nLwZkdkh2Ocy4KTxAuKe55YxnlFca1XnpwrtHyBOEaXP7mXTyRs4aLxmaR1S092eE456rhCcI1uLtfX4Ykrjl5cLJDcc7VwBOEa1CrNu3kP7Pz+fK4fhzUuV2yw3HO1cAThGtQf3ltKakp4jsTBiU7FOdcLTxBuAazbON2ps8r4LJjBtCjY1qyw3HO1cIThGswd726lPTUFL59opcenGsKPEG4BvHJum38b/46vn7cQLq1b5PscJxzMfAE4RrEH19ZQse01nzzuIOTHYpzLkaeIFzCzc/fwiuLNvCt4w+mc3pqssNxzsXIE4RLuD+8vISu6alcMX5AskNxzh0ATxAuoWavLuatJYV8+8RBdEzz0oNzTYknCJcwZsYfXl5CRoc2fO2Y/skOxzl3gDxBuITYtbeM656Yx8zlRXx3wmDS2yS0Z3nnXAL4f62LuxWFO/i/R+ewdON2bjpjKJcdMyDZITnn6sAThIurFz9ez03/+YjU1q145OtHcdyQjGSH5JyrI08QLi7Kyiu48+Ul3PfWckb17czfvnokfbp4Z3zONWWeIFy9bdpRwrWPz2Xm8iK+clQ/fvrF4bRtnZLssJxz9eQJwtXLnDWb+c6jc9i8ay93XjiKC47sm+yQnHNxktC7mCRNlLRY0jJJN0dZ3k/SG5LmSpovaVLEslvC7RZLOiORcboDZ2b8a9YqLr5/FqmtxbTvHOvJwblmJmElCEkpwD3AaUA+kCNphpktiljtx8BUM7tX0nDgeWBA+HoycBjQG3hV0iFmVp6oeF3sdu8t59bpC5g2t4CTh/XgrouO8C40nGuGElnFNA5YZmYrACQ9AZwDRCYIAzqFrzsDa8PX5wBPmFkJsFLSsnB/sxIYr4vBqk07uerR2SzesJ0bTjuEqycMplUrJTss51wCJDJB9AHyIqbzgaOqrHMb8LKka4D2wKkR275fZds+VQ8g6UrgSoB+/frFJWhXvVcXbeD6qfNIaSWmXDGOEw/JTHZIzrkESvaT1JcAU8ysLzAJ+JekmGMyswfMLNvMsjMz/WSVKOUVxp0vLeabj+QyoHt7nr36OE8OzrUAiSxBFABZEdN9w3mRvgFMBDCzWZLSgIwYt3UNoHjnXq57Yi7vLN3E5LFZ3Hb2YaSl+i2szrUEiSxB5ABDJA2U1Iag0XlGlXXWAKcASDoUSAMKw/UmS2oraSAwBPgwgbG6KD7K28IX//ouH6ws5rfnj+CO80d6cnCuBUlYCcLMyiRdDbwEpAAPmdlCSbcDuWY2A7gR+Luk6wkarC83MwMWSppK0KBdBnzX72BqOGbG4x/mcduMhWR2bMvTVx3LiL6dkx2Wc66BKTgf17CClNIUTs7Z2dmWm5ub7DCavD2l5fz4mY95anY+JxySyZ8vPoKuPoa0c82WpNlmlh1tWSwliKWSngb+WeUZBtfMrCnaxVWPzmbRum1ce8oQrjtlCCl+C6tzLVYsCWIUQfvBg+EdRg8RPKOwLaGRuQb19pJCrnl8LmbGQ5dnc/KwnskOyTmXZLU2UpvZdjP7u5kdC/wQ+BmwTtLDkgYnPEKXcHtKy7n633Po1SmN56453pODcw6IoQQRdpnxBeAKYADwB+Ax4HiCrjEOSWB8rgG8+PF6tu0p476vDqdf9/Rkh+OcayRiaoMA3gB+b2YzI+Y/JemExITlGtLU3DyyurXj6IO7JzsU51wjEkuCGGlmO6ItMLNr4xyPa2BrinYxc3kRN5x2iPep5JzbRywPyt0jqUvlhKSukh5KXEiuIT01Ow8J76rbObefWBLESDPbUjlhZpuB0QmLyDWY8grjP7PzOX5IJr19eFDnXBWxJIhWkrpWTkjqho9E1yy8u2wT67bu4eLsrNpXds61OLGc6P8AzJL0H0DABcCvEhqVaxBTc/Lomp7KqcN7JDsU51wjVGuCMLNHJM0GJoSzzvMnqpu+4p17eXnRer56dH/atvYO+Jxz+4upqijsZK+QoLdVJPUzszUJjcwl1DNzCygtNy7y6iXnXDVqbYOQdLakpcBK4C1gFfBCguNyCWRmTM3NY2Tfzhx6UKfaN3DOtUixNFL/AjgaWGJmAwnGb3i/5k1cY7agYCufrt/upQfnXI1iSRClZlZEcDdTKzN7A4jaNaxrGp7MyaNt61Z8cVTvZIfinGvEYmmD2CKpA/A28JikjcDOxIblEmX33nJmzFvLpBEH0bldarLDcc41YrGUIM4BdgHXAy8Cy4EvJjIolzgvLlzH9pIyLsz2J6edczWrsQQR9uT6nJlNACqAhxskKpcwU3Py6dctnaMHesd8zrma1ViCCIcarZDkAxI3A6uLdjJrRREXHtnXO+ZzztUqljaIHcACSa8Q0fYQS0+ukiYCfwZSgAfN7I4qy+/i8wfw0oEeZtYlXFYOLAiXrTGzs2OI1dXgqdn5Qcd8Xr3knItBLAliWvhzQMLqqXuA04B8IEfSjMinsM3s+oj1r2HfTgB3m9kRB3pcF115hfHU7HxOGJLJQZ29Yz7nXO1i6Wqjru0O44BlZrYCQNITBA3e1XXTcQnBcKYuAd5ZWsi6rXv4yVnDkx2Kc66JiGXI0ZWAVZ1vZgfXsmkfIC9iOh84qppj9AcGAq9HzE6TlAuUAXeY2TNRtrsSuBKgX79+tYTTsk3NzaNb+zaceqiPN+2ci00sVUyRD8WlARcC3eIcx2TgqbBRvFJ/MyuQdDDwuqQFZrY8ciMzewB4ACA7O3u/JOYCRTtKeGXRBi49egBtWsdyZ7NzzsXwHISZFUX8FJjZn4AvxLDvAiCyL4e+4bxoJgOPVzluQfh7BfAmPkhRnT0zby2l5cbFY71rDedc7GKpYhoTMdmKoEQRS8kjBxgiaSBBYpgMfDnK/ocBXYFZEfO6ArvMrERSBjAe+F0Mx3RVmBlTc/IY1bczQ3t1THY4zrkmJNYBgyqVEfTqelFtG5lZmaSrgZcIbnN9KOw2/HYg18xmhKtOBp4ws8gqokOB+yVVECSlO3wMirqZn7+VxRu286svHZ7sUJxzTUwsdzFNqG2dGrZ9Hni+yryfVpm+Lcp2M4ERdT2u+9yTuXmkpXrHfM65AxfLeBC/ltQlYrqrpF8mNCoXF7v3lvPsvLVMOvwgOqV5x3zOuQMTyy0tZ5rZlsoJM9sMTEpYRC5uXvi4smM+b5x2zh24WBJEiqS2lROS2gFta1jfNRJTc/Po3z2dow+O913JzrmWIJZG6seA1yT9M5y+Au/VtdFbXbST91cUc9MZQ5G8Yz7n3IGLpZH6t5I+Ak4NZ/3CzF5KbFiuvv6Tm08rwfljvGM+51zdxPIcxEDgTTN7MZxuJ2mAma1KdHCubio75jvxkEx6dU5LdjjOuSYqljaI/xAMFlSpPJznGqm3lxSyftseLvLGaedcPcSSIFqb2d7KifB1m8SF5OqrsmO+U7xjPudcPcSSIAolfTZYj6RzgE2JC8nVR9GOEl79ZANfGt3HO+ZzztVLLHcxXQU8JuluQARdeH8toVG5Ops+t4DScvPqJedcvcVyF9Ny4GhJHcLpHQmPytWJmTE1N49RWV28Yz7nXL3FUoJA0heAwwgG8QHAzG5PYFyuDj7K38qSDTv49Ze8GyvnXP3F0hfTfcDFwDUEVUwXAv0THJergydzgo75zhp1ULJDcc41A7G0Yh5rZl8DNpvZz4FjgEMSG5Y7ULv3lvPsR2uZNMI75nPOxUcsCWJ3+HuXpN5AKeCXqI3M8wvWsaOkjIu9cdo5FyextEE8F3b3/XtgDmDA3xMZlDtwU3PzGNA9nXEDvWM+51x8xHIX0y/Cl09Leg5IM7OtiQ3LHYhVm3bywUrvmM85F18x3cVUycxKgJIExeLqaGpunnfM55yLO3/UtokrK6/g6Tn5nDS0h3fM55yLq4QmCEkTJS2WtEzSzVGW3yVpXvizRNKWiGWXSVoa/lyWyDibsreXFrJhWwkXZXvpwTkXX7F09z0myuytwGozK6thuxTgHuA0IB/IkTTDzBZVrmNm10esfw0wOnzdDfgZkE3QKD473HZzTO+qBZmak0/39m04eZh3zOeci69YShB/A94HHiC4e2kWQXffiyWdXsN244BlZrYi7AH2CeCcGta/BHg8fH0G8IqZFYdJ4RVgYgyxtiibvGM+51wCxXJWWQuMNrNsMzuS4Cp/BUHJ4Hc1bNeHoGO/SvnhvP1I6g8MBF4/kG0lXSkpV1JuYWFhDG+leXlmbgFlFcbFY/3ZB+dc/MWSIA4xs4WVE2EV0TAzWxHHOCYDT5lZ+YFsZGYPhIkrOzMzM47hNH5mxpM5eYzu14UhPb1jPudc/MWSIBZKulfSieHP34BFktoSPFVdnQIg8tK2bzgvmsl8Xr10oNu2SPPytrB04w7v1ts5lzCxJIjLgWXA98KfFeG8UmBCDdvlAEMkDZTUhiAJzKi6kqRhQFeCto1KLwGnS+oqqStwejjPhabm5tEuNYWzRnqvJ865xIjlSerdwB/Cn6qqHRvCzMokXU1wYk8BHjKzhZJuB3LNrDJZTAaeMDOL2LZY0i8IkgzA7WZWHNM7agF27S3j2Y/WMWnEQXT0jvmccwkSy22u44HbCLr4/mx9Mzu4tm3N7Hng+Srzflpl+rZqtn0IeKi2Y7REzy9YH3TM543TzrkEiqWrjX8A1wOzgQNqRHaJMTUnj4EZ7Rk7oGuyQ3HONWOxJIitZvZCwiNxMVlRuIMPVxXzg4neMZ9zLrFiSRBvSPo9MI2IjvrMbE7ConJRlVcYf3ltqXfM55xrELEkiKPC39kR8ww4Of7huOqUlJVz/ZPzeH7Beq45eTA9O3nHfM65xIrlLqaabmV1DWD7nlK+/a/ZzFxexK2TDuVbJ9R6f4BzztVbtQlC0lfN7FFJN0RbbmZ/TFxYrlLh9hIu/+eHLF6/nT9eNIrzvGrJOddAaipBtA9/R+vHwaLMc3G2pmgXlz70ARu27eHvl2UzYWiPZIfknGtBqk0QZnZ/+PJVM3svcln4bIRLoIVrt3LZQzmUVVTw728dzZh+fkurc65hxdLVxl9jnOfiZNbyIibf/z6pKeKpq47x5OCcS4qa2iCOAY4FMqu0Q3Qi6DrDJcCLH6/j2sfn0a97Oo98fRy9u7RLdkjOuRaqpjaINkCHcJ3IdohtwAWJDKqleuyD1fzkmY8ZldWFhy4bS9f2bZIdknOuBaupDeIt4C1JU8xsNYCkVkAHM9vWUAG2BGbGX15bxl2vLmHC0Ezu+coY0tvE8oiKc84lTixtEL+R1ElSe+BjgrEgbkpwXC1GeYXx0/8u5K5Xl3DemD488LVsTw7OuUYhlgQxPCwxnAu8QDA06KWJDKqlKCkr59rH5/Kv91dz5QkHc+cFo0hN8bGlnXONQyyXqqmSUgkSxN1mVirJn4Oop8ino380aRhXnjAo2SE559w+YkkQ9wOrgI+AtyX1J2iodnVUuL2EK6Z8yCfrtvOHC0dx/pH+dLRzrvGJpS+mvwB/iZi1WpL3z1RHkU9HP/i1bCYM86ejnXONU60V3pJ6SvqHpBfC6eHAZQmPrBlauHYr5983ky27Snnsm0d7cnDONWqxtIhOIRhXunc4vQT4XoLiabYqn45u3Sp4OvrI/v50tHOucas2QUiqrH7KMLOpQAWAmZUR49CjkiZKWixpmaSbq1nnIkmLJC2U9O+I+eWS5oU/M2J+R43Qix+v47J/fkjPzmk8/X/HMqRntP4PnXOucampDeJDYAywU1J3wh5cJR0NbK1tx5JSgHuA04B8IEfSDDNbFLHOEOAWYLyZbZYUWeey28yOOMD30+j8+4M1/PiZBf50tHOuyakpQVQOeHwDMAMYJOk9IJPYutoYBywzsxUAkp4AzgEWRazzLeAeM9sMYGYbDyz8xsvM+Ovry/jjK0s4aWgmf/Ono51zTUxNZ6zITvqmA88TJI0S4FRgfi377gPkRUzn8/nwpZUOAQgTTwpwm5m9GC5Lk5QLlAF3mNkztRyvUXl+wXr++MoSzhvdh99eMNIfgHPONTk1JYgUgs76VGV+epyPPwQ4CehL8JzFCDPbAvQ3swJJBwOvS1pgZssjN5Z0JXAlQL9+/eIYVv09mZtHny7tuPPCUbRqVfUjdM65xq+mBLHOzG6vx74LgKyI6b7hvEj5wAdmVgqslLSEIGHkmFkBgJmtkPQmMBrYJ0GY2QPAAwDZ2dmN5unuDdv28O7SQr5z0mBPDs65Jqumeo/6ntlygCGSBkpqA0wmaMuI9AxB6QFJGQRVTiskdZXUNmL+ePZtu2jU/juvgAqDL43pk+xQnHOuzmoqQZxSnx2bWZmkqwmeoUgBHjKzhZJuB3LNbEa47HRJiwhunb3JzIokHQvcL6mCIIndEXn3U2M3bU4BR2R1YVBmh2SH4pxzdVbTeBDF9d25mT1P0LgdOe+nEa+N4C6pG6qsMxMYUd/jJ8Oitdv4dP12bj/nsGSH4pxz9eK31sTZtDn5pKaIs0b2rn1l55xrxDxBxFFZeQXPzFvLhKE96OYPxDnnmjhPEHH0zrJNbNpRwnljvPtu51zT5wkijqbNKaBLeioThmUmOxTnnKs3TxBxsm1PKS8vXM8XR/ambeuUZIfjnHP15gkiTl5csJ6SsgrO82cfnHPNhCeIOHl6Tj4DM9pzRFaXZIfinHNx4QkiDvKKd/HBymLOG90HybvWcM41D54g4uCZuUEXU+eO9uol51zz4QminsyMaXMLOGpgN7K6xbOjW+ecSy5PEPU0N28LKzft5Hx/9sE518x4gqin6XMKaNu6FWeO6JXsUJxzLq48QdRDSVk5z85fyxmH9aJjWmqyw3HOubjyBFEPb3xayJZdpT7ug3OuWfIEUQ/T5uST0aEtxw/OSHYozjkXd54g6qh4517eWLyRc4/oTesU/xidc82Pn9nq6Ln5ayktN++51TnXbHmCqKNpcwoY1qsjw3t3SnYozjmXEJ4g6mB54Q7m5W3xZx+cc82aJ4g6mD6ngFaCc47wYUWdc81XQhOEpImSFktaJunmata5SNIiSQsl/Tti/mWSloY/lyUyzgNRUWFMn1vA8UMy6dEpLdnhOOdcwrRO1I4lpQD3AKcB+UCOpBlmtihinSHALcB4M9ssqUc4vxvwMyAbMGB2uO3mRMUbqw9WFlOwZTc/mDg02aE451xCJbIEMQ5YZmYrzGwv8ARwTpV1vgXcU3niN7ON4fwzgFfMrDhc9gowMYGxxmzanHzat0nh9OHetYZzrnlLZILoA+RFTOeH8yIdAhwi6T1J70uaeADbIulKSbmScgsLC+MYenS795bzwsfrmTTiINq18WFFnXPNW7IbqVsDQ4CTgEuAv0vqEuvGZvaAmWWbWXZmZmZiIozw8qL17Cgp82cfnHMtQiITRAGQFTHdN5wXKR+YYWalZrYSWEKQMGLZtsFNm1NAny7tOGpgt2SH4pxzCZfIBJEDDJE0UFIbYDIwo8o6zxCUHpCUQVDltAJ4CThdUldJXYHTw3lJs3HbHt5ZWsiXRvehVSsfVtQ51/wl7C4mMyuTdDXBiT0FeMjMFkq6Hcg1sxl8nggWAeXATWZWBCDpFwRJBuB2MytOVKyx+O+8tVQY3nOrc67FkJklO4a4yM7Ottzc3ITtf+Kf3qZtagr//e74hB3DOecamqTZZpYdbVmyG6mbhEVrt/Hp+u2c76UH51wL4gkiBtPn5pOaIs4a6V1rOOdaDk8QtSgrr+CZeWuZMLQH3dq3SXY4zjnXYDxB1OLdZZso3F7izz4451ocTxC1mDangC7pqUwYlvgH8ZxzrjHxBFGD7XtKeWnher44sjdtW3vXGs65lsUTRA1e+Hg9JWUV/uyDc65F8gRRg2lz8hmY0Z7RWV2SHYpzzjU4TxDVyN+8i/dXFHPe6D5I3rWGc67l8QRRjWfmBn0Dnjvaq5eccy2TJ4gozIxpcwo4amA3srqlJzsc55xLCk8QUczL28KKTTs53599cM61YJ4gopg2p4C2rVtx5ggfVtQ513J5gqhib1kFz85fyxmH9aJjWmqyw3HOuaTxBFHFG4s3smVXqT/74Jxr8TxBVDFtTj4ZHdpy/OCMZIfinHNJ5Qkiwuade3n9042ce0RvWqf4R+Oca9n8LBjhuflrKS0377nVOefwBLGPp+cUMKxXR4b37pTsUJxzLukSmiAkTZS0WNIySTdHWX65pEJJ88Kfb0YsK4+YPyORcQKsKNzBvLwt/uyDc86FWidqx5JSgHuA04B8IEfSDDNbVGXVJ83s6ii72G1mRyQqvqqmzy2gleCcI3xYUeecg8SWIMYBy8xshZntBZ4Azkng8eqsoiLoWuO4IZn06JSW7HCcc65RSGSC6APkRUznh/OqOl/SfElPScqKmJ8mKVfS+5LOjXYASVeG6+QWFhbWOdAPVxVTsGU35/uzD84595lkN1I/Cwwws5HAK8DDEcv6m1k28GXgT5IGVd3YzB4ws2wzy87MrPuQoNPm5NO+TQqnD/euNZxzrlIiE0QBEFki6BvO+4yZFZlZSTj5IHBkxLKC8PcK4E1gdCKC3L23nOcXrGfSiINo18aHFXXOuUqJTBA5wBBJAyW1ASYD+9yNJOmgiMmzgU/C+V0ltQ1fZwDjgaqN23GxbU8pE4b14MLsrNpXds65FiRhdzGZWZmkq4GXgBTgITNbKOl2INfMZgDXSjobKAOKgcvDzQ8F7pdUQZDE7ohy91Nc9OyUxl8vSUjhxDnnmjSZWbJjiIvs7GzLzc1NdhjOOdekSJodtvfuJ9mN1M455xopTxDOOeei8gThnHMuKk8QzjnnovIE4ZxzLipPEM4556LyBOGccy6qZvMchKRCYHU9dpEBbIpTOInWlGKFphVvU4oVmla8TSlWaFrx1ifW/mYWtTO7ZpMg6ktSbnUPizQ2TSlWaFrxNqVYoWnF25RihaYVb6Ji9Som55xzUXmCcM45F5UniM89kOwADkBTihWaVrxNKVZoWvE2pVihacWbkFi9DcI551xUXoJwzjkXlScI55xzUbX4BCFpoqTFkpZJujnZ8dREUpakNyQtkrRQ0nXJjqk2klIkzZX0XLJjqY2kLpKekvSppE8kHZPsmKoj6frwO/CxpMclpSU7pkiSHpK0UdLHEfO6SXpF0tLwd9dkxlipmlh/H34P5kuaLqlLEkPcR7R4I5bdKMnCkTjrrUUnCEkpwD3AmcBw4BJJw5MbVY3KgBvNbDhwNPDdRh4vwHWEQ8k2AX8GXjSzYcAoGmnckvoA1wLZZnY4wYiNk5Mb1X6mABOrzLsZeM3MhgCvhdONwRT2j/UV4HAzGwksAW5p6KBqMIX940VSFnA6sCZeB2rRCQIYBywzsxVmthd4AjgnyTFVy8zWmdmc8PV2ghNYn+RGVT1JfYEvAA8mO5baSOoMnAD8A8DM9prZlqQGVbPWQDtJrYF0YG2S49mHmb1NMIxwpHOAh8PXDwPnNmRM1YkWq5m9bGZl4eT7QN8GD6wa1Xy2AHcBPwDidudRS08QfYC8iOl8GvEJN5KkAcBo4IMkh1KTPxF8YSuSHEcsBgKFwD/DKrEHJbVPdlDRmFkBcCfBleI6YKuZvZzcqGLS08zWha/XAz2TGcwB+DrwQrKDqImkc4ACM/sonvtt6QmiSZLUAXga+J6ZbUt2PNFIOgvYaGazkx1LjFoDY4B7zWw0sJPGUwWyj7Du/hyCpNYbaC/pq8mN6sBYcH99o7/HXtKtBFW7jyU7lupISgd+BPw03vtu6QmiAMiKmO4bzmu0JKUSJIfHzGxasuOpwXjgbEmrCKruTpb0aHJDqlE+kG9mlSWypwgSRmN0KrDSzArNrBSYBhyb5JhisUHSQQDh741JjqdGki4HzgK+Yo37gbFBBBcLH4X/b32BOZJ61XfHLT1B5ABDJA2U1IagoW9GkmOqliQR1JF/YmZ/THY8NTGzW8ysr5kNIPhcXzezRnuVa2brgTxJQ8NZpwCLkhhSTdYAR0tKD78Tp9BIG9SrmAFcFr6+DPhvEmOpkaSJBNWjZ5vZrmTHUxMzW2BmPcxsQPj/lg+MCb/T9dKiE0TYCHU18BLBP9hUM1uY3KhqNB64lOBqfF74MynZQTUj1wCPSZoPHAH8OrnhRBeWcp4C5gALCP6PG1W3EJIeB2YBQyXlS/oGcAdwmqSlBKWgO5IZY6VqYr0b6Ai8Ev6f3ZfUICNUE29ijtW4S07OOeeSpUWXIJxzzlXPE4RzzrmoPEE455yLyhOEc865qDxBOOeci8oThHNRSNoR/h4g6ctx3vePqkzPjOf+nYsXTxDO1WwAcEAJIuxAryb7JAgzawpPQbsWyBOEczW7Azg+fFjq+nB8i99LygnHCvg2gKSTJL0jaQbhE9iSnpE0Oxy34cpw3h0EvbDOk/RYOK+ytKJw3x9LWiDp4oh9vxkxVsVj4RPUziVUbVc6zrV0NwPfN7OzAMIT/VYzGyupLfCepMqeVMcQjCGwMpz+upkVS2oH5Eh62sxulnS1mR0R5VjnETzBPQrICLd5O1w2GjiMoFvv9wieqn833m/WuUhegnDuwJwOfE3SPIKu1rsDQ8JlH0YkB4BrJX1EMJ5AVsR61TkOeNzMys1sA/AWMDZi3/lmVgHMI6j6ci6hvATh3IERcI2ZvbTPTOkkgi7CI6dPBY4xs12S3gTqMyxoScTrcvx/1zUAL0E4V7PtBJ22VXoJ+L+w23UkHVLNwEKdgc1hchhGMERspdLK7at4B7g4bOfIJBjh7sO4vAvn6sCvQpyr2XygPKwqmkIwbvUAgv72RTAK3blRtnsRuErSJ8BigmqmSg8A8yXNMbOvRMyfDhwDfEQwmM4PzGx9mGCca3Dem6tzzrmovIrJOedcVJ4gnHPOReUJwjnnXFSeIJxzzkXlCcI551xUniCcc85F5QnCOedcVP8PgKHKVQZdnRsAAAAASUVORK5CYII=", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# 使用 MNIST 进行分类\n", + "\n", + "# 主要参数\n", + "training_data_num = 500\n", + "testing_data_num = 200\n", + "qubit_num = 4\n", + "\n", + "# 选择3和6两个类，将 MNIST 从 28*28 重采样为 4*4，再用振幅编码方式进行编码 \n", + "train_dataset = MNIST(mode='train', encoding='amplitude_encoding', num_qubits=qubit_num, classes=[3,6],\n", + " data_num=training_data_num,need_cropping=True,\n", + " downscaling_method='resize', target_dimension=16, return_state=True)\n", + "\n", + "val_dataset = MNIST(mode='test', encoding='amplitude_encoding', num_qubits=qubit_num, classes=[3,6],\n", + " data_num=testing_data_num,need_cropping=True,\n", + " downscaling_method='resize', target_dimension=16,return_state=True)\n", + "\n", + "quantum_train_x, train_y = train_dataset.quantum_image_states, train_dataset.labels\n", + "quantum_test_x, test_y = val_dataset.quantum_image_states, val_dataset.labels\n", + "\n", + "acc = QClassifier2(\n", + " quantum_train_x, # 训练特征\n", + " train_y, # 训练标签\n", + " quantum_test_x, # 测试特征\n", + " test_y, # 测试标签\n", + " N = num_qubit, # 使用的量子比特数目\n", + " DEPTH = 3, # 分类器电路的深度\n", + " EPOCH = 5, # 迭代次数\n", + " LR = 0.1, # 学习率\n", + " BATCH = 40, # 一个批量的大小\n", + " )\n", + "plt.plot(acc)\n", + "plt.title(\"Classify MNIST 3&6 using amplitude encoding\")\n", + "plt.xlabel(\"Iteration\")\n", + "plt.ylabel(\"Testing accuracy\")\n", + "plt.show()" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -1010,7 +1387,9 @@ "\n", "[2] Farhi, Edward, and Hartmut Neven. Classification with quantum neural networks on near term processors. [arXiv preprint arXiv:1802.06002 (2018).](https://arxiv.org/abs/1802.06002)\n", "\n", - "[3] Schuld, Maria, et al. Circuit-centric quantum classifiers. [Physical Review A 101.3 (2020): 032308.](https://arxiv.org/abs/1804.00633)" + "[3] Schuld, Maria, et al. Circuit-centric quantum classifiers. [Physical Review A 101.3 (2020): 032308.](https://arxiv.org/abs/1804.00633)\n", + "\n", + "[4] Schuld, Maria. Supervised quantum machine learning models are kernel methods. [arXiv preprint arXiv:2101.11020 (2021).](https://arxiv.org/pdf/2101.11020)" ] } ], @@ -1030,7 +1409,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.11" + "version": "3.8.12" }, "toc": { "base_numbering": 1, diff --git a/tutorial/machine_learning/QClassifier_EN.ipynb b/tutorial/machine_learning/QClassifier_EN.ipynb index 9d25fd9..a0740c4 100644 --- a/tutorial/machine_learning/QClassifier_EN.ipynb +++ b/tutorial/machine_learning/QClassifier_EN.ipynb @@ -15,7 +15,7 @@ "source": [ "## Overview\n", "\n", - "In this tutorial, we will discuss the workflow of Variational Quantum Classifiers (VQC) and how to use quantum neural networks (QNN) to accomplish a **binary classification** task. The main representatives of this approach include the [Quantum Circuit Learning (QCL)](https://arxiv.org/abs/1803.00745) [1] by Mitarai et al. (2018), Farhi & Neven ( 2018) [2] and [Circuit-Centric Quantum Classifiers](https://arxiv.org/abs/1804.00633) [3] by Schuld et al. (2018). Here, we mainly talk about classification in the language of supervised learning. Unlike classical methods, quantum classifiers require pre-processing to encode classical data into quantum data, and then train the parameters in the quantum neural network. Finally, we benchmark the optimal classification performance through test data.\n", + "In this tutorial, we will discuss the workflow of Variational Quantum Classifiers (VQC) and how to use quantum neural networks (QNN) to accomplish a **binary classification** task. The main representatives of this approach include the [Quantum Circuit Learning (QCL)](https://arxiv.org/abs/1803.00745) [1] by Mitarai et al. (2018), Farhi & Neven (2018) [2] and [Circuit-Centric Quantum Classifiers](https://arxiv.org/abs/1804.00633) [3] by Schuld et al. (2018). Here, we mainly talk about classification in the language of supervised learning. Unlike classical methods, quantum classifiers require pre-processing to encode classical data into quantum data, and then train the parameters in the quantum neural network. Using different encoding methods, we can benchmark the optimal classification performance through test data. Finally, we demonstrate how to use built-in quantum datasets to accomplish quantum classification.\n", "\n", "### Background\n", "\n", @@ -53,7 +53,16 @@ "cell_type": "code", "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Users\\yeruilin\\Anaconda3\\envs\\paddle_quantum_env\\lib\\site-packages\\matplotlib_inline\\config.py:66: DeprecationWarning: InlineBackend._figure_formats_changed is deprecated in traitlets 4.1: use @observe and @unobserve instead.\n", + " def _figure_formats_changed(self, name, old, new):\n" + ] + } + ], "source": [ "# Import numpy and paddle\n", "import numpy as np\n", @@ -63,8 +72,8 @@ "from paddle_quantum.circuit import UAnsatz\n", "# Some functions\n", "from numpy import pi as PI\n", - "from paddle import matmul, transpose # paddle matrix multiplication and transpose\n", - "from paddle_quantum.utils import pauli_str_to_matrix,dagger # N qubits Pauli matrix, complex conjugate\n", + "from paddle import matmul, transpose, reshape # paddle matrix multiplication and transpose\n", + "from paddle_quantum.utils import pauli_str_to_matrix, dagger # N qubits Pauli matrix, complex conjugate\n", "\n", "# Plot figures, calculate the run time\n", "from matplotlib import pyplot as plt\n", @@ -84,17 +93,19 @@ "metadata": {}, "outputs": [], "source": [ - "Ntrain = 200 # Specify the training set size\n", - "Ntest = 100 # Specify the test set size\n", - "gap = 0.5 # Set the width of the decision boundary\n", - "N = 4 # Number of qubits required\n", - "DEPTH = 1 # Circuit depth\n", - "BATCH = 20 # Batch size during training\n", + "# Parameters for generating the data set\n", + "Ntrain = 200 # Specify the training set size\n", + "Ntest = 100 # Specify the test set size\n", + "boundary_gap = 0.5 # Set the width of the decision boundary\n", + "seed_data = 2 # Fixed random seed required to generate the data set\n", + "# Parameters for training\n", + "N = 4 # Number of qubits required\n", + "DEPTH = 1 # Circuit depth\n", + "BATCH = 20 # Batch size during training\n", "EPOCH = int(200 * BATCH / Ntrain)\n", - " # Number of training epochs, the total iteration number \"EPOCH * (Ntrain / BATCH)\" is chosen to be about 200\n", - "LR = 0.01 # Set the learning rate\n", - "seed_paras = 19 # Set random seed to initialize various parameters\n", - "seed_data = 2 # Fixed random seed required to generate the data set\n" + " # Number of training epochs, the total iteration number \"EPOCH * (Ntrain / BATCH)\" is chosen to be about 200\n", + "LR = 0.01 # Set the learning rate\n", + "seed_paras = 19 # Set random seed to initialize various parameters" ] }, { @@ -167,7 +178,7 @@ " print(\"The dimensions of the training set x {} and y {}\".format(np.shape(train_x[0:Ntrain]), np.shape(train_y[0:Ntrain])))\n", " print(\"The dimensions of the test set x {} and y {}\".format(np.shape(train_x[Ntrain:]), np.shape(train_y[Ntrain:])), \"\\n\")\n", "\n", - " return train_x[0:Ntrain], train_y[0:Ntrain], train_x[Ntrain:], train_y[Ntrain:]\n" + " return train_x[0:Ntrain], train_y[0:Ntrain], train_x[Ntrain:], train_y[Ntrain:]" ] }, { @@ -228,7 +239,7 @@ }, { "data": { - "image/png": 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", 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", 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", 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", "text/plain": [ "
    " ] @@ -267,12 +278,6 @@ } ], "source": [ - "# Set parameters\n", - "Ntrain = 200 # Specify the training set size\n", - "Ntest = 100 # Specify the test set size\n", - "boundary_gap = 0.5 # Set the width of the decision boundary\n", - "seed_data = 2 # Fixed random seed\n", - "\n", "# Generate data set\n", "train_x, train_y, test_x, test_y = circle_data_point_generator(\n", " Ntrain, Ntest, boundary_gap, seed_data)\n", @@ -463,9 +468,9 @@ " state_tmp=np.dot(state_tmp, Rz(np.arccos(data[sam][1] ** 2)).T)\n", " res_state=np.kron(res_state, state_tmp)\n", " res.append(res_state)\n", - "\n", " res = np.array(res)\n", - " return res.astype(\"complex128\")\n" + "\n", + " return res.astype(\"complex128\")" ] }, { @@ -509,7 +514,7 @@ "
    Figure 3: Parameterized Quantum Circuit
    \n", "\n", "\n", - "For convenience, we call the parameterized quantum neural network as $U(\\boldsymbol{\\theta})$. $U(\\boldsymbol{\\theta})$ is a key component of our classifier, and it needs a certain complex structure to fit our decision boundary. Similar to traditional neural networks, the structure of a quantum neural network is not unique. The structure shown above is just one case. You could design your own structure. Let’s take the previously mentioned data point $x = (x_0, x_1)= (1,0)$ as an example. After encoding, we have obtained a quantum state $|\\psi_{\\rm in}\\rangle$,\n", + "For convenience, we call the parameterized quantum neural network as $U(\\boldsymbol{\\theta})$. $U(\\boldsymbol{\\theta})$ is a key component of our classifier, and it needs a certain complex structure to fit our decision boundary. Similar to traditional neural networks, the structure of a quantum neural network is not unique. The structure shown above is just one case. You could design your own structure. Let's take the previously mentioned data point $x = (x_0, x_1)= (1,0)$ as an example. After encoding, we have obtained a quantum state $|\\psi_{\\rm in}\\rangle$,\n", "\n", "$$\n", "|\\psi_{\\rm in}\\rangle =\n", @@ -562,7 +567,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T04:03:37.426687Z", @@ -572,7 +577,7 @@ "outputs": [], "source": [ "# Simulation of building a quantum neural network\n", - "def cir_Classifier(theta, n, depth): \n", + "def cir_Classifier(theta, n, depth):\n", " \"\"\"\n", " :param theta: dim: [n, depth + 3], \"+3\" because we add an initial generalized rotation gate to each qubit\n", " :param n: number of qubits\n", @@ -599,7 +604,7 @@ " for i in range(n):\n", " cir.ry(theta[i][d], i)\n", "\n", - " return cir\n" + " return cir" ] }, { @@ -677,6 +682,7 @@ "metadata": {}, "source": [ "### Loss function\n", + "\n", "To calculate the loss function in Eq. (1), we need to measure all training data in each iteration. In real practice, we devide the training data into \"Ntrain/BATCH\" groups, where each group contains \"BATCH\" data pairs.\n", "\n", "The loss function for the i-th group is \n", @@ -690,7 +696,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T04:03:37.439183Z", @@ -707,12 +713,13 @@ " :return: local observable: Z \\otimes I \\otimes ...\\otimes I\n", " \"\"\"\n", " Ob = pauli_str_to_matrix([[1.0,'z0']], n)\n", + "\n", " return Ob" ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T04:03:37.503213Z", @@ -731,7 +738,6 @@ " super(Opt_Classifier, self).__init__()\n", " self.n = n\n", " self.depth = depth\n", - " \n", " # Initialize the parameters theta with a uniform distribution of [0, 2*pi]\n", " self.theta = self.create_parameter(\n", " shape=[n, depth + 3], # \"+3\" because we add an initial generalized rotation gate to each qubit\n", @@ -757,28 +763,27 @@ " \"\"\"\n", " # Convert Numpy array to tensor\n", " Ob = paddle.to_tensor(Observable(self.n))\n", - " label_pp = paddle.to_tensor(label)\n", + " label_pp = reshape(paddle.to_tensor(label), [-1, 1])\n", "\n", " # Build the quantum circuit\n", " cir = cir_Classifier(self.theta, n=self.n, depth=self.depth)\n", " Utheta = cir.U\n", - " \n", + "\n", " # Because Utheta is achieved by learning, we compute with row vectors to speed up without affecting the training effect\n", " state_out = matmul(state_in, Utheta) # shape:[-1, 1, 2 ** n], the first parameter is BATCH in this tutorial\n", - " \n", - " # Measure the expected value of Pauli Z operator -- shape [-1,1,1]\n", + "\n", + " # Measure the expectation value of Pauli Z operator -- shape [-1,1,1]\n", " E_Z = matmul(matmul(state_out, Ob), transpose(paddle.conj(state_out), perm=[0, 2, 1]))\n", - " \n", + "\n", " # Mapping to the estimated value of the label\n", " state_predict = paddle.real(E_Z)[:, 0] * 0.5 + 0.5 + self.bias # |y^{i,k} - \\tilde{y}^{i,k}|^2\n", " loss = paddle.mean((state_predict - label_pp) ** 2) # Get average for \"BATCH\" |y^{i,k} - \\tilde{y}^{i,k}|^2: L_i：shape:[1,1]\n", - " \n", + "\n", " # Calculate the accuracy of cross-validation\n", " is_correct = (paddle.abs(state_predict - label_pp) < 0.5).nonzero().shape[0]\n", " acc = is_correct / label.shape[0]\n", "\n", - " return loss, acc, state_predict.numpy(), cir\n", - " " + " return loss, acc, state_predict.numpy(), cir" ] }, { @@ -846,20 +851,21 @@ }, "outputs": [], "source": [ - "def QClassifier(Ntrain, Ntest, gap, N, DEPTH, EPOCH, LR, BATCH, seed_paras, seed_data,):\n", + "def QClassifier(Ntrain, Ntest, gap, N, DEPTH, EPOCH, LR, BATCH, seed_paras, seed_data):\n", " \"\"\"\n", " Quantum Binary Classifier\n", - " Input：\n", - " Ntrain # Specify the training set size\n", - " Ntest # Specify the test set size\n", - " gap # Set the width of the decision boundary\n", - " N # Number of qubits required\n", - " DEPTH # Circuit depth\n", - " BATCH # Batch size during training\n", - " EPOCH # Number of training epochs, the total iteration number \"EPOCH * (Ntrain / BATCH)\" is chosen to be about 200\n", - " LR # Set the learning rate\n", - " seed_paras # Set random seed to initialize various parameters\n", - " seed_data # Fixed random seed required to generate the data set\n", + " Input:\n", + " Ntrain # Specify the training set size\n", + " Ntest # Specify the test set size\n", + " gap # Set the width of the decision boundary\n", + " N # Number of qubits required\n", + " DEPTH # Circuit depth\n", + " BATCH # Batch size during training\n", + " EPOCH # Number of training epochs, the total iteration number \"EPOCH * (Ntrain / BATCH)\" is chosen to be about 200\n", + " LR # Set the learning rate\n", + " seed_paras # Set random seed to initialize various parameters\n", + " seed_data # Fixed random seed required to generate the data set\n", + " plot_heat_map # Whether to plot heat map, default True\n", " \"\"\"\n", " # Generate data set\n", " train_x, train_y, test_x, test_y = circle_data_point_generator(Ntrain=Ntrain, Ntest=Ntest, boundary_gap=gap, seed_data=seed_data)\n", @@ -916,7 +922,7 @@ " # Draw the decision boundary represented by heatmap\n", " heatmap_plot(myLayer, N=N)\n", "\n", - " return summary_test_acc\n" + " return summary_test_acc" ] }, { @@ -970,7 +976,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "The main program finished running in 7.169757127761841 seconds.\n" + "The main program finished running in 8.05081820487976 seconds.\n" ] } ], @@ -996,6 +1002,7 @@ " \n", " time_span = time.time()-time_start\n", " print('The main program finished running in ', time_span, 'seconds.')\n", + "\n", "if __name__ == '__main__':\n", " main()" ] @@ -1007,6 +1014,387 @@ "By printing out the training results, you can see that the classification accuracy in the test set and the data set after continuous optimization has reached $100\\%$." ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Benchmarking Different Encoding Methods\n", + "\n", + "Encoding methods are fundemental in supervised quantum machine learning [4]. In paddle quantum, commonly used encoding methods such as amplitude encoding, angle encoding, IQP encoding, etc., are integrated. Simple classification data of users (without reducing dimensions) can be encoded by an instance of the ``SimpleDataset`` class and image data can be encoded by an instance of the ``VisionDataset`` class both using the method ``encode``." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "(100, 4)\n" + ] + } + ], + "source": [ + "# Use circle data above to accomplish classification\n", + "from paddle_quantum.dataset import *\n", + "\n", + "# The data are two-dimensional and are encoded by two qubits\n", + "quantum_train_x = SimpleDataset(2).encode(train_x, 'angle_encoding', 2)\n", + "quantum_test_x = SimpleDataset(2).encode(test_x, 'angle_encoding', 2)\n", + "\n", + "print(type(quantum_test_x)) # ndarray\n", + "print(quantum_test_x.shape) # (100, 4)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we define an ordinary classifier, and it will be used by different data afterwards." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [], + "source": [ + "# A simpler classifier\n", + "def QClassifier2(quantum_train_x, train_y,quantum_test_x,test_y, N, DEPTH, EPOCH, LR, BATCH):\n", + " \"\"\"\n", + " Quantum Binary Classifier\n", + " Input：\n", + " quantum_train_x # training x\n", + " train_y # training y\n", + " quantum_test_x # testing x\n", + " test_y # testing y\n", + " N # Number of qubits required\n", + " DEPTH # Circuit depth\n", + " EPOCH # Number of training epochs\n", + " LR # Set the learning rate\n", + " BATCH # Batch size during training\n", + " \"\"\"\n", + " Ntrain = len(quantum_train_x)\n", + " \n", + " paddle.seed(1)\n", + "\n", + " net = Opt_Classifier(n=N, depth=DEPTH)\n", + "\n", + " # Test accuracy list\n", + " summary_iter, summary_test_acc = [], []\n", + "\n", + " # Adam can also be replaced by SGD or RMSprop\n", + " opt = paddle.optimizer.Adam(learning_rate=LR, parameters=net.parameters())\n", + "\n", + " # Optimize\n", + " for ep in range(EPOCH):\n", + " for itr in range(Ntrain // BATCH):\n", + " # Import data\n", + " input_state = quantum_train_x[itr * BATCH:(itr + 1) * BATCH] # paddle.tensor\n", + " input_state = reshape(input_state, [-1, 1, 2 ** N])\n", + " label = train_y[itr * BATCH:(itr + 1) * BATCH]\n", + " test_input_state = reshape(quantum_test_x, [-1, 1, 2 ** N])\n", + "\n", + " loss, train_acc, state_predict_useless, cir = net(state_in=input_state, label=label)\n", + "\n", + " if itr % 5 == 0:\n", + " # get accuracy on test dataset (test_acc)\n", + " loss_useless, test_acc, state_predict_useless, t_cir = net(state_in=test_input_state, label=test_y)\n", + " print(\"epoch:\", ep, \"iter:\", itr,\n", + " \"loss: %.4f\" % loss.numpy(),\n", + " \"train acc: %.4f\" % train_acc,\n", + " \"test acc: %.4f\" % test_acc)\n", + " summary_test_acc.append(test_acc)\n", + "\n", + " loss.backward()\n", + " opt.minimize(loss)\n", + " opt.clear_grad()\n", + "\n", + " return summary_test_acc" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can test different encoding methods on the circle data generated above. Here we choose five encoding methods: amplitude encoding, angle encoding, pauli rotation encoding, IQP encoding, and complex entangled encoding. Then the curves of the testing accuracy are shown below." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Encoding method: amplitude_encoding\n", + "epoch: 0 iter: 0 loss: 0.3066 train acc: 0.4000 test acc: 0.5400\n", + "epoch: 0 iter: 5 loss: 0.2378 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 10 loss: 0.2308 train acc: 0.8000 test acc: 0.6700\n", + "epoch: 0 iter: 15 loss: 0.2230 train acc: 0.8000 test acc: 0.6100\n", + "Encoding method: angle_encoding\n", + "epoch: 0 iter: 0 loss: 0.2949 train acc: 0.5000 test acc: 0.3600\n", + "epoch: 0 iter: 5 loss: 0.1770 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 10 loss: 0.1654 train acc: 0.8000 test acc: 0.7000\n", + "epoch: 0 iter: 15 loss: 0.1966 train acc: 0.7000 test acc: 0.5800\n", + "Encoding method: pauli_rotation_encoding\n", + "epoch: 0 iter: 0 loss: 0.2433 train acc: 0.6000 test acc: 0.7000\n", + "epoch: 0 iter: 5 loss: 0.2142 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 10 loss: 0.2148 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 15 loss: 0.2019 train acc: 0.8000 test acc: 0.7600\n", + "Encoding method: IQP_encoding\n", + "epoch: 0 iter: 0 loss: 0.2760 train acc: 0.6000 test acc: 0.4200\n", + "epoch: 0 iter: 5 loss: 0.1916 train acc: 0.6000 test acc: 0.6200\n", + "epoch: 0 iter: 10 loss: 0.1355 train acc: 0.9000 test acc: 0.7300\n", + "epoch: 0 iter: 15 loss: 0.1289 train acc: 0.9000 test acc: 0.6700\n", + "Encoding method: complex_entangled_encoding\n", + "epoch: 0 iter: 0 loss: 0.3274 train acc: 0.3000 test acc: 0.2900\n", + "epoch: 0 iter: 5 loss: 0.2120 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 10 loss: 0.2237 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 15 loss: 0.2095 train acc: 0.8000 test acc: 0.7200\n" + ] + } + ], + "source": [ + "# Testing different encoding methods\n", + "encoding_list = ['amplitude_encoding', 'angle_encoding', 'pauli_rotation_encoding', 'IQP_encoding', 'complex_entangled_encoding']\n", + "num_qubit = 2 # If qubit number is 1, CNOT gate in cir_classifier can not be used\n", + "dimension = 2\n", + "acc_list = []\n", + "\n", + "for i in range(len(encoding_list)):\n", + " encoding = encoding_list[i]\n", + " print(\"Encoding method:\", encoding)\n", + " # Use SimpleDataset to encode the data\n", + " quantum_train_x= SimpleDataset(dimension).encode(train_x, encoding, num_qubit)\n", + " quantum_test_x= SimpleDataset(dimension).encode(test_x, encoding, num_qubit)\n", + " quantum_train_x = paddle.to_tensor(quantum_train_x)\n", + " quantum_test_x = paddle.to_tensor(quantum_test_x)\n", + " \n", + " acc = QClassifier2(\n", + " quantum_train_x, # Training x\n", + " train_y, # Training y\n", + " quantum_test_x, # Testing x\n", + " test_y, # Testing y\n", + " N = num_qubit, # Number of qubits required\n", + " DEPTH = 1, # Circuit depth\n", + " EPOCH = 1, # Number of training epochs\n", + " LR = 0.1, # Set the learning rate\n", + " BATCH = 10, # Batch size during training\n", + " )\n", + " acc_list.append(acc)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Benchmarking different encoding methods\n", + "x=[2*i for i in range(len(acc_list[0]))]\n", + "for i in range(len(encoding_list)):\n", + " plt.plot(x,acc_list[i])\n", + "plt.legend(encoding_list)\n", + "plt.title(\"Benchmarking different encoding methods\")\n", + "plt.xlabel(\"Iteration\")\n", + "plt.ylabel(\"Test accuracy\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Quantum Classification on Built-In MNIST and Iris Datasets\n", + "\n", + "Paddle Quantum provides datasets commonly used in quantum classification tasks, and users can use the `paddle_quantum.dataset` module to get the encoding circuits or encoded states. There are four built-in datasets in Paddle Quantum at present, including MNIST, FashionMNIST, Iris and BreastCancer. We can easily accomplishing quantum classification using these quantum datasets.\n", + "\n", + "The first case is Iris. It has three types of labels and 50 samples of each type. There are only four features in Iris data, and it is very easy to fulfill its classification." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Users\\yeruilin\\Anaconda3\\envs\\paddle_quantum_env\\lib\\site-packages\\paddle\\fluid\\dygraph\\math_op_patch.py:237: UserWarning: The dtype of left and right variables are not the same, left dtype is paddle.float64, but right dtype is paddle.int32, the right dtype will convert to paddle.float64\n", + " warnings.warn(\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "epoch: 0 iter: 0 loss: 0.3113 train acc: 0.0000 test acc: 0.0000\n", + "epoch: 0 iter: 5 loss: 0.4818 train acc: 0.0000 test acc: 0.3500\n", + "epoch: 0 iter: 10 loss: 0.2171 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 0 iter: 15 loss: 0.1688 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 1 iter: 0 loss: 0.1350 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 1 iter: 5 loss: 0.1110 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 1 iter: 10 loss: 0.0879 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 1 iter: 15 loss: 0.0490 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 2 iter: 0 loss: 0.0733 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 2 iter: 5 loss: 0.0740 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 2 iter: 10 loss: 0.0660 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 2 iter: 15 loss: 0.0394 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 3 iter: 0 loss: 0.0654 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 3 iter: 5 loss: 0.0557 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 3 iter: 10 loss: 0.0602 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 3 iter: 15 loss: 0.0397 train acc: 1.0000 test acc: 1.0000\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Using Iris\n", + "test_rate = 0.2\n", + "num_qubit = 4\n", + "\n", + "# acquire Iris data as quantum states\n", + "iris =Iris (encoding='angle_encoding', num_qubits=num_qubit, test_rate=test_rate,classes=[0, 1], return_state=True)\n", + "\n", + "quantum_train_x, train_y = iris.train_x, iris.train_y\n", + "quantum_test_x, test_y = iris.test_x, iris.test_y\n", + "testing_data_num = len(test_y)\n", + "training_data_num = len(train_y)\n", + "\n", + "acc = QClassifier2(\n", + " quantum_train_x, # training x\n", + " train_y, # training y\n", + " quantum_test_x, # testing x\n", + " test_y, # testing y\n", + " N = num_qubit, # Number of qubits required\n", + " DEPTH = 1, # Circuit depth\n", + " EPOCH = 4, # Number of training epochs, the total iteration number \"EPOCH * (Ntrain / BATCH)\" is chosen to be about 200\n", + " LR = 0.1, # Set the learning rate\n", + " BATCH = 4, # Batch size during training\n", + " )\n", + "plt.plot(acc)\n", + "plt.title(\"Classify Iris 0&1 using angle encoding\")\n", + "plt.xlabel(\"Iteration\")\n", + "plt.ylabel(\"Testing accuracy\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The second case is MNIST. It is a handwritten digit dataset and has 10 classes. Each figure has $28\\times28$ pixels, and downscaling methods such as ``resize`` and ``PCA`` should be used to transform it into the target dimension." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "epoch: 0 iter: 0 loss: 0.3237 train acc: 0.3250 test acc: 0.5450\n", + "epoch: 0 iter: 5 loss: 0.2124 train acc: 0.7500 test acc: 0.6500\n", + "epoch: 0 iter: 10 loss: 0.2294 train acc: 0.6500 test acc: 0.6850\n", + "epoch: 1 iter: 0 loss: 0.1970 train acc: 0.7250 test acc: 0.7850\n", + "epoch: 1 iter: 5 loss: 0.1521 train acc: 0.8500 test acc: 0.8150\n", + "epoch: 1 iter: 10 loss: 0.1726 train acc: 0.7750 test acc: 0.8900\n", + "epoch: 2 iter: 0 loss: 0.1742 train acc: 0.7250 test acc: 0.8650\n", + "epoch: 2 iter: 5 loss: 0.1167 train acc: 0.9000 test acc: 0.8900\n", + "epoch: 2 iter: 10 loss: 0.1654 train acc: 0.8000 test acc: 0.8950\n", + "epoch: 3 iter: 0 loss: 0.1609 train acc: 0.8000 test acc: 0.8850\n", + "epoch: 3 iter: 5 loss: 0.1148 train acc: 0.9250 test acc: 0.8850\n", + "epoch: 3 iter: 10 loss: 0.1649 train acc: 0.8000 test acc: 0.8750\n", + "epoch: 4 iter: 0 loss: 0.1629 train acc: 0.8250 test acc: 0.8750\n", + "epoch: 4 iter: 5 loss: 0.1112 train acc: 0.9000 test acc: 0.8700\n", + "epoch: 4 iter: 10 loss: 0.1630 train acc: 0.8500 test acc: 0.8850\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# using MNIST\n", + "\n", + "# main parameters\n", + "training_data_num = 500\n", + "testing_data_num = 200\n", + "qubit_num = 4\n", + "\n", + "# MNIST data with amplitude encoding, resized to 4*4\n", + "train_dataset = MNIST(mode='train', encoding='amplitude_encoding', num_qubits=qubit_num, classes=[3, 6],\n", + " data_num=training_data_num, need_cropping=True,\n", + " downscaling_method='resize', target_dimension=16, return_state=True)\n", + "\n", + "val_dataset = MNIST(mode='test', encoding='amplitude_encoding', num_qubits=qubit_num, classes=[3, 6],\n", + " data_num=testing_data_num, need_cropping=True,\n", + " downscaling_method='resize', target_dimension=16,return_state=True)\n", + "\n", + "quantum_train_x, train_y = train_dataset.quantum_image_states, train_dataset.labels\n", + "quantum_test_x, test_y = val_dataset.quantum_image_states, val_dataset.labels\n", + "\n", + "acc = QClassifier2(\n", + " quantum_train_x, # Training x\n", + " train_y, # Training y\n", + " quantum_test_x, # Testing x\n", + " test_y, # Testing y\n", + " N = qubit_num, # Number of qubits required\n", + " DEPTH = 3, # Circuit depth\n", + " EPOCH = 5, # Number of training epochs, the total iteration number \"EPOCH * (Ntrain / BATCH)\" is chosen to be about 200\n", + " LR = 0.1, # Set the learning rate\n", + " BATCH = 40, # Batch size during training\n", + " )\n", + "\n", + "plt.plot(acc)\n", + "plt.title(\"Classify MNIST 3&6 using amplitude encoding\")\n", + "plt.xlabel(\"Iteration\")\n", + "plt.ylabel(\"Testing accuracy\")\n", + "plt.show()" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -1020,7 +1408,9 @@ "\n", "[2] Farhi, Edward, and Hartmut Neven. Classification with quantum neural networks on near term processors. [arXiv preprint arXiv:1802.06002 (2018).](https://arxiv.org/abs/1802.06002)\n", "\n", - "[3] Schuld, Maria, et al. Circuit-centric quantum classifiers. [Physical Review A 101.3 (2020): 032308.](https://arxiv.org/abs/1804.00633)\n" + "[3] Schuld, Maria, et al. Circuit-centric quantum classifiers. [Physical Review A 101.3 (2020): 032308.](https://arxiv.org/abs/1804.00633)\n", + "\n", + "[4] Schuld, Maria. Supervised quantum machine learning models are kernel methods. [arXiv preprint arXiv:2101.11020 (2021).](https://arxiv.org/pdf/2101.11020)" ] } ], @@ -1040,7 +1430,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.11" + "version": "3.8.12" }, "toc": { "base_numbering": 1, diff --git a/tutorial/machine_learning/VQSVD_CN.ipynb b/tutorial/machine_learning/VQSVD_CN.ipynb index 567582b..e66328d 100644 --- a/tutorial/machine_learning/VQSVD_CN.ipynb +++ b/tutorial/machine_learning/VQSVD_CN.ipynb @@ -919,7 +919,7 @@ "\n", "## 参考文献\n", "\n", - "[1] Wang, X., Song, Z. & Wang, Y. Variational Quantum Singular Value Decomposition. [arXiv:2006.02336 (2020).](https://arxiv.org/abs/2006.02336)" + "[1] Wang, X., Song, Z., & Wang, Y. Variational Quantum Singular Value Decomposition. [Quantum, 5, 483 (2021).](https://quantum-journal.org/papers/q-2021-06-29-483/)" ] } ], diff --git a/tutorial/machine_learning/VQSVD_EN.ipynb b/tutorial/machine_learning/VQSVD_EN.ipynb index 9093612..deb5f6c 100644 --- a/tutorial/machine_learning/VQSVD_EN.ipynb +++ b/tutorial/machine_learning/VQSVD_EN.ipynb @@ -921,7 +921,7 @@ "\n", "## References\n", "\n", - "[1] Wang, X., Song, Z. & Wang, Y. Variational Quantum Singular Value Decomposition. [arXiv:2006.02336 (2020).](https://arxiv.org/abs/2006.02336)" + "[1] Wang, X., Song, Z., & Wang, Y. Variational Quantum Singular Value Decomposition. [Quantum, 5, 483 (2021).](https://quantum-journal.org/papers/q-2021-06-29-483/)" ] } ], diff --git a/tutorial/machine_learning/VSQL_CN.ipynb b/tutorial/machine_learning/VSQL_CN.ipynb index 3ce547f..2fe4622 100644 --- a/tutorial/machine_learning/VSQL_CN.ipynb +++ b/tutorial/machine_learning/VSQL_CN.ipynb @@ -445,7 +445,7 @@ "\n", "## 参考文献\n", "\n", - "[1] Li, Guangxi, et al. \"VSQL: Variational Shadow Quantum Learning for Classification.\" [arXiv:2012.08288 (2020).](https://arxiv.org/abs/2012.08288)\n", + "[1] Li, Guangxi, Zhixin Song, and Xin Wang. \"VSQL: Variational Shadow Quantum Learning for Classification.\" [Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 35. No. 9. 2021.](https://ojs.aaai.org/index.php/AAAI/article/view/17016)\n", "\n", "[2] Goodfellow, Ian, et al. Deep learning. Vol. 1. No. 2. Cambridge: MIT press, 2016.\n", "\n", diff --git a/tutorial/machine_learning/VSQL_EN.ipynb b/tutorial/machine_learning/VSQL_EN.ipynb index b0f4d87..147cbb9 100644 --- a/tutorial/machine_learning/VSQL_EN.ipynb +++ b/tutorial/machine_learning/VSQL_EN.ipynb @@ -450,7 +450,7 @@ "\n", "## References\n", "\n", - "[1] Li, Guangxi, et al. \"VSQL: Variational Shadow Quantum Learning for Classification.\" [arXiv:2012.08288 (2020).](https://arxiv.org/abs/2012.08288)\n", + "[1] Li, Guangxi, Zhixin Song, and Xin Wang. \"VSQL: Variational Shadow Quantum Learning for Classification.\" [Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 35. No. 9. 2021.](https://ojs.aaai.org/index.php/AAAI/article/view/17016)\n", "\n", "[2] Goodfellow, Ian, et al. Deep learning. Vol. 1. No. 2. Cambridge: MIT press, 2016.\n", "\n", diff --git a/tutorial/qnn_research/BarrenPlateaus_CN.ipynb b/tutorial/qnn_research/BarrenPlateaus_CN.ipynb index 09583a2..6159f81 100644 --- a/tutorial/qnn_research/BarrenPlateaus_CN.ipynb +++ b/tutorial/qnn_research/BarrenPlateaus_CN.ipynb @@ -2,58 +2,67 @@ "cells": [ { "cell_type": "markdown", - "metadata": {}, "source": [ "# 量子神经网络的贫瘠高原效应\n", "\n", "\n", " Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. " - ] + ], + "metadata": {} }, { "cell_type": "markdown", - "metadata": {}, "source": [ "## 概览\n", "\n", - "在经典神经网络的训练中，基于梯度的优化方法不仅仅会遇到局部最小值的问题，同时还要面对鞍点等附近梯度近似于零的几何结构。相对应的，在量子神经网络中也存在着一种**贫瘠高原效应**（barren plateaus）。这个奇特的现象首先是由 McClean et al. 在 2018 年发现 [[arXiv:1803.11173]](https://arxiv.org/abs/1803.11173)。简单来说，就是当你选取的随机电路结构满足一定复杂程度时优化曲面（optimization landscape）会变得很平坦，从而导致基于梯度下降的优化方法很难找到全局最小值。对于大多数的变分量子算法（VQE等等），这个现象意味着当量子比特数量越来越多时，选取随机结构的电路有可能效果并不好。这会让你设计的损失函数所对应的优化曲面变成一个巨大的高原，让从而导致量子神经网络的训练愈加困难。你随机找到的初始值很难逃离这个高原，梯度下降收敛速度会很缓慢。\n", + "在经典神经网络的训练中，基于梯度的优化方法不仅仅会遇到局部最小值的问题，同时还要面对鞍点等附近梯度近似于零的几何结构。相对应的，在量子神经网络中也存在着一种**贫瘠高原效应**（barren plateaus）。这个奇特的现象首先是由 McClean et al. 在 2018 年发现 [[1]](https://arxiv.org/abs/1803.11173)。简单来说，就是当你选取的随机电路结构满足一定复杂程度时优化曲面（optimization landscape）会变得很平坦，从而导致基于梯度下降的优化方法很难找到全局最小值。对于大多数的变分量子算法（VQE等），这个现象意味着当量子比特数量越来越多时，选取随机结构的电路有可能效果并不好。这会让你设计的损失函数所对应的优化曲面变成一个巨大的高原，让从而导致量子神经网络的训练愈加困难。你随机找到的初始值很难逃离这个高原，梯度下降收敛速度会很缓慢。\n", "\n", "![BP-fig-barren](./figures/BP-fig-barren-cn.png)\n", "\n", "图片由 [Gradient Descent Viz](https://github.com/lilipads/gradient_descent_viz) 生成\n", "\n", - "本教程主要讨论如何在量桨（Paddle Quantum）平台上展示贫瘠高原这一现象。其中并不涉及任何算法创新，但能提升读者对于量子神经网络训练中梯度问题的认识。首先我们先引入必要的 library和 package：\n", - "\n" - ] + "\n", + "基于梯度变化对这类变分量子算法训练的影响，我们在量桨（Paddle Quantum）平台提供了梯度分析工具模块，辅助用户对 QML 模型进行诊断，便于贫瘠高原等问题的研究。\n", + "\n", + "本教程主要讨论如何在量桨（Paddle Quantum）平台上展示贫瘠高原现象，以及如何使用梯度分析工具对用户自定义量子神经网络中的参数梯度进行分析。其中并不涉及任何算法创新，但能提升读者对于量子神经网络训练中梯度问题的认识。\n", + "\n", + "首先我们先引入必要的 library 和 package：\n" + ], + "metadata": {} }, { "cell_type": "code", - "execution_count": 1, - "metadata": { - "ExecuteTime": { - "end_time": "2021-03-02T12:20:39.463025Z", - "start_time": "2021-03-02T12:20:36.336398Z" - } - }, - "outputs": [], + "execution_count": 55, "source": [ + "# 需要用的包\n", "import time\n", "import numpy as np\n", - "from matplotlib import pyplot as plt \n", + "import random\n", "import paddle\n", "from paddle import matmul\n", "from paddle_quantum.circuit import UAnsatz\n", "from paddle_quantum.utils import dagger\n", - "from paddle_quantum.state import density_op" - ] + "from paddle_quantum.state import density_op\n", + "# 画图工具\n", + "from matplotlib import pyplot as plt \n", + "# 忽略 waring 输出\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\")" + ], + "outputs": [], + "metadata": { + "ExecuteTime": { + "end_time": "2021-03-02T12:20:39.463025Z", + "start_time": "2021-03-02T12:20:36.336398Z" + } + } }, { "cell_type": "markdown", - "metadata": {}, "source": [ "## 随机的网络结构\n", "\n", - "这里我们按照原作者 McClean (2018)论文中提及的类似方法搭建如下随机电路（目前我们不支持内置的 control-Z 门，方便起见用 CNOT 替代）：\n", + "这里我们按照原作者 McClean (2018) [[1]](https://arxiv.org/abs/1803.11173) 论文中提及的类似方法搭建如下随机电路：\n", "\n", "![BP-fig-Barren_circuit](./figures/BP-fig-Barren_circuit.png)\n", "\n", @@ -62,21 +71,15 @@ "其余的结构加起来构成一个模块（Block）, 每个模块共分为两层：\n", "\n", "- 第一层搭建随机的旋转门, 其中 $R_{\\ell,n} \\in \\{R_x, R_y, R_z\\}$。下标 $\\ell$ 表示处于第 $\\ell$ 个重复的模块， 上图中 $\\ell =1$。第二个下标 $n$ 表示作用在第几个量子比特上。\n", - "- 第二层由 CNOT 门组成，作用在每两个相邻的量子比特上。\n", + "- 第二层由 CZ 门组成，作用在每两个相邻的量子比特上。\n", "\n", "在量桨中, 我们可以这么搭建。" - ] + ], + "metadata": {} }, { "cell_type": "code", - "execution_count": 2, - "metadata": { - "ExecuteTime": { - "end_time": "2021-03-02T12:20:39.972053Z", - "start_time": "2021-03-02T12:20:39.962259Z" - } - }, - "outputs": [], + "execution_count": 56, "source": [ "def rand_circuit(theta, target, num_qubits):\n", " # 我们需要将 Numpy array 转换成 Paddle 中的 Tensor\n", @@ -101,20 +104,26 @@ " cir.rx(theta[i], i)\n", " \n", " # ============== 第三层 ==============\n", - " # 搭建两两相邻的 CNOT 门\n", + " # 搭建两两相邻的 CZ 门\n", " for i in range(num_qubits - 1):\n", - " cir.cnot([i, i + 1])\n", + " cir.cz([i, i + 1])\n", " \n", - " return cir.U" - ] + " return cir" + ], + "outputs": [], + "metadata": { + "ExecuteTime": { + "end_time": "2021-03-02T12:20:39.972053Z", + "start_time": "2021-03-02T12:20:39.962259Z" + } + } }, { "cell_type": "markdown", - "metadata": {}, "source": [ "## 损失函数与优化曲面 \n", "\n", - "当我们确定了电路的结构之后，我们还需要定义一个损失函数（loss function）来确定优化曲面。按照原作者 McClean (2018)论文中提及的，我们采用 VQE算法中常用的损失函数：\n", + "当我们确定了电路的结构之后，我们还需要定义一个损失函数（loss function）来确定优化曲面。按照原作者 McClean (2018) [[1]](https://arxiv.org/abs/1803.11173) 论文中提及的，我们采用 VQE算法中常用的损失函数：\n", "\n", "$$\n", "\\mathcal{L}(\\boldsymbol{\\theta})= \\langle0| U^{\\dagger}(\\boldsymbol{\\theta})H U(\\boldsymbol{\\theta}) |0\\rangle,\n", @@ -131,28 +140,12 @@ "$$\n", "\n", "具体推导请参见：[arXiv:1803.00745](https://arxiv.org/abs/1803.00745)" - ] + ], + "metadata": {} }, { "cell_type": "code", - "execution_count": 3, - "metadata": { - "ExecuteTime": { - "end_time": "2021-03-02T12:20:52.236108Z", - "start_time": "2021-03-02T12:20:40.850822Z" - } - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "主程序段总共运行了 4.447464466094971 秒\n", - "采样 300 个随机网络关于第一个参数梯度的均值是： 0.005925709445960606\n", - "采样 300 个随机网络关于第一个参数梯度的方差是： 0.028249053148446363\n" - ] - } - ], + "execution_count": 26, "source": [ "# 超参数设置\n", "np.random.seed(42) # 固定 Numpy 的随机种子\n", @@ -197,11 +190,11 @@ " # 生成随机目标，在 rand_circuit 中随机选取电路门\n", " target = np.random.choice(3, N) \n", " \n", - " U = rand_circuit(theta, target, N)\n", + " U = rand_circuit(theta, target, N).U\n", " U_dagger = dagger(U) \n", - " U_plus = rand_circuit(theta_plus, target, N)\n", + " U_plus = rand_circuit(theta_plus, target, N).U\n", " U_plus_dagger = dagger(U_plus) \n", - " U_minus = rand_circuit(theta_minus, target, N)\n", + " U_minus = rand_circuit(theta_minus, target, N).U\n", " U_minus_dagger = dagger(U_minus) \n", "\n", " # 计算解析梯度\n", @@ -235,11 +228,27 @@ "print('主程序段总共运行了', time_span, '秒')\n", "print(\"采样\", samples, \"个随机网络关于第一个参数梯度的均值是：\", np.mean(grad_info))\n", "print(\"采样\", samples, \"个随机网络关于第一个参数梯度的方差是：\", np.var(grad_info))" - ] + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "主程序段总共运行了 5.709956169128418 秒\n", + "采样 300 个随机网络关于第一个参数梯度的均值是： 0.005925709445960606\n", + "采样 300 个随机网络关于第一个参数梯度的方差是： 0.028249053148446363\n" + ] + } + ], + "metadata": { + "ExecuteTime": { + "end_time": "2021-03-02T12:20:52.236108Z", + "start_time": "2021-03-02T12:20:40.850822Z" + } + } }, { "cell_type": "markdown", - "metadata": {}, "source": [ "## 优化曲面的可视化\n", "\n", @@ -248,38 +257,12 @@ "![BP-fig-landscape2](./figures/BP-fig-landscape2.png)\n", "\n", "可以看到的是最后一张图中 $R_z$-$R_z$ 结构所展示出的平原结构是我们非常不想见到的。在这种情况下，我们不能收敛到理论最小值。如果你想自己试着画一些优化曲面，不妨参见以下代码：" - ] + ], + "metadata": {} }, { "cell_type": "code", "execution_count": 4, - "metadata": { - "ExecuteTime": { - "end_time": "2021-03-02T12:21:49.972769Z", - "start_time": "2021-03-02T12:21:45.792119Z" - } - }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
    " - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "主程序段总共运行了 1.7720370292663574 秒\n" - ] - } - ], "source": [ "# 引入必要的 package\n", "from matplotlib import cm\n", @@ -316,8 +299,8 @@ " [0, np.exp(1j * theta/2)]])\n", " return mat\n", "\n", - "def CNOT():\n", - " mat = np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]])\n", + "def CZ():\n", + " mat = np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, -1]])\n", " return mat\n", "\n", "# ============= 第一张图 =============\n", @@ -328,7 +311,7 @@ "def cost_yy(para):\n", " L1 = np.kron(ry(np.pi/4), ry(np.pi/4))\n", " L2 = np.kron(ry(para[0]), ry(para[1]))\n", - " U = np.matmul(np.matmul(L1, L2), CNOT())\n", + " U = np.matmul(np.matmul(L1, L2), CZ())\n", " H = np.zeros((2 ** N, 2 ** N))\n", " H[0, 0] = 1\n", " val = (U.conj().T @ H@ U).real[0][0]\n", @@ -349,7 +332,7 @@ "def cost_xz(para):\n", " L1 = np.kron(ry(np.pi/4), ry(np.pi/4))\n", " L2 = np.kron(rx(para[0]), rz(para[1]))\n", - " U = np.matmul(np.matmul(L1, L2), CNOT())\n", + " U = np.matmul(np.matmul(L1, L2), CZ())\n", " H = np.zeros((2 ** N, 2 ** N))\n", " H[0, 0] = 1\n", " val = (U.conj().T @ H @ U).real[0][0]\n", @@ -366,157 +349,495 @@ "\n", "time_span = time.time() - time_start \n", "print('主程序段总共运行了', time_span, '秒')" - ] + ], + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
    " + ], + "image/png": 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" + }, + "metadata": { + "needs_background": "light" + } + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "主程序段总共运行了 1.7720370292663574 秒\n" + ] + } + ], + "metadata": { + "ExecuteTime": { + "end_time": "2021-03-02T12:21:49.972769Z", + "start_time": "2021-03-02T12:21:45.792119Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "## 梯度分析工具\n", + "\n", + "基于梯度在贫瘠高原等现象中的表现出的重要作用，我们在量桨平台开发了一个简单的梯度分析工具，辅助用户查看电路中各参数的梯度情况，方便对量子神经网络做后续研究。\n", + "\n", + "需要注意的是，我们使用梯度分析工具时仅需用户**单独定义传入的电路和损失函数，不需要用户自己写网络训练**，减少使用负担" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### 应用 一：无监督学习\n", + "\n", + "对于该类情况，主要关注类似变分量子本征求解器（VQE）的变分量子算法。该类变分算法要优化的目标函数通常是量子电路关于哈密顿量 $H$ 的期望值，即 $O(\\theta) = \\left\\langle0\\dots 0\\right\\lvert U^{\\dagger}(\\theta)HU(\\theta) \\left\\lvert0\\dots 0\\right\\rangle$，这里的 $U(\\theta)$ 表示的就是参数化量子电路，其中 $\\theta = [\\theta_1, \\theta_2, \\dots, \\theta_n]$ 是电路中的可训练参数，$H$ 是哈密顿量。 \n", + "\n", + "这里我们就以 VQE 做代表，演示该梯度分析工具的用法。" + ], + "metadata": {} }, { "cell_type": "markdown", - "metadata": {}, "source": [ - "## 更多的量子比特\n", + "#### Paddle Quantum 实现\n", "\n", - "接着我们再看看不断的增加量子比特的数量，会对我们的梯度带来什么影响。" - ] + "首先导入该问题需要的包：" + ], + "metadata": {} }, { "cell_type": "code", - "execution_count": 5, - "metadata": { - "ExecuteTime": { - "end_time": "2021-03-02T12:24:12.650054Z", - "start_time": "2021-03-02T12:22:06.472689Z" - } - }, + "execution_count": 22, + "source": [ + "# 需要用的包\n", + "from paddle_quantum.utils import pauli_str_to_matrix, random_pauli_str_generator\n", + "# 导入梯度工具包\n", + "from paddle_quantum.gradtool import random_sample, show_gradient, plot_distribution, plot_loss_grad" + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "#### 定义量子电路\n", + "\n", + "接着，构造目标函数 $O(\\theta) = \\left\\langle00\\right\\lvert U^{\\dagger}(\\theta)HU(\\theta) \\left\\lvert00\\right\\rangle$ 中的参数化量子电路 $U(\\theta)$。这里我们还是采用上文中定义的随机电路。" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "#### 定义目标函数\n", + "\n", + "之后给出要优化的目标函数（这里需要注意的是，在梯度分析模块中我们是以 ``loss_func(circuit, *args)`` 的形式调用函数计算目标函数值的。这也就是说，第二个参数是可变参数，用户可以根据需要灵活的构造自己模型的目标函数形式）：" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 24, + "source": [ + "# 要优化的目标函数，其中参数分别是电路和哈密顿量\n", + "def loss_func(circuit, H_l):\n", + " circuit.run_state_vector()\n", + " return (circuit.expecval(H_l))" + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "接着设置一些应用所需的参数" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 25, + "source": [ + "# 超参数设置\n", + "np.random.seed(42) # 固定 Numpy 的随机种子\n", + "N = 2 # 设置量子比特数量 \n", + "samples = 300 # 设定采样随机网络结构的数量\n", + "THETA_SIZE = N # 设置参数 theta 的大小 \n", + "ITR = 120 # 设置迭代次数\n", + "LR = 0.1 # 设定学习速率\n", + "SEED = 1 # 固定优化器中随机初始化的种子" + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "随机生成参数化量子电路，以及哈密顿量信息列表。" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 26, + "source": [ + "paddle.seed(SEED)\n", + "target = np.random.choice(3, N)\n", + "# 在 0 - 2*Pi 间随机生成各参数值\n", + "theta = np.random.uniform(low=0., high= 2 * np.pi, size=(THETA_SIZE))\n", + "theta = paddle.to_tensor(theta, stop_gradient=False, dtype='float64')\n", + "cir = rand_circuit(theta, target, N)\n", + "print(cir)\n", + "# 随机生成哈密顿量列表，以 Pauli 字符串形式表现\n", + "H_l = random_pauli_str_generator(N, terms=7)\n", + "print('Hamiltonian info: ', H_l)" + ], "outputs": [ { - "name": "stdout", "output_type": "stream", + "name": "stdout", "text": [ - "主程序段总共运行了 96.94419932365417 秒\n" + "--Ry(0.785)----Rx(1.153)----*--\n", + " | \n", + "--Ry(0.785)----Rz(4.899)----z--\n", + " \n", + "Hamiltonian info: [[0.7323522915498704, 'z0'], [-0.8871768419457995, 'y0'], [-0.9984424683179713, 'x0,x1'], [0.22330632097656178, 'x0'], [-0.9538751499171685, 'z1'], [-0.20027805656948905, 'z0'], [-0.8187871309343584, 'y1']]\n" ] } ], + "metadata": {} + }, + { + "cell_type": "markdown", "source": [ - "# 超参数设置\n", - "selected_qubit = [2, 4, 6, 8]\n", - "samples = 300\n", - "grad_val = []\n", - "means, variances = [], []\n", - "\n", - "\n", - "# 记录运算时长\n", - "time_start = time.time()\n", - "\n", - "# 不断增加量子比特数量\n", - "for N in selected_qubit:\n", - " grad_info = []\n", - " THETA_SIZE = N\n", - " for i in range(samples):\n", - " class manual_gradient(paddle.nn.Layer):\n", - " # 初始化一个长度为 THETA_SIZE 的可学习参数列表\n", - " def __init__(self, shape, param_attr=paddle.nn.initializer.Uniform(low=0.0, high=2 * np.pi),dtype='float64'):\n", - " super(manual_gradient, self).__init__()\n", - "\n", - " # 转换成 Paddle 中的 Tensor\n", - " self.H = paddle.to_tensor(density_op(N))\n", - "\n", - " # 定义损失函数和前向传播机制 \n", - " def forward(self):\n", - "\n", - " # 初始化三个 theta 参数列表\n", - " theta_np = np.random.uniform(low=0., high= 2 * np.pi, size=(THETA_SIZE))\n", - " theta_plus_np = np.copy(theta_np) \n", - " theta_minus_np = np.copy(theta_np) \n", - "\n", - " # 修改用以计算解析梯度\n", - " theta_plus_np[0] += np.pi/2\n", - " theta_minus_np[0] -= np.pi/2\n", - "\n", - " # 转换成 Paddle 中的 Tensor\n", - " theta = paddle.to_tensor(theta_np)\n", - " theta_plus = paddle.to_tensor(theta_plus_np)\n", - " theta_minus = paddle.to_tensor(theta_minus_np)\n", - "\n", - " # 生成随机目标，在 rand_circuit 中随机选取电路门\n", - " target = np.random.choice(3, N) \n", - " \n", - " U = rand_circuit(theta, target, N)\n", - " U_dagger = dagger(U) \n", - " U_plus = rand_circuit(theta_plus, target, N)\n", - " U_plus_dagger = dagger(U_plus) \n", - " U_minus = rand_circuit(theta_minus, target, N)\n", - " U_minus_dagger = dagger(U_minus) \n", - "\n", - " \n", - " # 计算解析梯度\n", - " grad = (paddle.real(matmul(matmul(U_plus_dagger, self.H), U_plus))[0][0] \n", - " - paddle.real(matmul(matmul(U_minus_dagger, self.H), U_minus))[0][0])/2\n", - " \n", - " return grad \n", - " \n", - " \n", - " # 定义主程序段 \n", - " def main():\n", - " \n", - " # 设置QNN的维度\n", - " sampling = manual_gradient(shape=[THETA_SIZE])\n", - "\n", - " # 采样获得梯度信息\n", - " grad = sampling()\n", - "\n", - " return grad.numpy()\n", - " \n", - " if __name__ == '__main__':\n", - " grad = main()\n", - " grad_info.append(grad)\n", - " \n", - " # 记录采样信息\n", - " grad_val.append(grad_info) \n", - " means.append(np.mean(grad_info))\n", - " variances.append(np.var(grad_info))\n", + "``cir`` 和 ``H_l`` 就是要优化的目标函数 ``loss_func`` 所需的参数。" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "用户可以通过我们提供的梯度分析工具，查看电路中各参数梯度采样的结果。同时，可以根据需求在 ``single``, ``max``, 以及 ``random`` 三种模式间选择，其中 ``single`` 会返回电路多次采样后每个参数的平均值和方差， ``max`` 模式返回每轮采样中所有参数梯度最大值的均值和方差，``random`` 则是在每轮采样得到的各参数梯度中随机选择一个后计算均值和方差。\n", "\n", - "time_span = time.time() - time_start\n", - "print('主程序段总共运行了', time_span, '秒')" - ] + "我们首先对该电路采样 300 次，这里我们选择 ``single`` 模式，看看电路中每个可变参数梯度的平均值和方差，同时默认 ``param=0`` 表示我们查看第一个参数的梯度分布情况。" + ], + "metadata": {} }, { "cell_type": "code", - "execution_count": 6, - "metadata": { - "ExecuteTime": { - "end_time": "2021-03-02T12:24:30.342035Z", - "start_time": "2021-03-02T12:24:29.346060Z" - } - }, + "execution_count": 27, + "source": [ + "grad_mean_list, grad_variance_list = random_sample(cir, loss_func, samples, H_l, mode='single', param=0) " + ], "outputs": [ { + "output_type": "stream", + "name": "stderr", + "text": [ + "Sampling: 100%|###################################################| 300/300 [00:14<00:00, 21.14it/s]\n" + ] + }, + { + "output_type": "stream", "name": "stdout", + "text": [ + "Mean of gradient for all parameters: \n", + "theta 1 : -0.03157116754124028\n", + "theta 2 : -0.004525341240963983\n", + "Variance of gradient for all parameters: \n", + "theta 1 : 0.07237471326311368\n", + "theta 2 : 0.027855249806997346\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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" + }, + "metadata": { + "needs_background": "light" + } + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "用户如果想要查看该量子电路在训练过程中梯度和损失值的变化情况，还可以使用 ``plot_loss_grad`` 函数，辅助查看电路的训练效果。" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 12, + "source": [ + "plot_loss_grad(cir, loss_func, ITR, LR, H_l)" + ], + "outputs": [ + { "output_type": "stream", + "name": "stderr", "text": [ - "我们接着画出这个采样出来的梯度的统计结果：\n" + "Training: 100%|###################################################| 120/120 [00:03<00:00, 38.59it/s]\n" ] }, { + "output_type": "display_data", "data": { - "image/png": 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\n", 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q1Z57wrBhbgcxs7JxgNQqadsd6WZmZeAAqWVNTbBiBWzenHclZlaDOhUgknaW1Ceb3l/ScZL6lbc067EJE2DTJli1Ku9KzKwGdfYIZCHpkSIjgVuAjwA/LVdRViITsgvYli/Ptw4zq0mdDRBFxEbgfcCPIuJE4IDylWUlMW4cNDQ4QMysLDodIJIOAT4E3JAtayhPSVYyAwbA/vs7QMysLDobIJ8HzgF+ExEPZQ82vKNsVVnpTJjgADGzsujUnegR8Xvg9wBZY/pzEfEv5SzMSmTCBJg3D155JT1k0cysRDp7FdaVknaVtDOwAnhY0pfKW5qVxMSJabxiRb51mFnN6ewprPER8TKp17+bgLGkK7Gs0vlKLDMrk84GSL/svo/jgfkRsRmoj741qt3ee8MuuzhAzKzkOhsgFwGPAzsDCyXtDfg54dWgTx9obHSAmFnJdSpAIuI/ImJkRBwTyRPA4WWuzUqlcCVW+KDRzEqns43ob5X0PUkt2fDvpKMRqwYTJsALL8BTT+VdiZnVkM6ewroUeAU4KRteBi4rV1FWYm5IN7My6GyAvC0i/jUi1mTD14F9ylmYlZADxMzKoLMB8qqkv/WLKmkq8Gp5SrKSGzoURozwvSBmVlKd7RP9U8DPJL01m38ROLU8JVlZNDY6QMyspDp7FdbSiJgETAQmRsSBwBHd/VBJQyTdKmlVNt6tnW0Ol7SkaHhN0vHZup9KeqxoXVN3a6kbjY2wciW0tuZdiZnViC71SBgRL2d3pAOc2YPPPRu4PSL2A27P5tt+1h0R0RQRTaSw2kjqi6TgS4X1EbGkB7XUh8ZGePVVeOyxvCsxsxrRky5t1YPXzgIuz6YvJ93hvj0fAG7K+iSx7mhsTGOfxjKzEulJgPTkrrThEbE+m34aGL6D7U8Grmqz7JuSlkm6UNKAHtRSH8aPT2MHiJmVyHYb0SW9QvtBIWCnHbz2NmCPdlbNKZ6JiJDUYRhJGgFMABYULT6HFDz9gbnAV4BvdPD62cBsgNGjR2+v5Nq2yy4wZowDxMxKZrsBEhHd7kAiImZ0tE7SM5JGRMT6LCCe3c5bnUTqyGpz0XsXjl5el3QZcNZ26phLChmam5vr+1kevhLLzEqoJ6ewemI+2y4DPhW4bjvbnkKb01dZ6CBJpPYT/yp2RmMjPPIIbNqUdyVmVgPyCpDzgXdLWgXMyOaR1Czp4sJGksYAe5H1hljkCknLgeXA7sB5vVF01WtshC1bYNWqvCsxsxrQ2RsJSyoingfe1c7yFuATRfOPAyPb2a7b96DUteIrsQ44IN9azKzq5XUEYnl4+9uhocHtIGZWEg6QejJwIOy3nwPEzErCAVJvfCWWmZWIA6TeHHAAPPoobPRN/WbWMw6QetPYmLq2Xbky70rMrMo5QOpNoXMpn8Yysx5ygNSbt70NBgxwgJhZjzlA6k3fvjBunAPEzHrMAVKPfCWWmZWAA6QeNTbC2rXw0kt5V2JmVcwBUo8KjzR56KF86zCzquYAqUfundDMSsABUo9Gj4ZBg2D58rwrMbMq5gCpR5Ib0s2sxxwg9aoQIFHfnTSaWfc5QOpVYyM8/zw880zelZhZlXKA1Cs3pJtZDzlA6pUDxMx6yAFSr/7u72DYMF+JZWbd5gCpZxMnwrJleVdhZlXKAVLPJk5Mp7BaW/OuxMyqUG4BIulESQ9J2iqpeTvbHS3pEUmrJZ1dtHyspPuy5VdL6t87ldeQSZPgtddg9eq8KzGzKpTnEcgK4H3Awo42kNQA/BCYCYwHTpE0Plv9beDCiNgXeBE4vbzl1qCJE9N46dJ86zCzqpRbgETEyoh4ZAebTQFWR8SaiNgE/BKYJUnAEcA12XaXA8eXrdhaNW4cNDS4HcTMuqXS20BGAk8Wza/Nlg0FXoqILW2Wv4mk2ZJaJLVs2LChrMVWnYED4e1vd4CYWbeUNUAk3SZpRTvDrHJ+brGImBsRzRHRPGzYsN762OoxaZJPYZlZt/Qt55tHxIwevsU6YK+i+VHZsueBwZL6ZkchheXWVRMnwlVXpc6lBg/OuxozqyKVfgrrAWC/7Iqr/sDJwPyICOAO4APZdqcC1+VUY3UrNKT7hkIz66I8L+M9QdJa4BDgBkkLsuV7SroRIDu6+CywAFgJzIuIQjd6XwHOlLSa1CZySW/vQ02YNCmNfRrLzLqorKewticifgP8pp3lTwHHFM3fCNzYznZrSFdpWU/suScMGeKGdDPrsko/hWXlJvmRJmbWLQ4QSwGyfLkfaWJmXeIAsdQOsnEjPPpo3pWYWRVxgBg0NaXxgw/mWoaZVRcHiKXOpfr3h0WL8q7EzKqIA8RSeEyY4AAxsy5xgFhy0EGweDFE5F2JmVUJB4gl73hHepzJY4/lXYmZVQkHiCUHHZTGPo1lZp3kALFkwgTo188BYmad5gCxZMCAdDXW4sV5V2JmVcIBYtscdFA6AnFDupl1ggPEtjnoIHjhBXjiibwrMbMq4ACxbdyQbmZd4ACxbSZMgL593Q5iZp3iALFtBg6EAw6Alpa8KzGzKuAAsTc6+GC4914/2t3MdsgBYm80dSq8/DI89NCOtzWzuuYAsTeaOjWN77473zrMrOI5QOyNxo6FPfaAP/wh70rMrMLlEiCSTpT0kKStkpo72GYvSXdIejjb9nNF686VtE7Skmw4pveqr3FSOgrxEYiZ7UBeRyArgPcBC7ezzRbgixExHjgY+Iyk8UXrL4yIpmy4sYy11p+pU9NTedevz7sSM6tguQRIRKyMiEd2sM36iFicTb8CrARG9kZ9dc/tIGbWCVXRBiJpDHAgcF/R4s9KWibpUkm7bee1syW1SGrZsGFDuUutDU1N6Z4QB4iZbUfZAkTSbZJWtDPM6uL77AL8Gvh8RLycLf4x8DagCVgP/HtHr4+IuRHRHBHNw4YN697O1Jv+/WHKFAeImW1X33K9cUTM6Ol7SOpHCo8rIuLaovd+pmib/wdc39PPsjamToULLoCNG+Etb8m7GjOrQBV7CkuSgEuAlRHxvTbrRhTNnkBqlLdSmjoVtmyB++7b8bZmVpfyuoz3BElrgUOAGyQtyJbvKalwRdVU4CPAEe1crvsdScslLQMOB77Q2/tQ86ZNSw9WvOWWvCsxswqlqKPOg5qbm6PFDwrsvMMPhxdfhCVL8q7EzHIkaVFEvOmevYo9hWUVYOZMWLoU1q3LuxIzq0AOEOvYzJlpfPPN+dZhZhXJAWIda2yEkSPhppvyrsTMKpADxDompaOQW2+FzZvzrsbMKowDxLbvmGNS/yD33JN3JWZWYRwgtn3vele6nNenscysDQeIbd+uu8Khh8L//A/U0SXfZrZjDhDbsZNOSl3cLl6cdyVmVkEcILZjp5ySns578cV5V2JmFcQBYjs2eDCceCJceWV6uKKZGQ4Q66zTT09XY11zTd6VmFmFcIBY50yfDvvuC5dcknclZlYhHCDWOVI6Clm4EP70p7yrMbMKULYOpawGnXoq/Ou/wje+Ab/4RWnec9MmWLEiDStXpjaWrVthwADYe28YMwYmToTRo1OImVnFcIBY540YAV/+Mpx3Hnzyk3DYYd17nwj47W/hqqvg2mvTI+MB+vWDnXeGPn3g1VfTUPzZ//iPcOSRcNRRKVzMLFfuD8S6ZuNGOOCA9EP/4IPpR7+ztm5NgXHeeekx8YMGwaxZ8N73pqOMffdNd71DCpkNG2DNGli0KD1KZeFCePLJtH78+PS6974XDj4YGhpKv69mBnTcH4gDxLpu/vz0w//d78IXv9i519xyC5x1FixfDvvvD1/9Knzwg+n+ks6KgD/+MT1e/oYb4Pe/T93uDh2antl1zDEwYwbsvnv39svM2uUAwQFSMhHpL//bboPLLks3GnZk8WKYMyf96I8dC9/8ZrqzvRRHDC+9BAsWwPXXw403wgsvpHaSgw5Kp9emT0+nvRwoZj3iAMEBUlLPPQfvex/ceSd87Wvw9a+ntguA1la491644AK47rp0I+LXvgaf/WxqHC+H1lZoaUlHOrfeCvfdlxroITXEH3QQTJqUTr+NHw/77AP9+5enFrMa4wDBAVJymzbBP/9zujfkrW+FCRNgt91SqLz0Ulp25pnwuc+l6d702mvwwAMpyFpa0rBmzbb1ffqkK7vGjk0N8nvvDXvtBaNGbRvvumvv1mxWoSoqQCSdCJwLjAOmRES7v+qSHgdeAVqBLYUdkDQEuBoYAzwOnBQRL+7ocx0gZRABv/oV/O53qX1jwwaYOhXe/e7UGVVvB8f2/PWv6VLhlSvh0Udh1Sp4/PE0rF//5qcNDxr0xlAZPXrbUAgcH8VYHai0ABkHbAUuAs7aQYA0R8RzbZZ/B3ghIs6XdDawW0R8ZUef6wCxDm3aBE89la7yWrsW1q3bNl0Yr1//xtdIsOee2+5XGTMmTRcCZtSoFEJmVa6jAMnlPpCIWAmg7t8YNgt4ZzZ9OfA7YIcBYtah/v23hUBHXn89Bcmf/wxPPJGOXArje+6BefPSVWHFdt01BcmIEbDHHjB8eGrUHzo0tQ0NHpxCZued09C/fxr69Uun2fr0SUdGEamdp7U1fcbmzduGTZveON68OW1TGLZuTUPxH4tSeu+GhjT07Zs+s1+/bTUMGPDmcWG6ocE3dlrF30gYwC2SArgoIuZmy4dHROHPwaeB4R29gaTZwGyA0aNHl7NWq3UDBsDb3paG9rS2piOXQsAUjmLWrYOnn4a7706n+P76196tuxykbWFTCJ6+fbcFUiH8+vRJ2xaGgkIoFoZCwBVPFy8rvGZHNRXGxZ9XPL+jZcXjttN5KVUNF10E06aV5r0yZQsQSbcBe7Szak5EXNfJtzk0ItZJ+jvgVkl/jIiFxRtERGQB064sdOZCOoXVyc8167qGhm1tJIce2vF2r74Kzz+fLjT4y1/SU443bkzBsmnTtiOJwlFH4WihT59tP9KFH+3iH/HCkUPhaKL4B73wHvDGH+qtW7cdqbQ9qnn99TePC9PFdW7a9OYjntbW9oOg7Y9zYSgETXHgtBc+Hf2YFodM29Dp7LLicdvpvJSyhjKcTi1bgETEjBK8x7ps/Kyk3wBTgIXAM5JGRMR6SSOAZ3v6WWa9Zqed0mmtUaPyrsSsRyr2abySdpY0qDANHAmsyFbPB07Npk8FOntEY2ZmJZJLgEg6QdJa4BDgBkkLsuV7Srox22w4cJekpcD9wA0RcXO27nzg3ZJWATOyeTMz60W+kdDMzLaro8t4K/YUlpmZVTYHiJmZdYsDxMzMusUBYmZm3eIAMTOzbqmrq7AkbQCe6OLLdgee2+FW1cH7Upm8L5WplvYFerY/e0fEsLYL6ypAukNSS3uXr1Uj70tl8r5UplraFyjP/vgUlpmZdYsDxMzMusUBsmNzd7xJ1fC+VCbvS2WqpX2BMuyP20DMzKxbfARiZmbd4gDpgKSjJT0iaXXW73rVkLSXpDskPSzpIUmfy5YPkXSrpFXZeLe8a+0sSQ2SHpR0fTY/VtJ92fdztaT+edfYWZIGS7pG0h8lrZR0SLV+N5K+kP0bWyHpKkkDq+W7kXSppGclrSha1u73oOQ/sn1aJukd+VX+Zh3sywXZv7Flkn4jaXDRunOyfXlE0lHd/VwHSDskNQA/BGYC44FTJI3Pt6ou2QJ8MSLGAwcDn8nqPxu4PSL2A27P5qvF54CVRfPfBi6MiH2BF4HTc6mqe34A3BwRfw9MIu1X1X03kkYC/wI0R0Qj0ACcTPV8Nz8Fjm6zrKPvYSawXzbMBn7cSzV21k95877cCjRGxETgT8A5ANlvwcnAAdlrfpT95nWZA6R9U4DVEbEmIjYBvwRm5VxTp0XE+ohYnE2/QvqBGknah8uzzS4Hjs+lwC6SNAo4Frg4mxdwBHBNtkk17ctbgenAJQARsSkiXqJKvxtSr6Y7SeoLvAVYT5V8N1n32C+0WdzR9zAL+Fkk9wKDs95QK0J7+xIRt0TElmz2XqDQBeYs4JcR8XpEPAasJv3mdZkDpH0jgSeL5tdmy6qOpDHAgcB9wPCIWJ+teprUaVc1+D7wZWBrNj8UeKnoP0c1fT9jgQ3AZdkpuYuzHjer7rvJupz+LvBnUnD8BVhE9X430PH3UO2/CR8HbsqmS7YvDpAaJmkX4NfA5yPi5eJ1kS6/q/hL8CS9B3g2IhblXUuJ9AXeAfw4Ig4E/kqb01VV9N3sRvprdiywJ7Azbz6NUrWq5XvYEUlzSKe1ryj1eztA2rcO2KtoflS2rGpI6kcKjysi4tps8TOFw+5s/Gxe9XXBVOA4SY+TTiUeQWpDGJydNoHq+n7WAmsj4r5s/hpSoFTjdzMDeCwiNkTEZuBa0vdVrd8NdPw9VOVvgqTTgPcAH4pt92yUbF8cIO17ANgvu5qkP6nBaX7ONXVa1kZwCbAyIr5XtGo+cGo2fSpwXW/X1lURcU5EjIqIMaTv4bcR8SHgDuAD2WZVsS8AEfE08KSkt2eL3gU8TBV+N6RTVwdLekv2b66wL1X53WQ6+h7mAx/NrsY6GPhL0amuiiTpaNKp3+MiYmPRqvnAyZIGSBpLujDg/m59SER4aGcAjiFdufAoMCfverpY+6GkQ+9lwJJsOIbUdnA7sAq4DRiSd61d3K93Atdn0/tk/+hXA78CBuRdXxf2owloyb6f/wZ2q9bvBvg68EdgBfBzYEC1fDfAVaS2m82kI8PTO/oeAJGuzHwUWE668iz3fdjBvqwmtXUUfgN+UrT9nGxfHgFmdvdzfSe6mZl1i09hmZlZtzhAzMysWxwgZmbWLQ4QMzPrFgeImZl1iwPErBsk/W82HiPpn0r83l9tM/+HUr6/Wak4QMx6ZgzQpQApuku7I28IkIj4xy7WZNYrHCBmPXM+ME3SkqxvjIasH4YHsn4Y/g+ApHdKulPSfNLd2kj6b0mLsv40ZmfLzic93XaJpCuyZYWjHWXvvULSckkfLHrv32lbHyNXZHeGm5XVjv4SMrPtOxs4KyLeA5AFwV8iYrKkAcDdkm7Jtn0HqX+Gx7L5j0fEC5J2Ah6Q9OuIOFvSZyOiqZ3Peh/pLvZJwO7ZaxZm6w4k9e/wFHA36ZlUd5V6Z82K+QjErLSOJD0zaQnpEfpDSc8aAri/KDwA/kXSUlJfDXsVbdeRQ4GrIqI1Ip4Bfg9MLnrvtRGxlfTYijEl2Bez7fIRiFlpCTgjIha8YaH0TtKj24vnZwCHRMRGSb8DBvbgc18vmm7F/7etF/gIxKxnXgEGFc0vAD6dPU4fSftnHUa19VbgxSw8/p7U9XDB5sLr27gT+GDWzjKM1LNh956ialYC/ivFrGeWAa3ZqaifkvoqGQMszhqyN9B+l643A5+StJL0RNR7i9bNBZZJWhzp0fUFvwEOAZaSnrb85Yh4Ogsgs17np/GamVm3+BSWmZl1iwPEzMy6xQFiZmbd4gAxM7NucYCYmVm3OEDMzKxbHCBmZtYtDhAzM+uW/w8CQqrjaX1C+wAAAABJRU5ErkJggg==" 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" }, - "output_type": "display_data" + "metadata": { + "needs_background": "light" + } } ], - "source": [ - "grad = np.array(grad_val)\n", + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "如上图所示，可以看出 iteration 在几十次后损失函数的值就基本不发生变化了，而梯度也非常的接近 0。为了更直观的看到训练得到的最优解和理论值的差距，我们计算哈密顿量 ``H_l`` 的特征值。" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 13, + "source": [ + "loss, grad = show_gradient(cir, loss_func, ITR, LR, H_l)\n", + "H_matrix = pauli_str_to_matrix(H_l, N)\n", + "\n", + "print(\"最终的优化结果： \", loss[-1])\n", + "print(\"实际的基态能量：\", np.linalg.eigh(H_matrix)[0][0])" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + "Training: 100%|###################################################| 120/120 [00:03<00:00, 39.95it/s]" + ] + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "最终的优化结果： -1.506230314972159\n", + "实际的基态能量： -2.528866656129176\n" + ] + }, + { + "output_type": "stream", + "name": "stderr", + "text": [ + "\n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "通过对比可以看出，该电路训练得到的最优解和我们要得到的实际值之间还存在一定的差距。" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "#### 更多的量子比特\n", + "\n", + "由于在贫瘠高原效应中，梯度会随着量子比特数的增加呈指数级消失。所以我们可以进一步对比增加电路中量子比特的数量，看看会对我们的梯度带来什么影响 (这里我们采样时选择 ``max`` 模式，对参数列表中的最大值做计算)。" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 34, + "source": [ + "# 超参数设置\n", + "selected_qubit = [2, 4, 6, 8]\n", + "means, variances = [], []\n", + "\n", + "# 不断增加量子比特数量\n", + "for N in selected_qubit:\n", + " grad_info = []\n", + " THETA_SIZE = N \n", + " target = np.random.choice(3, N)\n", + " theta = np.random.uniform(low=0., high= 2 * np.pi, size=(THETA_SIZE))\n", + " theta = paddle.to_tensor(theta, stop_gradient=False, dtype='float64')\n", + " cir = rand_circuit(theta, target, N)\n", + " H_l = random_pauli_str_generator(N, terms=10)\n", + " \n", + " grad_mean_list, grad_variance_list = random_sample(cir, loss_func, samples, H_l, mode='max') \n", + " # 记录采样信息\n", + " means.append(grad_mean_list)\n", + " variances.append(grad_variance_list)\n" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + "Sampling: 100%|###################################################| 300/300 [00:22<00:00, 13.28it/s]\n" + ] + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Mean of max gradient\n", + "0.31080108926858796\n", + "Variance of max gradient\n", + "0.01671146619361498\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
    " + ], + "image/png": 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" + }, + "metadata": { + "needs_background": "light" + } + }, + { + "output_type": "stream", + "name": "stderr", + "text": [ + "Sampling: 100%|###################################################| 300/300 [00:33<00:00, 8.86it/s]\n" + ] + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Mean of max gradient\n", + "0.18860559161991128\n", + "Variance of max gradient\n", + "0.00513813734318612\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
    " + ], + "image/png": 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" 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" + }, + "metadata": { + "needs_background": "light" + } + }, + { + "output_type": "stream", + "name": "stderr", + "text": [ + "Sampling: 100%|###################################################| 300/300 [00:51<00:00, 5.86it/s]\n" + ] + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Mean of max gradient\n", + "0.08909871218516183\n", + "Variance of max gradient\n", + "0.001158520193967305\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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" + }, + "metadata": { + "needs_background": "light" + } + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "接着对采样不同量子比特数量电路得到的各参数最大梯度的平均值和方差作图，方便比较。" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 35, + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", "means = np.array(means)\n", "variances = np.array(variances)\n", + "\n", "n = np.array(selected_qubit)\n", "print(\"我们接着画出这个采样出来的梯度的统计结果：\")\n", "fig = plt.figure(figsize=plt.figaspect(0.3))\n", "\n", - "\n", "# ============= 第一张图 =============\n", "# 统计出随机采样的梯度平均值和量子比特数量的关系\n", "plt.subplot(1, 2, 1)\n", @@ -525,48 +846,348 @@ "plt.ylabel(r\"$ \\partial \\theta_{i} \\langle 0|H |0\\rangle$ Mean\")\n", "plt.title(\"Mean of {} sampled gradient\".format(samples))\n", "plt.xlim([1,9])\n", - "plt.ylim([-0.06, 0.06])\n", "plt.grid()\n", "\n", "# ============= 第二张图 =============\n", "# 统计出随机采样的梯度的方差和量子比特数量的关系\n", "plt.subplot(1, 2, 2)\n", - "plt.semilogy(n, variances, \"v\")\n", - "\n", - "# 多项式拟合\n", - "fit = np.polyfit(n, np.log(variances), 1)\n", - "slope = fit[0] \n", - "intercept = fit[1] \n", - "plt.semilogy(n, np.exp(n * slope + intercept), \"r--\", label=\"Slope {:03.4f}\".format(slope))\n", + "plt.plot(n, np.log(variances), \"v-\")\n", "plt.xlabel(r\"Qubit #\")\n", "plt.ylabel(r\"$ \\partial \\theta_{i} \\langle 0|H |0\\rangle$ Variance\")\n", "plt.title(\"Variance of {} sampled gradient\".format(samples))\n", - "plt.legend()\n", "plt.xlim([1,9])\n", - "plt.ylim([0.0001, 0.1])\n", "plt.grid()\n", "\n", "plt.show()" - ] + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "我们接着画出这个采样出来的梯度的统计结果：\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
    " + ], + "image/png": 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" + }, + "metadata": { + "needs_background": "light" + } + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "可以看出，随着量子比特数量的增加，多次采样获得所有参数梯度的最大值不断接近于 0，且方差也是呈下降趋势。" + ], + "metadata": {} }, { "cell_type": "markdown", - "metadata": {}, "source": [ - "要注意的是，在理论上，只有当我们选取的网络结构还有损失函数满足一定条件时 (2-design)详见论文 [[1]](https://arxiv.org/abs/1803.11173), 才会出现这种效应。接着我们不妨可视化一下不同量子比特数量对的优化曲面的影响：\n", + "为了进一步看看梯度随量子比特数量增加发生的变化，我们不妨可视化一下不同量子比特数量对的优化曲面的影响：\n", "\n", "![BP-fig-qubit_landscape_compare](./figures/BP-fig-qubit_landscape_compare.png \"(a)不固定 z 轴尺度时，采样出的优化曲面分别从左至右对应2、4和6量子比特的情形。（b）同样的优化曲面但是固定 z 轴尺度作为对比。\")\n", - "
    (a)不固定 z 轴尺度时，采样出的优化曲面分别从左至右对应2、4和6量子比特的情形。（b）同样的优化曲面但是固定 z 轴尺度作为对比。
    \n", " \n", "\n", "画图时 $\\theta_1$ 和 $\\theta_2$ 是前两个电路参数, 剩余参数全部固定为 $\\pi$。不然我们画不出这个高维度的流形。\n", - "结果不出所料，陡峭程度随着 $n$ 的增大越来越小了，**注意到 Z 轴尺度的极速减小**。相对于2量子比特的情况，6量子比特的优化曲面已经非常扁平了。\n", + "结果不出所料，陡峭程度随着 $n$ 的增大越来越小了，**注意到 Z 轴尺度的极速减小**。相对于 2 量子比特的情况，6 量子比特的优化曲面已经非常扁平了。\n", + "\n", + "在理论上，只有当我们选取的网络结构还有损失函数满足一定条件时 (2-design)[[1]](https://arxiv.org/abs/1803.11173), 才会出现这种梯度随量子比特数增加而急剧消失的现象。\n", "\n" - ] + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### 应用 二：基于经典数据量子编码的监督学习\n", + "\n", + "监督学习是量子神经网络的重要应用之一，然而贫瘠高原现象同样制约着量子变分算法在此类问题上的表现。因此，如何设计更有效的电路和损失函数来避免贫瘠高原现象的出现，是当前量子神经网络的重要研究方向之一。实际上，已有学者证明，在生成模型 (generative traning) 的训练之中使用瑞丽熵 (Renyi divergence) 作为损失函数，可以有效避免贫瘠高原现象 [[3]](https://arxiv.org/abs/2106.09567)。 基于量桨的梯度分析模块，我们可以快速分析一个监督学习模型中梯度的相关信息，从而便于研究者尝试探索不同的量子电路和损失函数。" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "这里，我们利用量桨的[量子态编码经典数据](./tutorial/machine_learning/DataEncoding_CN.ipynb)提供的数据集为例进行介绍。" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "#### Paddle Quantum 实现\n", + "\n", + "首先，导入需要的包" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 14, + "source": [ + "from paddle_quantum.circuit import UAnsatz\n", + "from paddle import matmul, transpose,reshape\n", + "from paddle_quantum.utils import pauli_str_to_matrix\n", + "import paddle.fluid as fluid\n", + "import paddle.fluid.layers as layers\n", + "\n", + "from paddle_quantum.dataset import Iris\n", + "from paddle_quantum.gradtool import random_sample_supervised, plot_supervised_loss_grad" + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "#### 定义参数化量子电路\n", + "\n", + "接着，构建参数化量子电路 $U(\\theta)$ " + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 15, + "source": [ + "def U_theta(theta, n, depth):\n", + " \"\"\"\n", + " :param theta: 维数: [n, depth + 3]\n", + " :param n: 量子比特数量\n", + " :param depth: 电路深度\n", + " :return: U_theta\n", + " \"\"\"\n", + " # 初始化网络\n", + " cir = UAnsatz(n)\n", + "\n", + " # 先搭建广义的旋转层\n", + " for i in range(n):\n", + " cir.rz(theta[i][0], i)\n", + " cir.ry(theta[i][1], i)\n", + " cir.rz(theta[i][2], i)\n", + "\n", + " # 默认深度为 depth = 1\n", + " # 搭建纠缠层和 Ry旋转层\n", + " for d in range(3, depth + 3):\n", + " for i in range(n - 1):\n", + " cir.cnot([i, i + 1])\n", + " cir.cnot([n - 1, 0])\n", + " for i in range(n):\n", + " cir.ry(theta[i][d], i)\n", + " return cir" + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "#### 定义目标函数\n", + "\n", + "这里定义要优化的目标函数，第二个参数仍然是可变参数 ``*args``。" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 16, + "source": [ + "def loss_func(cir,*args):\n", + " #传入量子态和训练标签\n", + " state_in = args[0]\n", + " label = args[1]\n", + " # 将 Numpy array 转换成 tensor\n", + " label_pp = reshape(paddle.to_tensor(label),(-1,1))\n", + " \n", + " Utheta = cir.U\n", + " \n", + " # 因为 Utheta是学习到的，我们这里用行向量运算来提速而不会影响训练效果\n", + " state_out = matmul(state_in,Utheta)\n", + " \n", + " # 测量得到泡利 Z 算符的期望值 \n", + " Ob = paddle.to_tensor(pauli_str_to_matrix([[1.0, 'z0']], qubit_num))\n", + " E_Z = matmul(matmul(state_out, Ob), transpose(paddle.conj(state_out), perm=[0, 2, 1]))\n", + "\n", + " # 映射 处理成标签的估计值\n", + " state_predict = paddle.real(E_Z)[:, 0] * 0.5 + 0.5\n", + " loss = paddle.mean((state_predict - label_pp) ** 2)#均方误差\n", + " \n", + " return loss\n", + " " + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "#### 定义数据集\n", + "\n", + "接着导入量子编码后的 Iris 数据集。" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 17, + "source": [ + "time_start = time.time()\n", + "\n", + "#超参数设置,这里不需要太多qubit，不然严重过拟合\n", + "test_rate = 0.2\n", + "qubit_num = 2\n", + "depth = 1\n", + "lr = 0.1\n", + "BATCH = 4\n", + "EPOCH = 4\n", + "SAMPLE = 300\n", + "# 验证数据集\n", + "iris = Iris(encoding='amplitude_encoding', num_qubits=qubit_num, test_rate=test_rate, classes=[0,1], return_state=True)\n", + "\n", + "# 获取数据集的输入和标签\n", + "train_x, train_y = iris.train_x, iris.train_y #这里的 train_x, train_y，test_x, test_y 都是 paddle.tensor\n", + "test_x, test_y = iris.test_x, iris.test_y\n", + "testing_data_num = len(test_y)\n", + "training_data_num = len(train_y)\n", + "\n", + "\n", + "# 为量子电路创建可训练的参数\n", + "theta = layers.create_parameter(shape=[qubit_num,depth+3], default_initializer=paddle.nn.initializer.Uniform(low=0.0, high=2 * np.pi),\n", + " dtype='float64',is_bias=False)\n", + "# 创建电路\n", + "circuit = U_theta(theta, qubit_num, depth)\n", + "\n", + "print(circuit)" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "--Rz(3.338)----Ry(2.554)----Rz(1.318)----*----x----Ry(4.679)--\n", + " | | \n", + "--Rz(0.246)----Ry(3.961)----Rz(5.514)----x----*----Ry(3.248)--\n", + " \n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "我们先看看在 EPOCH=4，BATCH=4 的情况下，训练过程中的损失函数值及梯度的变化情况" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 18, + "source": [ + "loss,grad = plot_supervised_loss_grad(circuit, loss_func, N=qubit_num, EPOCH = EPOCH, LR = lr,BATCH = BATCH, TRAIN_X=train_x, TRAIN_Y=train_y)" + ], + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
    " + ], + "image/png": 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AjcEEqvp26LoAMA9AaNABzgTwlqpuU9XtAN4CcFactmYnZ5xhc0o8+KCtO4Fo1gxo165+BKJ9e6vIYiUTISQO4hYIETkJwKUApoW25cU4pwiAd9huRWhbJL4H4F91PDf7GTUKaN4cePJJaws+aFB4X7rHQqiGBWLAAKC8HNi1K33vRwjJCeIViBsA3Arg76q6XER6Ang7VUaIyGUAhgKYlOB5V4lImYiUbd68OVXmpIcWLUwk9u8H+vQJzz4HpF8gdu8GKivDHoRquKKKEEIiEJdAqOq7qjpWVX8dSlZvUdUfxThtPYAjPevFoW01EJExAG4HMFZVDyRyrqo+oapDVXVox44d4/lVMosbVe3CS45OndLb8tuVuDqBAJiHIITEJN4qphdEpI2ItASwDMAKEbk5xmkLAPQSkR4i0gzAJQCm+q47CMDjMHHY5Nk1A8AZItIulJw+I7StYXNWKI1y4ok1t6fbg9i+3Zbt2llvqfbtKRCEkJjEG2Lqq6o7AZwHyxP0gFUyRURVKwFcB7uxrwTwUig8dY+IuNaokwC0AvA3EVkiIlND524D8L8wkVkA4J7QtoZNv37AO+8A3/1uze2dO1tOYN++9Lyv14MQMS+CAkEIiUG8U47mh8Y9nAfgYVU9JCIx+zWo6nQA033b7vS8HhPl3KcAPBWnfQ2HU0+tvc07FqJ799S/p1cgABOIRx+1vERTzjpLCAkmXg/icQBrAbQEMDs0oG1nuoxqdKR7sJxfIAYMsGT5J5+k5/0IITlBvEnq36tqkap+U43PAHw9zbY1HupbIJioJoTEQbxJ6sNF5EFXUioi/wfzJkgqiCQQa9cC06fXOjwi8+aFE9Jetm0DCgqs1BawSYqaNaNAEEKiEm+I6SkAuwD8T+hnJ4Cn02VUoyNSu4277wbGjwcOHYp9jQULgJEjgYceqr3PDZJzNGtmEyBRIAghUYhXII5W1btCbTPWqOovAPRMp2GNioIC4PDDawvE/PnAwYPAmjXRz6+qAq65xgbArV1be79fIAC23CCExCRegdgnIie7FREpAZCmmsxGin8sxFdfAR9/bK9Xrox+7hNP2CRELVoA62uNJ4wsEF9+aY0DCSEkgHhrHK8G8KyIHB5a3w6gYbfgzjb8AuEmFQLCQhHEpk3AbbcBp51mA+GWL699zLZt1sXVy0kn2fL9923ebUII8RFvFdNSVR0A4AQAJ6jqIACnpdWyxoZfIObPt2XbttE9iJ/9zOazfuQRm3ciEQ+iRQtg7txkLSeE5CgJzSinqjtDI6oB4MY02NN48QvEBx/YrHNDhkQWiNJS4JlngJtussqkoiIbkb3TN0QlSCDy84FhwygQhJCIJDPlqKTMCmICsWOHzRmhah7E8OHW+fXjj22bn5tvBo48ErjjDlsvCnVE93oR+/bZj18gAKt6WrQofS0+CCENmmQEImarDZIAbizEpk2WON640Zr69eljXsGGDTWP373bROSKK4CWoSEpQQLhxkVEEojKypr5DkIICRFVIERkl4jsDPjZBaBrPdnYOHACsXGjhZcA8yB697bX/kR1WRlQXQ2MGBHeVhyakM8rEP5R1F5cojrdYaY9ezjmgpAGSFSBUNXWqtom4Ke1qrLLWyrxjqb+4AMbzDZggHkQQO08xLx5thw+PLwtyIOIJhAdOlieI90C8dhj5g3t3Rv7WEJI1pBMiImkEq9AzJ9vVUbNm1sr8DZtagvE/PlAr15AYWF4W4sWVuoar0AAFmaaOzc4x5EqPv/cBvxt2ZK+9yCEpBwKRLbgBGLDBgsfOc9AJJyodqiaB+GfeAioXeoaj0Bs2WLzVKcLJwwUCEIaFBSIbOGww2ye6nfesZi99+bfp09ND2LdOstVePMPjqKimqOj4xEIIL1hJjdfeLbPG04IqQEFIpvo3BmYPdtee3MLvXsDX3xh7TeAcP4hyIMoLq7tQTRtauITRJ8+1gcqnQJBD4KQBgkFIpvo1MnKTtu2tfyCwyWqXZhp/nxr8HfCCbWvUVRkeQzXAdYNkpMIw1aaNLFqpvrwICgQhDQoKBDZhMtDDB9e84bur2SaNw8YPNgqnfwUFVmOYuNGWw8aRe1n5Ejr4bRjR1LmB6JKgSCkgUKByCa8AuGlRw8Tg48/tmqgRYuC8w9A7VLXeAXCjd5ONXv22OhwgDkIQhoYFIhswgmEP7fQtKmFnFauBD780OaTDso/AGGBcInqeARi+HALNaUjzOQVBXoQhDQoKBDZxPHHWzI5yDtwpa7uKT+SB+EfTR2PQLRubfkMCgQhxAMFIpu44AKrVurQofa+3r2B1autyqlzZ2vSF0RhoQ2wS0QgAPNIyspSP2DOiULXrhQIQhoYFIhsQiR6OWpVFTB1qnkPkaqSROxmvH69VTLt2hWfQBx3nCWp3biJVOE8iD59mIMgpIFBgWgouEqmaPkHhxtN7Tq5tmsX+/rHHGPLVI+odl5Dnz7A1q3WYJAQ0iCgQDQUjj02/DpS/sHhBCLWKGov6RKIzZttcqKePc0DcoP9CCFZDwWiodCyJdCtm1UbDR0a/VjXbmPrVluPRyB69LDwVDoEomNH+3HrhJAGAQWiITF4sE1BGilP4SgutlDU6tW2Ho9AFBRY4tudEw1VYMoUS6jHYssWS7q7xDsT1YQ0GCgQDYknnwRefz32cW4sxEcf2TIegQCAo4+Oz4P461+BCROAP/0p9rF+D4ICQUiDgQLRkGjfHjjiiNjH1VUgjjkmtkB8+ilw3XX22tsUMBL0IAhpsFAgchGvQIhYt9Z4OOYYe+KPlEiurAS+/W27ZlFRuN9TNJwH4QSCOQhCGgwUiFyka2i68A0brDNsXl5857lKpkh5iF//GigtBR59FOjXL3YO4tAhG1vRsaMl2Vu0CPYgHnoIeOSR+GwkhNQbFIhcpFmzcCgq3vASEL3UdcEC4O67gUsuAb71LaBLl9gC4aqonPfQoUOwQPzxj8Af/hC/nYSQeqFppg0gaaKoCNi0KTGBOPpoWwZ5ED/4gYnCo49aiKlzZwsxVVdb6W0QLpzkEtRBAlFdDaxda+Gr/futmooQkhXQg8hVXB4iEYFo2dJu/H4PYuNGYPFi4Prrw6Oyu3Sxm7rzEoJwAuH1IPw5iA0brIV5dXXNebcJIRknrQIhImeJyCoRKReRWwL2jxKRRSJSKSIX+vZViciS0M/UdNqZk9RFIIDgSqb33rPlKaeEt3XpYstoYSbnLTgPomPH2h7EmjXh167qihCSFaRNIEQkD8AjAL4BoC+ACSLS13fY5wAuB/BCwCX2qerA0M/YdNmZs6RSIObMsQTz4MHhbfEIRDwhJq9ALFuWmK2EkLSSTg9iOIByVV2jqgcBTAEwznuAqq5V1Q8BsINbqnHzQtRFIDZsAPbuDW977z3r/+Sd4tQJRLRSVycGzoYOHayE1s2XDZhANGli7cwpEIRkFekUiCIA6zzrFaFt8VIgImUiMk9Ezgs6QESuCh1Ttpn19TVJxoMAwk/2O3cCS5bUDC8B8XsQ7dpZsz4geLDcmjXW4mPwYIaYCMkysjlJ3U1VhwL4FoCHRORo/wGq+oSqDlXVoR1dGIMY3bvbsnPnxM5zlUwuzPT++5ZA9gvEYYcBbdrEFgjv9xLUbmPNGuv02r8/sG4du70SkkWkUyDWA/BOe1Yc2hYXqro+tFwD4B0Ag1JpXM5z7LHAzJnA+ecndp5fIObMsYF2QS3GO3eOnaT2zo4XyYPo2dMG3gHA8uWJ2UsISRvpFIgFAHqJSA8RaQbgEgBxVSOJSDsRaR563QFACYAVabM0Vxk9umbeIB7atbNpS70CMXhwcAfZWIPl/B6Ev93G3r3Al1/WFAjmIQjJGtImEKpaCeA6ADMArATwkqouF5F7RGQsAIjIMBGpAHARgMdFxD0+9gFQJiJLAbwN4FeqSoGoL1wl04EDwPz5wMknBx8XSyBieRCffmrLnj2Bo44yEWIegpCsIa0jqVV1OoDpvm13el4vgIWe/OfNBdA/nbaRKBxzjFUulZWZSPjzDw4nEKq158hWNSHwehCFhbZ0AuES4T16WCVTv370IAjJIrI5SU0yxTHHWMJ41ixbj+ZB7N0L7N5de58rZ/UKRH6+NQ/0C0TPnrbs1888CNXItlVUAMcfz1HXhNQDFAhSm6OPtsqlv/7VxidEqhCLVurqRMAbYnLrLgexZo2Fldwx/fpZ644vv4xs2xtvACtWAO++G//vkyrefx8oKQH27Kn/9yYkA1AgSG28XV0jhZeAcAltkED4R1E7vO02XAWTC0/Fk6guLbXlJ59EPiZdPPkkMHcu8OGH9f/ehGQACgSpjRMIILpARPMg/I36HN52G59+Gg4vATYWAshOgaiuBqaH0mkMb5FGAgWC1KZDBxsEB9RdIPyN+rzX3rLF8gzOg3AccYQdH0kgNm8OC0N9C8TixeG2IhQI0kigQJDaiJgXUVwMdOsW+bh27YDmzRMLMbkcxMaNwL59NQUCCCeqg5g715YjR9qcFVVV8f0+qWDaNPtcunalQJBGAwWCBHPHHcCkSbXLV724iYMieRAFBdaSw0vHjlY660QgSCCWL7eQjp/SUhv4d8klNodERUViv1MyTJsGDB8OnHQSBYI0GigQJJjx4+1GHIsuXYI7urpR1H6BcTmJDz6wZY8eNff3729VQp99VvuapaXAkCHhXEV9hZk2bbIpV88+26q6Vq82gSIkx6FAkOSINJra32bD4RcI11TQ4SqZ/GGm/ftt4F5JSTiJXl8C8a9/Wc7ECURVVfC0rITkGBQIkhzRQkz+CiagpkAUFdWeg/r4423pF4iFC+2pvaTE8gAtWtSfQEybZkI4aJAJBMAwE2kUUCBIcnTpAmzbZnkFL5E8CLfNNenz06aNeRGTJ9dMQnsT1E2amBdRHwJx6BAwYwbwzW9auOy442w7BYI0AigQJDkizSwXy4MAggUCAH7+c0tUT54c3lZaaqJwxBG23qtX/QhEaalNmnT22bbeurV5PhQI0gigQJDkCBoLceAAsGtXsAdx+OFA01CPyEgCceGFwMCBwF13WVhJ1TyIkpLwMb162TiKysqU/BoRmTbNekiNGRPe1rs3BYI0CigQJDmCBCLSGAjAwjTOi4gkEE2aAPfdZwLw1FPmKWzeXFsgDh0CPv+8bnarWqJ56tSaExj5mTYNGDXKPAeHE4hoTQUJyQEoECQ5gkJMkRr1OWIJBAB84xvWRfaee2xmPKC2QACJh5mefRY49VTrKnvMMcC4ccC99wYfu3YtsHJlOLzk6N3bwk5B5b2E5BAUCJIcbqxDvB4EEJ9AiAC//KVd9/bbbdS2qyAC6lbqWl0N3HijeR2XXgo88YRNzfqf/wQfv3ixLf3tzlnJRBoJFAiSHE2bWuLYKxAzZliYKJIAdOhgZaqdOkW/9imnAGedBezYYSOYm3j+XLt0AVq2rC0QL78MnH56cBuOxYutnfi99wKPPgpceaUNunMz2/lx81V4mxcCFAjSaKBAkOTxDpb78ku7+V56qVX7BHHhhcC110Zv4+G47z5bnnpqze2uX5SbO9vxwAMWknr//drXevNNW3oTzj17mkAEtfZYs8ZCUe3a1dxeVGTiRIGIza5dwMMPB3++JOuhQJDk8QrEpElWxXTHHZGPv/hiOy4eBg8GliwBrr++9j5/qeuqVdYSAwD+8Y/ax7/1FjBgQE3PpUcPszdosN/q1TZ5kh8R8yJWrYrvd2jMPP+8fXfvvZdpS0gdoECQ5HECsWlT2Hs49tjUXX/AAAtJ+enVy57+Xanr889bGGrQIOC112pWGe3ZYzepM86oeQ0XBgsKM/nbkXthqWt8lJXZ0gk3aVBQIEjydOlioaVf/Sq295BKevUycVi71sTgueeA0aMtt1BebhVIjnfftbLY00+veQ0nAC7f4KiqsutGE4jPPrM5udNBVRWwYUN6rl2fOIFwvbdIbNautfxbkFdbz1AgSPJ07mwx5j/8IfXeQzS8pa5z55oXcNllwNixtt0bZnrrLev75K9IOuooCxn5BaKiwgQlKMQEhBPVkSqgkuW550ycNm1K/lpVVcD991tLlPpk377w5E/0IOJn6lTzdqdNy7QlFAiSAtxYiOrq+vMegJoC8dxzFoYaP96SyMOG1RSIN9+0pzJ/qKp5c5sYyR9icoIRzYMA0hdmWrLEvLF585K/1vvvA7fdZiG4+mTpUhOnkSPt8402IJGEmT/fllmQt6FAkORxAlGf3gNg5bWtWlnfphdfNHFwI57HjbN/tC++ANavB1asqJ1/cPTsWduDcO28I3kQxxxj+Y50CYRLvrubRTK48Rwffpj8tRLBhZeuvrrmOomOeyiYMyezdoACQVLB4MHANdeES1LrCxHzIl54Adi+3cJLjnHjbPnPf1p4Caidf3D06FFbINassTEexcXB5xQU2FwW6RIIV74bKXY/fTrw0kvxXcsJxNKlyduVCGVlJuLnnWffFcNMsdm82f72iottmeE8FAWCJE9BgVUvHXlk/b93r17A7t12I/IKwPHHm2fwj3+YQHTqFJ6Jzk/PnvaPuH9/eNvq1TYft2ssGES6KpmqqsKC9cEHwWMIbrrJnswPHYp9PScQy5bV7zzeZWXA0KHm1fXuTYGIB/dA8OMf27K0NHO2gAJBGjouDzFhQs2buYh5ETNn2sjuMWNqjsT24vIMa9eGt61ZEzm85HBjIVJ90123zm78JSXW88mfCK+oMGHavj12GOLAAROGoiJLGvsHFqaL3butimzoUFsfNswEgg0OozNvnv2dfv/7Np97hsNMFAjSsDnhBFt+5zu1940bZ+3Ct26NnH8AwvNie8NM0cZAOPr1M6/DH55KFncTv/RSW/rzELNm2VIE+Pvfo19r+XIrBXafT32FmZYsMc/HKxAbN1o+iERm/nzzdNu2tfYyGU5UUyBIw+aCC+wmOHhw7X0lJUD79vba217Dj3+w3I4dVhIay4OINH+2Y/nyurUjdwnqs8+28Iw/DzFzpjVCPPfc2gMC/bjw0qWXAnl59ScQCxfacsgQWw4bZsuGEmbatQsYMaJ+n+Crq+27PvFEWz/5ZPu+du6sPxt8UCBIwyYvD+jbN3hf06bAt79t8zl07Rr5Gp06Wfmr8wRilbg6+va1p3hX6+9n3Djg8sujXyOI8nKzp7jYbqxeD0LVBGL0aOD88y3c5G7GQSxebCLTp4+FxOpLIMrK7DN3n/uAAfZ9NJQBc2+/bZ/7lCn1956rVgFffWXCBJhAVFcH9xWrJygQJLd56CEbRR0NkZqVTG4Zy4No2dJEJEggtm61RPfs2YkPUCsvt/du0gQYPtxu6i6BvmKFhWrGjAHOOccEMlqYafFim52vSRO7SddXqatLUDsKCiwcmG4PQtU+rwceAE47zT6/f/878eu4OUhmz06tfdFwDwLOgxgxwr7fDOYhKBCEAOGurkB4DITLTUSjf//gENOiRbasqgL+9a/EbCkvD7cYP/FEyyG4UJG7cY0ZAxQWmnf02mvB16mqspvloEG2PmCAJcD9grVmjd1QU9VxdedOexr2CgRg3lBZWfo6uy5ebMn4gQOBn/3MBuZt3Wre1sSJiQ3Uc3meZcuCz1u0yDzE3btTYjoAE4g2bcKDMFu1su8ug3kICgQhQHiwnKotO3Swf9ZY9OtnOQNviSwQDvu0b29jMeKlutoEygnE8OG2dKGZmTNtX7dutj5+vHkVQS0/ysutSaFXIIDaXsR999kN9ckn47czGosX2+cYJBBffZW+Sqq//916gj31lCXDP/zQbvC33WZjZXr3tvlCYrFhg32mbixN0A36scesJcZzz6XO/vnz7TPyVtudcoptP3gwde+TABQIQgDzFnbtCoeGYoWXHP3725O6fzzEwoUmOuefbx5EvP/g69dbaaor3+3a1XIR8+db6es779RMuLubWJAX4bwYv0B48xAHDgCvvGKvf/Yzu8Emixsx7RLUjngS1W+/XfcnZlcBdMUV4dxHixYmgIsX2/dx6aWx27Q77+GWWyw05g8zVVcDr79urx9+ODWlu3v3mqC5/IPj5JPt4SNanimNY1soEIQANSuZ4ilxdbhKJn8eYuFCu0Gee66FXOKNZbsKJu8sdsOHmwfxwQcW0vAKxFFH2fsE5SEWLwaaNQsn8Tt1suonrwfxxhv2VP/b35q3cdNNNa+xc6fNDz56dPyNA8vKzK4jjqi5vW9fu2FHE4irrwauuiq+9/HirwDy06+fPfG3aAH88IfRb+qzZln4bvhwKzX157AWLrQWLqNHW6VaUI5r0SIT7XjDaQsX2o3eb7+bhz2aaF5ySfQy7iRIq0CIyFkiskpEykXkloD9o0RkkYhUisiFvn0TReST0M/EdNpJyH8FYdUqK02N14Po1QvIz6+Zh9i2zYRmyBC7mRcU2M0pHlz4xSsQJ55oXs2UKZZQP+20muecd54NsPK3ZVi82G6M+fm2LmJehNeDmDzZbobXXmtPzM8/H85zbNli7zVzpnXLHTYsviS3P0HtaNrUypEjCYQbFLhypeVKEuGTT6w8OZJAANZ1+Fe/sqR1pMaF3iqxJk0sx7NkiYmo45//tH3PPGMhxIcfrnmNzZttqtzx401knEcSDX+C2tGpk/U3i5aoLisLl3OnmLQJhIjkAXgEwDcA9AUwQUT89YifA7gcwAu+c9sDuAvAiQCGA7hLRHzzPhKSQlxC+t137UkuXg8iP99KSL0ehAvtDB5so2FPP90EIp5QRHl5uMOsw+UhnnzSbrz+KVDHj7elV4RUTSD840MGDDBbKyvNG5k6FbjoIvs9brvNhOmHPzRBOuUUe0J+7TV7gnWdWSMlxQG7SZeXBwsEYCKzaFFwixCXiAfC08PGS6QbrJ+rrrJjbrzRRqL7WbXKwnyjR9v6qFHmBcydGz5m6lR7si8uthHPr71WU9Cuv94+h1//2sRizBgTDP/86V7mzbPeXn6vC7AwU2lpsDeyZYt1APCH81JEOj2I4QDKVXWNqh4EMAXAOO8BqrpWVT8E4P/NzwTwlqpuU9XtAN4CcFYabSWNnZYt7Z/TNfaLVyAAe0qPJBCAzU/x2WeRB9R5KS+39/YmKocOtfX9+4MH/PXtaz+//KXdkAAbH7F1azj/4BgwwPIO//mP3ej27bM2JYB5On/8o93Ijj/ebpRvvGED9oYMsSf/vn1NkJ55Jth+V7HlQiN+TjrJfo+g8Rguzt62rbVHSYT588M9n6LRpIklmLdtA269tfZ+97TvPucRI0w8XRjp88/N9nPPtfVrrrEb9+OP2/orr1hn4bvuAn76UxOc3/zGBMDbTDLIfn/+wXHyyWZvUN8v95lFEuQkSadAFAHw+okVoW0pO1dErhKRMhEp2+z+MQipKz172o0ciD/EBFhi9PPPw2GIhQvtabCw0NbPOceW8YSZvCWujlatwnmEIIEQAZ591nIEEybULIsNEgjAQkWTJ9tTsHcSpTFjbHBfmzaWMD711PC+Ll3sRjliBHDnncHJ0aeeMm/MPzGTY+RIWwY1oVu40MpUx4+3ME8iydd588w7ycuLfezAgdYM7/HHaw9CmznT7HcPCIcdZtd1OSSXnHaTUnXvbmLxxBMmqD/8oT0Y/PSntr+gwPI6994bziP5KS83QY/k/TixjfSZAcGdBFJAg05Sq+oTqjpUVYd27Ngx0+aQho67KTRvHn3ktR+XqF6+3JYuQe3o3Nn++WOVu6oGCwRgN9bDDgvfYP0MGWJPxrNmWaho0SITDterytG7tz0Rv/22PaVffHHtJoZ//rOFTILCFi1aADffbPv9M56tXWvvf/nlkRsjFhdbAjvSzW7IEODMMy38E+/8Efv2meDFCi95+cUvrPvwxReHx79UVtrn4sJLjlGjzHvau9dEvlcv4Ljjwvuvu848t5NPNruffjqc93FMnGgejj9fAVgoqlkzC/UF0auXFRcEfWZlZbb/8MPj/90TIJ0CsR6At/9zcWhbus8lpG64PESPHpFvcEG4NuIffWSx59Wra99cx461p8do8wxv2GA3O1fi6uXeey0PUFAQ+fzLL7eQx6RJlq847jgLnXlp1sxyJk8/bXkAF17y0qSJiWQkxo41AX300Zrb//IXW06MUVNSUmI3O29OZtcuC3u5xL5I7TBTZaUl0r1zjQMmhpWViQlEq1Ym2Hv2AF//unmOixaZF+j30kaNsuu/9ZYJiPMeHKNH22e9di3w85/XFmXAxGHiRAs/eavB1q61cN2VV5r3FISIPRhEEog0hZcAAKqalh8ATQGsAdADQDMASwEcH+HYZwBc6FlvD+BTAO1CP58CaB/t/YYMGaKEJMWf/6wKqH7zm4mdV12t2qqV6nXXqc6aZdeYMaPmMR99ZNsnTFCdPVv10KHa13nnHTvmzTfr/jscOKB60knh9wri29+2/b16me114e677RqffGLrVVWq3bqpnn567HMfftjO/fTT8LZ337Vtr79u68OGqY4cWfO8xx+3Y847r+b2//s/2/7FF4n/HgsXqrZtq9qjh+o119h1Nm2qecxXX6k2aaJ6wgm2/513al9n2jTViRNVDx6M/F4rV9r5990X3nbllarNmqmuWxfdzgcesHM3bgxv+/JL2/ab38T8NaMBoEwj3ccj7UjFD4BvAvgPgNUAbg9tuwfA2NDrYbD8wh4AWwEs95z7XQDloZ8rYr0XBYIkzdtv27/Eddclfu6IEaqnnhr+R96ypeb+6mq7gTRtavvbt1e97DLViorwMU8+afvWrEnil1DV9etV+/RRfe654P2/+Y29z513JvceeXmqN91k6zNn2jUnT4597uLFdqzXvgcfrHmTv+MOu/727ba+e7dq5872+YmolpeHz/2f/1E96qi6/y4LFqgefri9/8CBwccMGWL727ULFvd4GTNGtbjYrrF2rf0+P/xh7PNKS+39X301vG369MiClQAZE4j6/KFAkKRZt87+JX7/+8TPvfJK1cJC1YsvtifpSOzYofq3v5lYtGhholJVZftuuUU1Pz+5G1A8LF2qeuSRNW+ydeHCC03o9u5V/da37El8377Y51VWmsd1zTXhbZdeqtq1a3h9zhz7Ll55xdbvucfW//Y3+4x+9KPwsd26qV50UXK/y7x5JhL/+7/B+3/yE3v/Sy9N7n3+8Q+7zssvq/7gB/a7fP557PP271dt3jwsyKr2mYiYh5MEFAhC4mXGDHtaTZTf/U7/6xmcf35857iQ1m9/a+sXXqh67LGJv3em+Pe/zf6HHlItKFC99tr4zx0zRnXAgPB6796qY8eG1w8eVG3dWvWqqyyU0qqV6vjxtu+yy2x9xw4LuaQgzKKqJm5OrP24G/uLLyb3HpWVJmgnnGDicPXV8Z9bUmKeqmPcONXjjkvOHo0uEA26iomQlHPGGbUTu/HgEtXbtsU/aOmKK6wE9tZbrcb9k0+CK5iyla99zaqibr7ZxjZccUX855aUWFJ/505LUK9aVfNzy8+35O+MGVZxtG8fcP/9tu8nP7FBfn/+c/wD5OKhoCByccI551g7kwsuSO498vKsFNaNSA8aixGJkhKr9Nq3z9bTnaBGAy9zJSRrcKWuQPwCIQL86U8mSN/5jpW4BlUwZSsidrM7dMgqdxKpxS8psQFm8+ZZKwvV2p/bmWdaddEf/2gjoF1p6eDBVln0+9/bCOe8vLSNA/gvTZpYS5N4xlnE4nvfsyqq73/fSn7jpaTEPuuyMquGW7+eAkFIg6BjR+ubAyR2s+rc2W6ACxZYyWVD8iAAE7aiIuCGG0ww4mXECLvplpbWnp7UceaZtjzsMBuZ7OWGG0w8Hn3UxOmww+r6G9Q/hYVWqvvQQ4md5x1kGOkzSzFN03p1QhoT/fvb+IFEB21edJGNR5g8ueEJxOGH2yjgRGnd2m7spaU2QrtrVxNLLz162Kjq004Li69j7NjwHB6pCC/VN95eW/HSoYN5UaWl1i5FpPZI+RRDgSAkVTz4YN0nmHdPwl//emptymZKSmyQWFFR5CfhV18N3p6XB/zoR+ZJNESBqCslJeE24n36WKgqjTDEREiq6N8/cpO6WLRta6OEo41gzjVGjrSwmhtBnShXXWUNCi+8MPaxuUJJiRVCzJyZ9vASQA+CEJIpvGJal5tdixaJVQHlAu4zO3gw7QlqgB4EISRTHHVUuP9QPTwN5wTHHmu5CKBePjMKBCEkM4hYzqVbN0tUk9i4xn1Nmljb8jTDEBMhJHP87nc1p/MksfnZz6yyqy4DOhOEAkEIyRzt26dtPuWcZeTIyPOCpBiGmAghhARCgSCEEBIIBYIQQkggFAhCCCGBUCAIIYQEQoEghBASCAWCEEJIIBQIQgghgYhNSdrwEZHNAD5L4JQOALakyZxkyFa7gOy1LVvtArLXtmy1C6BtdSEZu7qpauAkJjkjEIkiImWqmv52iAmSrXYB2WtbttoFZK9t2WoXQNvqQrrsYoiJEEJIIBQIQgghgTRmgXgi0wZEIFvtArLXtmy1C8he27LVLoC21YW02NVocxCEEEKi05g9CEIIIVGgQBBCCAmk0QmEiJwlIqtEpFxEbsmwLU+JyCYRWebZ1l5E3hKRT0LLdhmw60gReVtEVojIchH5cRbZViAiH4jI0pBtvwht7yEi80Pf64si0qy+bQvZkScii0Xk9Syza62IfCQiS0SkLLQtG77PtiLysoh8LCIrReSkLLHruNBn5X52isgNWWLbT0J/+8tEZHLofyItf2eNSiBEJA/AIwC+AaAvgAki0jeDJj0D4CzftlsAzFLVXgBmhdbrm0oAN6lqXwAjAFwb+pyywbYDAE5T1QEABgI4S0RGAPg1gN+q6jEAtgP4XgZsA4AfA1jpWc8WuwDg66o60FMvnw3f5+8AvKGqvQEMgH12GbdLVVeFPquBAIYA2Avg75m2TUSKAPwIwFBV7QcgD8AlSNffmao2mh8AJwGY4Vm/FcCtGbapO4BlnvVVALqEXncBsCoLPrd/ADg922wDcBiARQBOhI0ibRr0PdejPcWwm8ZpAF4HINlgV+i91wLo4NuW0e8TwOEAPkWoWCZb7Aqw8wwApdlgG4AiAOsAtIdNGf06gDPT9XfWqDwIhD9cR0VoWzbRSVW/CL3eCKBTJo0Rke4ABgGYjyyxLRTGWQJgE4C3AKwGsENVK0OHZOp7fQjATwFUh9YLs8QuAFAAb4rIQhG5KrQt099nDwCbATwdCss9KSIts8AuP5cAmBx6nVHbVHU9gN8A+BzAFwC+ArAQafo7a2wC0aBQexzIWB2yiLQC8AqAG1R1p3dfJm1T1So1178YwHAAvTNhhxcROQfAJlVdmGlbInCyqg6GhVevFZFR3p0Z+j6bAhgM4I+qOgjAHvhCNlnwP9AMwFgAf/Pvy4RtoZzHOJi4dgXQErXD1CmjsQnEegBHetaLQ9uyiS9FpAsAhJabMmGEiOTDxOF5VX01m2xzqOoOAG/DXOq2ItI0tCsT32sJgLEishbAFFiY6XdZYBeA/z55QlU3wWLpw5H577MCQIWqzg+tvwwTjEzb5eUbABap6peh9UzbNgbAp6q6WVUPAXgV9reXlr+zxiYQCwD0CmX8m8Fcx6kZtsnPVAATQ68nwuL/9YqICIA/A1ipqg9mmW0dRaRt6HULWG5kJUwoLsyUbap6q6oWq2p32N/Vv1X10kzbBQAi0lJEWrvXsJj6MmT4+1TVjQDWichxoU2jAazItF0+JiAcXgIyb9vnAEaIyGGh/1P3maXn7yyTyZ9M/AD4JoD/wOLWt2fYlsmwOOIh2NPU92Bx61kAPgEwE0D7DNh1Msx1/hDAktDPN7PEthMALA7ZtgzAnaHtPQF8AKAcFg5onsHv9WsAXs8Wu0I2LA39LHd/91nyfQ4EUBb6Pl8D0C4b7ArZ1hLAVgCHe7Zl3DYAvwDwcejv/68Amqfr74ytNgghhATS2EJMhBBC4oQCQQghJBAKBCGEkEAoEIQQQgKhQBBCCAmEAkFIACKyO7TsLiLfSvG1b/Otz03l9QlJFRQIQqLTHUBCAuEZ0RqJGgKhqiMTtImQeoECQUh0fgXglNCcAD8JNQqcJCILRORDEfkBAIjI10RkjohMhY1shYi8FmqOt9w1yBORXwFoEbre86FtzluR0LWXheZuuNhz7Xc88yY8HxpFS0haifWkQ0hj5xYA/09VzwGA0I3+K1UdJiLNAZSKyJuhYwcD6Keqn4bWv6uq20ItQRaIyCuqeouIXKfWbNDP+bCRxQMAdAidMzu0bxCA4wFsAFAK67/zXqp/WUK80IMgJDHOAPCdULvx+bDWC71C+z7wiAMA/EhElgKYB2sS2QvRORnAZLVutV8CeBfAMM+1K1S1Gtb6pHsKfhdCokIPgpDEEADXq+qMGhtFvgZrV+1dHwPgJFXdKyLvAChI4n0PeF5Xgf+7pB6gB0FIdHYBaO1ZnwHgmlA7dIjIsaEOqX4OB7A9JA69YVO3Og65833MAXBxKM/REcAoWAM2QjICn0IIic6HAKpCoaJnYHM8dAewKJQo3gzgvIDz3gBwtYishE1TOc+z7wkAH4rIIrWW4I6/w+a2WArrpvtTVd0YEhhC6h12cyWEEBIIQ0yEEEICoUAQQggJhAJBCCEkEAoEIYSQQCgQhBBCAqFAEEIICYQCQQghJJD/D+TQ75YhpiXQAAAAAElFTkSuQmCC" 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" + }, + "metadata": { + "needs_background": "light" + } + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "我们可以看到在几十个 iteration 之后，损失函数的值只在一个较小的范围内波动，说明训练过程已经达到了稳定。" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "接着我们再对该模型的初始参数进行随机采样 300 次，这里我们首先选择 ``max`` 模式，看看 300 次采样中每次采样中最大梯度的平均值和方差" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 19, + "source": [ + "mean, variance = random_sample_supervised(circuit,loss_func, N=qubit_num, sample_num=SAMPLE, BATCH=BATCH, TRAIN_X=train_x, TRAIN_Y=train_y, mode='max')" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + "Sampling: 100%|###################################################| 300/300 [00:21<00:00, 13.65it/s]\n" + ] + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Mean of max gradient\n", + "0.19336918419398885\n", + "Variance of max gradient\n", + "0.011469917351120164\n" + ] + }, + { + "output_type": 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+ }, + "metadata": { + "needs_background": "light" + } + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "## 总结\n", + "\n", + "可训练性问题是目前量子神经网络的研究的一个核心方向，量桨提供的梯度分析工具支持用户对模型进行可训练性的诊断，便于贫瘠高原等问题的研究。\n" + ], + "metadata": {} }, { "cell_type": "markdown", - "metadata": {}, "source": [ "_______\n", "\n", @@ -574,15 +1195,17 @@ "\n", "[1] McClean, J. R., Boixo, S., Smelyanskiy, V. N., Babbush, R. & Neven, H. Barren plateaus in quantum neural network training landscapes. [Nat. Commun. 9, 4812 (2018).](https://www.nature.com/articles/s41467-018-07090-4)\n", "\n", - "[2] Cerezo, M., Sone, A., Volkoff, T., Cincio, L. & Coles, P. J. Cost-Function-Dependent Barren Plateaus in Shallow Quantum Neural Networks. [arXiv:2001.00550 (2020).](https://arxiv.org/abs/2001.00550)" - ] + "[2] Cerezo, M., Sone, A., Volkoff, T., Cincio, L. & Coles, P. J. Cost-Function-Dependent Barren Plateaus in Shallow Quantum Neural Networks. [arXiv:2001.00550 (2020).](https://arxiv.org/abs/2001.00550)\n", + "\n", + "[3] Kieferova, Maria, Ortiz Marrero Carlos, and Nathan Wiebe. \"Quantum Generative Training Using R\\'enyi Divergences.\" arXiv preprint [arXiv:2106.09567 (2021).](https://arxiv.org/abs/2106.09567)" + ], + "metadata": {} } ], "metadata": { "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" + "name": "python3", + "display_name": "Python 3.7.11 64-bit ('pq_env': conda)" }, "language_info": { "codemirror_mode": { @@ -594,7 +1217,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.10" + "version": "3.7.11" }, "toc": { "base_numbering": 1, @@ -637,8 +1260,11 @@ "_Feature" ], "window_display": false + }, + "interpreter": { + "hash": "3b61f83e8397e1c9fcea57a3d9915794102e67724879b24295f8014f41a14d85" } }, "nbformat": 4, "nbformat_minor": 4 -} +} \ No newline at end of file diff --git a/tutorial/qnn_research/BarrenPlateaus_EN.ipynb b/tutorial/qnn_research/BarrenPlateaus_EN.ipynb index 2067f71..36483a6 100644 --- a/tutorial/qnn_research/BarrenPlateaus_EN.ipynb +++ b/tutorial/qnn_research/BarrenPlateaus_EN.ipynb @@ -2,79 +2,83 @@ "cells": [ { "cell_type": "markdown", - "metadata": {}, "source": [ "# Barren Plateaus\n", "\n", " Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. " - ] + ], + "metadata": {} }, { "cell_type": "markdown", - "metadata": {}, "source": [ "## Overview\n", "\n", - "In the training of classical neural networks, gradient-based optimization methods encounter the problem of local minimum and saddle points. Correspondingly, the Barren plateau phenomenon could potentially block us from efficiently training quantum neural networks. This peculiar phenomenon was first discovered by McClean et al. in 2018 [[arXiv:1803.11173]](https://arxiv.org/abs/1803.11173). In few words, when we randomly initialize the parameters in random circuit structure meets a certain degree of complexity, the optimization landscape will become very flat, which makes it difficult for the optimization method based on gradient descent to find the global minimum. For most variational quantum algorithms (VQE, etc.), this phenomenon means that when the number of qubits increases, randomly choose a circuit ansatz and randomly initialize the parameters of it may not be a good idea. This will make the optimization landscape corresponding to the loss function into a huge plateau, which makes the quantum neural network's training much more difficult. The initial random value for the optimization process is very likely to stay inside this plateau, and the convergence time of gradient descent will be prolonged.\n", + "In the training of classical neural networks, gradient-based optimization methods encounter the problem of local minimum and saddle points. Correspondingly, the Barren plateau phenomenon could potentially block us from efficiently training quantum neural networks. This peculiar phenomenon was first discovered by McClean et al. in 2018 [[1]](https://arxiv.org/abs/1803.11173). In a few words, when we randomly initialize the parameters in random circuit structure meets a certain degree of complexity, the optimization landscape will become very flat, which makes it difficult for the optimization method based on gradient descent to find the global minimum. For most variational quantum algorithms (VQE, etc.), this phenomenon means that when the number of qubits increases, randomly choosing a circuit ansatz and randomly initializing the parameters of it may not be a good idea. This will make the optimization landscape corresponding to the loss function into a huge plateau, which makes the training of QNN much more difficult. The initial random value for the optimization process is very likely to stay inside this plateau, and the convergence time of gradient descent will be prolonged.\n", "\n", "![BP-fig-barren](./figures/BP-fig-barren.png)\n", "\n", "The figure is generated through [Gradient Descent Viz](https://github.com/lilipads/gradient_descent_viz)\n", "\n", - "This tutorial mainly discusses how to show the barren plateau phenomenon with Paddle Quantum. Although it does not involve any algorithm innovation, it can improve readers' understanding about gradient-based training for quantum neural network. We first introduce the necessary libraries and packages:" - ] + "Based on the impact of gradient variation on the training of such variational quantum algorithms, we provide a gradient analysis tool module in the Paddle Quantum to assist users in diagnosing models and facilitate the study of problems such as barren plateaus.\n", + "\n", + "This tutorial mainly discusses how to demonstrate the barren plateau phenomenon with Paddle Quantum and use the gradient analysis tool to analyze the parameter gradients in user-defined quantum neural networks. Although it does not involve any algorithmic innovation, it can help readers to understand the gradient-based training for QNN.\n", + "\n", + "We first import the necessary libraries and packages:\n" + ], + "metadata": {} }, { "cell_type": "code", - "execution_count": 1, - "metadata": { - "ExecuteTime": { - "end_time": "2021-03-02T12:13:41.746113Z", - "start_time": "2021-03-02T12:13:39.017668Z" - } - }, - "outputs": [], + "execution_count": 2, "source": [ + "# Import packages needed\n", "import time\n", "import numpy as np\n", - "from matplotlib import pyplot as plt \n", + "import random\n", "import paddle\n", + "# Import related modules from Paddle Quantum and PaddlePaddle\n", "from paddle import matmul\n", "from paddle_quantum.circuit import UAnsatz\n", "from paddle_quantum.utils import dagger\n", - "from paddle_quantum.state import density_op" - ] + "from paddle_quantum.state import density_op\n", + "# Drawing tools\n", + "from matplotlib import pyplot as plt \n", + "# ignore waring \n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\")" + ], + "outputs": [], + "metadata": { + "ExecuteTime": { + "end_time": "2021-03-02T12:20:39.463025Z", + "start_time": "2021-03-02T12:20:36.336398Z" + } + } }, { "cell_type": "markdown", - "metadata": {}, "source": [ "## Random network structure\n", "\n", - "Here we follow the original method mentioned in the paper by McClean (2018) and build the following random circuit (currently we do not support the built-in control-Z gate, use CNOT instead):\n", + "Here we follow the original method mentioned in the paper by McClean (2018) [[1]](https://arxiv.org/abs/1803.11173) and build the following random circuit:\n", "\n", "![BP-fig-Barren_circuit](./figures/BP-fig-Barren_circuit.png)\n", "\n", "First, we rotate all the qubits around the $y$-axis of the Bloch sphere with rotation gates $R_y(\\pi/4)$.\n", "\n", - "The remaining structure forms a block, each block can be further divided into two layers:\n", + "The remaining structure is in form of blocks, each block can be further divided into two layers:\n", "\n", - "- Build a layer of random rotation gates on all the qubits, where $R_{\\ell,n} \\in \\{R_x, R_y, R_z\\}$. The subscript $\\ell$ means the gate is in the $\\ell$-th repeated block. In the figure above, $\\ell =1$. The second subscript $n$ indicates which qubit it acts on.\n", - "- The second layer is composed of CNOT gates, which act on adjacent qubits.\n", + "- The first layer is a set of random rotation gates on all the qubits, where $R_{\\ell,n} \\in \\{R_x, R_y, R_z\\}$. The subscript $\\ell$ means the gate is in the $\\ell$-th repeated block. In the figure above, $\\ell =1$. The second subscript $n$ indicates which qubit it acts on.\n", + "- The second layer is composed of CZ gates, which act on adjacent qubits.\n", "\n", "In Paddle Quantum, we can build this circuit with the following code:" - ] + ], + "metadata": {} }, { "cell_type": "code", - "execution_count": 2, - "metadata": { - "ExecuteTime": { - "end_time": "2021-03-02T12:13:41.776722Z", - "start_time": "2021-03-02T12:13:41.749182Z" - } - }, - "outputs": [], + "execution_count": 3, "source": [ "def rand_circuit(theta, target, num_qubits):\n", "\n", @@ -100,27 +104,33 @@ " cir.rx(theta[i], i)\n", " \n", " # ============== Third layer ==============\n", - " # Build adjacent CNOT gates\n", + " # Build adjacent CZ gates\n", " for i in range(num_qubits - 1):\n", - " cir.cnot([i, i + 1])\n", + " cir.cz([i, i + 1])\n", " \n", - " return cir.U" - ] + " return cir" + ], + "outputs": [], + "metadata": { + "ExecuteTime": { + "end_time": "2021-03-02T12:20:39.972053Z", + "start_time": "2021-03-02T12:20:39.962259Z" + } + } }, { "cell_type": "markdown", - "metadata": {}, "source": [ "## Loss function and optimization landscape\n", "\n", - "After determining the circuit structure, we also need to define a loss function to determine the optimization landscape. Following the same set up with McClean (2018), we take the loss function from VQE:\n", + "After determining the circuit structure, we also need to define a loss function to determine the optimization landscape. Following the same set up with McClean (2018)[[1]](https://arxiv.org/abs/1803.11173), we take the loss function from VQE:\n", "\n", "$$\n", "\\mathcal{L}(\\boldsymbol{\\theta})= \\langle0| U^{\\dagger}(\\boldsymbol{\\theta})H U(\\boldsymbol{\\theta}) |0\\rangle,\n", "\\tag{1}\n", "$$\n", "\n", - "The unitary matrix $U(\\boldsymbol{\\theta})$ is the quantum neural network with the random structure we built from the last section. For Hamiltonian $H$, we also take the simplest form $H = |00\\cdots 0\\rangle\\langle00\\cdots 0|$. After that, we can start sampling gradients with the two-qubit case - generate 300 sets of random network structures and different random initial parameters $\\{\\theta_{\\ell,n}^{( i)}\\}_{i=1}^{300}$. Each time the partial derivative with respect to the **first parameter $\\theta_{1,1}$** is calculated according to the analytical gradient formula from VQE. Then analyze the mean and variance of these 300 sampled partial gradients. The formula for the analytical gradient is:\n", + "The unitary matrix $U(\\boldsymbol{\\theta})$ is the quantum neural network with the random structure that we build from the last section. For the Hamiltonian $H$, we also take the simplest form $H = |00\\cdots 0\\rangle\\langle00\\cdots 0|$. After that, we can start sampling gradients with the two-qubit case - generate 300 sets of random network structures and different random initial parameters $\\{\\theta_{\\ell,n}^{( i)}\\}_{i=1}^{300}$. Each time the partial derivative with respect to the **first parameter $\\theta_{1,1}$** is calculated according to the analytical gradient formula from VQE. Then we analyze the mean and variance of these 300 sampled partial gradients. The formula for the analytical gradient is:\n", "\n", "$$\n", "\\partial \\theta_{j} \n", @@ -129,29 +139,13 @@ "\\tag{2}\n", "$$\n", "\n", - "For a detailed derivation, see [arXiv:1803.00745](https://arxiv.org/abs/1803.00745)." - ] + "For a detailed derivation, see [arXiv:1803.00745](https://arxiv.org/abs/1803.00745).\n" + ], + "metadata": {} }, { "cell_type": "code", - "execution_count": 3, - "metadata": { - "ExecuteTime": { - "end_time": "2021-03-02T12:13:50.788968Z", - "start_time": "2021-03-02T12:13:41.786234Z" - } - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The main program segment has run in total 5.674382448196411 seconds\n", - "Use 300 samples to get the mean value of the gradient of the random network's first parameter, and we have： 0.005925709445960606\n", - "Use 300 samples to get the variance of the gradient of the random network's first parameter, and we have： 0.028249053148446363\n" - ] - } - ], + "execution_count": 4, "source": [ "# Hyper parameter settings\n", "np.random.seed(42) # Fixed Numpy random seed\n", @@ -196,11 +190,11 @@ " # Generate random targets, randomly select circuit gates in rand_circuit\n", " target = np.random.choice(3, N) \n", " \n", - " U = rand_circuit(theta, target, N)\n", + " U = rand_circuit(theta, target, N).U\n", " U_dagger = dagger(U) \n", - " U_plus = rand_circuit(theta_plus, target, N)\n", + " U_plus = rand_circuit(theta_plus, target, N).U\n", " U_plus_dagger = dagger(U_plus) \n", - " U_minus = rand_circuit(theta_minus, target, N)\n", + " U_minus = rand_circuit(theta_minus, target, N).U\n", " U_minus_dagger = dagger(U_minus) \n", "\n", " # Calculate the analytical gradient\n", @@ -234,11 +228,27 @@ "print('The main program segment has run in total ', time_span, ' seconds')\n", "print(\"Use \", samples, \" samples to get the mean value of the gradient of the random network's first parameter, and we have：\", np.mean(grad_info))\n", "print(\"Use \", samples, \"samples to get the variance of the gradient of the random network's first parameter, and we have：\", np.var(grad_info))" - ] + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "The main program segment has run in total 11.881862878799438 seconds\n", + "Use 300 samples to get the mean value of the gradient of the random network's first parameter, and we have： 0.005925709445960606\n", + "Use 300 samples to get the variance of the gradient of the random network's first parameter, and we have： 0.028249053148446363\n" + ] + } + ], + "metadata": { + "ExecuteTime": { + "end_time": "2021-03-02T12:20:52.236108Z", + "start_time": "2021-03-02T12:20:40.850822Z" + } + } }, { "cell_type": "markdown", - "metadata": {}, "source": [ "## Visualization of the Optimization landscape\n", "\n", @@ -247,38 +257,12 @@ "![BP-fig-landscape2](./figures/BP-fig-landscape2.png)\n", "\n", "The plain structure shown in the $R_z$-$R_z$ layer from the last figure is something we should avoid. In this case, it's nearly impossible to converge to the theoretical minimum. If you want to try to draw some optimization landscapes yourself, please refer to the following code:" - ] + ], + "metadata": {} }, { "cell_type": "code", - "execution_count": 4, - "metadata": { - "ExecuteTime": { - "end_time": "2021-03-02T12:14:18.147473Z", - "start_time": "2021-03-02T12:14:14.551262Z" - } - }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
    " - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The main program segment has run in total 1.9106006622314453 seconds\n" - ] - } - ], + "execution_count": 5, "source": [ "# Introduce the necessary packages\n", "from matplotlib import cm\n", @@ -315,8 +299,8 @@ " [0, np.exp(1j * theta/2)]])\n", " return mat\n", "\n", - "def CNOT():\n", - " mat = np.array([[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]])\n", + "def CZ():\n", + " mat = np.array([[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,-1]])\n", " return mat\n", "\n", "# ============= The first figure =============\n", @@ -327,7 +311,7 @@ "def cost_yy(para):\n", " L1 = np.kron(ry(np.pi/4), ry(np.pi/4))\n", " L2 = np.kron(ry(para[0]), ry(para[1]))\n", - " U = np.matmul(np.matmul(L1, L2), CNOT())\n", + " U = np.matmul(np.matmul(L1, L2), CZ())\n", " H = np.zeros((2 ** N, 2 ** N))\n", " H[0, 0] = 1\n", " val = (U.conj().T @ H@ U).real[0][0]\n", @@ -348,7 +332,7 @@ "def cost_xz(para):\n", " L1 = np.kron(ry(np.pi/4), ry(np.pi/4))\n", " L2 = np.kron(rx(para[0]), rz(para[1]))\n", - " U = np.matmul(np.matmul(L1, L2), CNOT())\n", + " U = np.matmul(np.matmul(L1, L2), CZ())\n", " H = np.zeros((2 ** N, 2 ** N))\n", " H[0, 0] = 1\n", " val = (U.conj().T @ H @ U).real[0][0]\n", @@ -365,207 +349,847 @@ "\n", "time_span = time.time() - time_start \n", "print('The main program segment has run in total ', time_span, ' seconds')" - ] + ], + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
    " + ], + "image/png": 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" + }, + "metadata": { + "needs_background": "light" + } + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "The main program segment has run in total 3.772348165512085 seconds\n" + ] + } + ], + "metadata": { + "ExecuteTime": { + "end_time": "2021-03-02T12:21:49.972769Z", + "start_time": "2021-03-02T12:21:45.792119Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "## Gradient Analysis Tool\n", + "\n", + "Based on an important role that gradients play in phenomena such as barren plateaus, we developed a simple gradient analysis tool in Paddle Quantum to assist users in viewing gradients of each parameter in the circuit. This tool can be used to facilitate subsequent research on quantum neural networks.\n", + "\n", + "Note that the users only need to define the **circuit** and **loss function** separately when using the gradient analysis tool, and there is no need to write their networks.\n" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### Application I: Unsupervised Learning\n", + "\n", + "For this case, we focus on variational quantum algorithms similar to the Variational Quantum Eigensolver (VQE). Suppose the objective function is the typical parameterized cost function used in VQA: $O(\\theta) = \\left\\langle0\\dots 0\\right\\lvert U^{\\dagger}(\\theta)HU(\\theta) \\left\\lvert0\\dots 0\\right\\rangle$，where $U(\\theta)$ is a parameterized quantum circuit, $H$ is a Hamiltonian and $\\theta = [\\theta_1, \\theta_2, \\dots, \\theta_n]$ is a list of trainable parameters in the circuit.\n", + "\n", + "Here we use VQE to demonstrate the usage of this gradient analysis tool.\n", + "\n" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "#### Paddle Quantum Implement\n", + "\n", + "Firstly, import the packages needed for the problem." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 2, + "source": [ + "# Import related modules from Paddle Quantum and PaddlePaddle\n", + "from paddle_quantum.circuit import UAnsatz\n", + "from paddle_quantum.utils import pauli_str_to_matrix, random_pauli_str_generator\n", + "# GradTool package\n", + "from paddle_quantum.gradtool import random_sample, show_gradient, plot_distribution, plot_loss_grad" + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "#### Define Quantum Circuits\n", + "\n", + "Next, construct the parameterized quantum circuit $U(\\theta)$ in the objective function. Here we still use the random circuit defined above." + ], + "metadata": {} }, { "cell_type": "markdown", - "metadata": {}, "source": [ - "## More qubits\n", + "#### Define Objective Function\n", "\n", - "Then, we will see what happens to the sampled gradients when we increase the number of qubits" - ] + "Note here that in the gradient analysis module we call the function in the form of ``loss_func(circuit, *args)`` to calculate the objective function value. This means that the second argument is a variable argument, and the user is able to construct their own objective function form as needed." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 4, + "source": [ + "# objective function\n", + "def loss_func(circuit, H_l):\n", + " circuit.run_state_vector()\n", + " return (circuit.expecval(H_l))" + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Then set some parameters required for the application." + ], + "metadata": {} }, { "cell_type": "code", "execution_count": 5, - "metadata": { - "ExecuteTime": { - "end_time": "2021-03-02T12:18:13.493641Z", - "start_time": "2021-03-02T12:15:55.484851Z" - } - }, + "source": [ + "# Hyper parameter settings\n", + "np.random.seed(42) # Fixed Numpy random seed\n", + "N = 2 # Set the number of qubits\n", + "samples = 300 # Set the number of sampled random network structures\n", + "THETA_SIZE = N # Set the size of the parameter theta\n", + "ITR = 120 # Set the number of iterations\n", + "LR = 0.1 # Set the learning rate\n", + "SEED = 1 # Fixed the randomly initialized seed in the optimizer" + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Randomly generate quantum circuits and a list of Hamiltonian information." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 6, + "source": [ + "paddle.seed(SEED)\n", + "target = np.random.choice(3, N)\n", + "# Random generate parameters between 0 and 2*Pi \n", + "theta = np.random.uniform(low=0., high= 2 * np.pi, size=(THETA_SIZE))\n", + "theta = paddle.to_tensor(theta, stop_gradient=False, dtype='float64')\n", + "cir = rand_circuit(theta, target, N)\n", + "print(cir)\n", + "# Random generate Hamiltonian information, in Pauli string format\n", + "H_l = random_pauli_str_generator(N, terms=7)\n", + "print('Hamiltonian info: ', H_l)" + ], "outputs": [ { - "name": "stdout", "output_type": "stream", + "name": "stdout", "text": [ - "The main program segment has run in total 90.05470848083496 seconds\n" + "--Ry(0.785)----Rx(1.153)----*--\n", + " | \n", + "--Ry(0.785)----Rz(4.899)----z--\n", + " \n", + "Hamiltonian info: [[0.7323522915498704, 'z0'], [-0.8871768419457995, 'y0'], [-0.9984424683179713, 'x0,x1'], [0.22330632097656178, 'x0'], [-0.9538751499171685, 'z1'], [-0.20027805656948905, 'z0'], [-0.8187871309343584, 'y1']]\n" ] } ], + "metadata": {} + }, + { + "cell_type": "markdown", "source": [ - "# Hyper parameter settings\n", - "selected_qubit = [2, 4, 6, 8]\n", - "samples = 300\n", - "grad_val = []\n", - "means, variances = [], []\n", - "\n", - "# Record operation time\n", - "time_start = time.time()\n", - "\n", - "# Keep increasing the number of qubits\n", - "for N in selected_qubit:\n", - " grad_info = []\n", - " THETA_SIZE = N\n", - " for i in range(samples):\n", - " class manual_gradient(paddle.nn.Layer):\n", - " \n", - " # Initialize a list of learnable parameters of length THETA_SIZE\n", - " def __init__(self, shape, param_attr=paddle.nn.initializer.Uniform(low=0.0, high=2 * np.pi),dtype='float64'):\n", - " super(manual_gradient, self).__init__()\n", - "\n", - " # Convert to Tensor in PaddlePaddle\n", - " self.H = paddle.to_tensor(density_op(N))\n", - "\n", - " # Define loss function and forward propagation mechanism \n", - " def forward(self):\n", - "\n", - " \n", - " # Initialize three theta parameter lists\n", - " theta_np = np.random.uniform(low=0., high= 2 * np.pi, size=(THETA_SIZE))\n", - " theta_plus_np = np.copy(theta_np) \n", - " theta_minus_np = np.copy(theta_np) \n", - "\n", - " \n", - " # Modify to calculate analytical gradient\n", - " theta_plus_np[0] += np.pi/2\n", - " theta_minus_np[0] -= np.pi/2\n", - "\n", - " # Convert to Tensor in PaddlePaddle\n", - " theta = paddle.to_tensor(theta_np)\n", - " theta_plus = paddle.to_tensor(theta_plus_np)\n", - " theta_minus = paddle.to_tensor(theta_minus_np)\n", - "\n", - " # Generate random targets, randomly select circuit gates in rand_circuit\n", - " target = np.random.choice(3, N) \n", - " \n", - " U = rand_circuit(theta, target, N)\n", - " U_dagger = dagger(U) \n", - " U_plus = rand_circuit(theta_plus, target, N)\n", - " U_plus_dagger = dagger(U_plus) \n", - " U_minus = rand_circuit(theta_minus, target, N)\n", - " U_minus_dagger = dagger(U_minus) \n", - "\n", - " \n", - " # Calculate analytical gradient\n", - " grad = (paddle.real(matmul(matmul(U_plus_dagger, self.H), U_plus))[0][0] \n", - " - paddle.real(matmul(matmul(U_minus_dagger, self.H), U_minus))[0][0])/2\n", - " \n", - " return grad \n", - " \n", - " \n", - " # Define the main program segment \n", - " def main():\n", - " \n", - " # Set the dimension of QNN\n", - " sampling = manual_gradient(shape=[THETA_SIZE])\n", - " \n", - " # Sampling to obtain gradient information\n", - " grad = sampling()\n", - " \n", - " return grad.numpy()\n", - " \n", - " if __name__ == '__main__':\n", - " grad = main()\n", - " grad_info.append(grad)\n", - " \n", - " # Record sampling information\n", - " grad_val.append(grad_info) \n", - " means.append(np.mean(grad_info))\n", - " variances.append(np.var(grad_info))\n", + "``cir`` and ``H_l`` are the parameters needed for the objective function ``loss_func``." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Using the gradient analysis tool, we can get the results of the gradient sampling of each parameter in the circuit. There are three modes ``single``, ``max``, and ``random`` for users to choose, where ``single`` returns the mean and variance of each parameter after sampling the circuit multiple times, ``max`` mode returns the mean and variance of the maximum value of all parameter gradients in each round, and ``random`` calculates the mean and variance of random value of all parameter gradients in each round.\n", "\n", - "time_span = time.time() - time_start\n", - "print('The main program segment has run in total ', time_span, ' seconds')" - ] + "We sample the circuit 300 times, and here we choose the ``single`` mode to see the mean and variance of the gradient of each variable parameter in the circuit, while the default ``param=0`` means plot gradient distribution of the first parameter.\n", + "\n" + ], + "metadata": {} }, { "cell_type": "code", - "execution_count": 6, - "metadata": { - "ExecuteTime": { - "end_time": "2021-03-02T12:19:16.260635Z", - "start_time": "2021-03-02T12:19:15.034594Z" - } - }, + "execution_count": 27, + "source": [ + "grad_mean_list, grad_variance_list = random_sample(cir, loss_func, samples, H_l, mode='single', param=0) " + ], "outputs": [ { - "name": "stdout", "output_type": "stream", + "name": "stderr", "text": [ - "We then draw the statistical results of this sampled gradient:\n" + "Sampling: 100%|###################################################| 300/300 [00:14<00:00, 21.14it/s]\n" + ] + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Mean of gradient for all parameters: \n", + "theta 1 : -0.03157116754124028\n", + "theta 2 : -0.004525341240963983\n", + "Variance of gradient for all parameters: \n", + "theta 1 : 0.07237471326311368\n", + "theta 2 : 0.027855249806997346\n" ] }, { + "output_type": "display_data", "data": { - "image/png": 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\n", 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" }, "metadata": { "needs_background": "light" - }, - "output_type": "display_data" + } } ], - "source": [ - "grad = np.array(grad_val)\n", - "means = np.array(means)\n", - "variances = np.array(variances)\n", - "n = np.array(selected_qubit)\n", - "print(\"We then draw the statistical results of this sampled gradient:\")\n", - "fig = plt.figure(figsize=plt.figaspect(0.3))\n", - "\n", - "\n", - "# ============= The first figure =============\n", - "# Calculate the relationship between the average gradient of random sampling and the number of qubits\n", - "plt.subplot(1, 2, 1)\n", - "plt.plot(n, means, \"o-.\")\n", - "plt.xlabel(r\"Qubit #\")\n", - "plt.ylabel(r\"$ \\partial \\theta_{i} \\langle 0|H |0\\rangle$ Mean\")\n", - "plt.title(\"Mean of {} sampled gradient\".format(samples))\n", - "plt.xlim([1,9])\n", - "plt.ylim([-0.06, 0.06])\n", - "plt.grid()\n", - "\n", - "# ============= The second figure =============\n", - "# Calculate the relationship between the variance of the randomly sampled gradient and the number of qubits\n", - "plt.subplot(1, 2, 2)\n", - "plt.semilogy(n, variances, \"v\")\n", - "\n", - "# Polynomial fitting\n", - "fit = np.polyfit(n, np.log(variances), 1)\n", - "slope = fit[0] \n", - "intercept = fit[1] \n", - "plt.semilogy(n, np.exp(n * slope + intercept), \"r--\", label=\"Slope {:03.4f}\".format(slope))\n", - "plt.xlabel(r\"Qubit #\")\n", - "plt.ylabel(r\"$ \\partial \\theta_{i} \\langle 0|H |0\\rangle$ Variance\")\n", - "plt.title(\"Variance of {} sampled gradient\".format(samples))\n", - "plt.legend()\n", - "plt.xlim([1,9])\n", - "plt.ylim([0.0001, 0.1])\n", - "plt.grid()\n", - "\n", - "plt.show()" - ] + "metadata": {} }, { "cell_type": "markdown", - "metadata": {}, "source": [ - "It should be noted that, in theory, only when the network structure and loss function we choose meet certain conditions (unitary 2-design), see paper [[1]](https://arxiv.org/abs/1803.11173), this effect will appear. Then we might as well visualize the influence of choosing different qubits on the optimization landscape:\n", - "\n", - "![BP-fig-qubit_landscape_compare](./figures/BP-fig-qubit_landscape_compare.png \"(a) Optimization landscape sampled for 2,4,and 6 qubits from left to right in different z-axis scale. (b) Same landscape in a fixed z-axis scale.\")\n", - "
    (a) Optimization landscape sampled for 2,4,and 6 qubits from left to right in different z-axis scale. (b) Same landscape in a fixed z-axis scale.
    \n", - "\n", - "\n", - "$\\theta_1$ and $\\theta_2$ are the first two circuit parameters, and the remaining parameters are all fixed to $\\pi$. This way, it helps us visualize the shape of this high-dimensional manifold. Unsurprisingly, the landscape becomes more flat as $n$ increases. **Notice the rapidly decreasing scale in the $z$-axis**. Compared with the 2-qubit case, the optimized landscape of 6 qubits is very flat." - ] + "The user can also use the ``plot_loss_grad`` function to show the gradient and loss values variation during the training process." + ], + "metadata": {} }, { - "cell_type": "markdown", - "metadata": {}, + "cell_type": "code", + "execution_count": 12, + "source": [ + "plot_loss_grad(cir, loss_func, ITR, LR, H_l)" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + "Training: 100%|###################################################| 120/120 [00:03<00:00, 38.59it/s]\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
    " + ], + "image/png": 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" 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" + }, + "metadata": { + "needs_background": "light" + } + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "As shown above, the loss value does not change after a few dozen times, and the gradient is very close to 0.\n", + "In order to see the difference between the optimal solution and the theoretical value clearly, we calculate the eigenvalues of the Hamiltonian ``H_l``." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 12, + "source": [ + "loss, grad = show_gradient(cir, loss_func, ITR, LR, H_l)\n", + "H_matrix = pauli_str_to_matrix(H_l, N)\n", + "\n", + "print(\"optimal result: \", loss[-1])\n", + "print(\"real energy：\", np.linalg.eigh(H_matrix)[0][0])" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + "Training: 100%|###################################################| 120/120 [00:02<00:00, 41.17it/s]" + ] + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "optimal result: -1.3504325097994594\n", + "real energy： -2.528866656129176\n" + ] + }, + { + "output_type": "stream", + "name": "stderr", + "text": [ + "\n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "The comparison shows that there is still a gap between the optimal solution obtained from the training of this circuit and the actual value." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "#### More qubits\n", + "\n", + "Since in the barren plateau effect, the gradient disappears exponentially with increasing the number of quantum bits. Then, we will see what happens to the sampled gradients when we increase the number of qubits(here we sample by choosing ``max`` mode)." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 34, + "source": [ + "# Hyper parameter settings\n", + "selected_qubit = [2, 4, 6, 8]\n", + "means, variances = [], []\n", + "\n", + "# Keep increasing the number of qubits\n", + "for N in selected_qubit:\n", + " grad_info = []\n", + " THETA_SIZE = N \n", + " target = np.random.choice(3, N)\n", + " theta = np.random.uniform(low=0., high= 2 * np.pi, size=(THETA_SIZE))\n", + " theta = paddle.to_tensor(theta, stop_gradient=False, dtype='float64')\n", + " cir = rand_circuit(theta, target, N)\n", + " H_l = random_pauli_str_generator(N, terms=10)\n", + " \n", + " grad_mean_list, grad_variance_list = random_sample(cir, loss_func, samples, H_l, mode='max') \n", + " # Record sampling information\n", + " means.append(grad_mean_list)\n", + " variances.append(grad_variance_list)" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + "Sampling: 100%|###################################################| 300/300 [00:22<00:00, 13.28it/s]\n" + ] + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Mean of max gradient\n", + "0.31080108926858796\n", + "Variance of max gradient\n", + "0.01671146619361498\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
    " + ], + "image/png": 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" + }, + "metadata": { + "needs_background": "light" + } + }, + { + "output_type": "stream", + "name": "stderr", + "text": [ + "Sampling: 100%|###################################################| 300/300 [00:33<00:00, 8.86it/s]\n" + ] + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Mean of max gradient\n", + "0.18860559161991128\n", + "Variance of max gradient\n", + "0.00513813734318612\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
    " + ], + "image/png": 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" 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" + }, + "metadata": { + "needs_background": "light" + } + }, + { + "output_type": "stream", + "name": "stderr", + "text": [ + "Sampling: 100%|###################################################| 300/300 [00:51<00:00, 5.86it/s]\n" + ] + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Mean of max gradient\n", + "0.08909871218516183\n", + "Variance of max gradient\n", + "0.001158520193967305\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
    " + ], + "image/png": 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" + }, + "metadata": { + "needs_background": "light" + } + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "To compare the mean and variance of the maximum gradient of each parameter, we plot them." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 36, + "source": [ + "means = np.array(means)\n", + "variances = np.array(variances)\n", + "\n", + "n = np.array(selected_qubit)\n", + "print(\"We then draw the statistical results of this sampled gradient:\")\n", + "fig = plt.figure(figsize=plt.figaspect(0.3))\n", + "\n", + "# ============= The first figure =============\n", + "# Calculate the relationship between the average gradient of random sampling and the number of qubits\n", + "plt.subplot(1, 2, 1)\n", + "plt.plot(n, means, \"o-.\")\n", + "plt.xlabel(r\"Qubit #\")\n", + "plt.ylabel(r\"$ \\partial \\theta_{i} \\langle 0|H |0\\rangle$ Mean\")\n", + "plt.title(\"Mean of {} sampled gradient\".format(samples))\n", + "plt.xlim([1,9])\n", + "plt.grid()\n", + "\n", + "# ============= The second figure =============\n", + "# Calculate the relationship between the variance of the randomly sampled gradient and the number of qubits\n", + "plt.subplot(1, 2, 2)\n", + "plt.plot(n, np.log(variances), \"v-\")\n", + "plt.xlabel(r\"Qubit #\")\n", + "plt.ylabel(r\"$ \\partial \\theta_{i} \\langle 0|H |0\\rangle$ Variance\")\n", + "plt.title(\"Variance of {} sampled gradient\".format(samples))\n", + "plt.xlim([1,9])\n", + "plt.grid()\n", + "\n", + "plt.show()" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "We then draw the statistical results of this sampled gradient:\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
    " + ], + "image/png": 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KlQ3cTvBd+y1BK8214b49/RmU9G2YZwnwDME4xp9VmsK/Gy4E/hEeP59whrKY8uQcgu//k9lJ+RPmfhf4HJhK0BpSRHDR7GfCn/EVBD//VQTv/7WY/W8RlE8fhLk+KOuFd/Y+diX8XJ4DFoTdwzSLVwVtn+lGRFKAmRUQDCZ/JOIc4wkGAz4WZQ4REUk8MxtCUPa03MWhic5xBEHZ02aXB0tKUwuKiOySmR1oZs3CLl5nE0z7udstYyIiIrtiZjXM7Miw7MkjaHl6JepckniqoIhIeeQTdAdbTTAA/oRwfIiIiEiiGHAzQRerqQRrjdwQaSKpFOriJSIiIiIiSUMtKCIiIiIikjQyog6QKPXr1/cOHTpEHaNc1q9fT61atXZ9YMSUM/5SJatyxleq5ASYPHnyCndvEnWOijKzqwlm7mvi7iXXCSIcS/XH8OGt7v5EyWNKUrkSf8oZX6mSE1Inq3LGV7nLlHgvTZ8st06dOnmqGDNmTNQRykU54y9VsipnfKVKTnd3YJInwXd6RW4EC7G9QzCFa+NS9jcEFoT/NgjvN9jV86pciT/ljK9UyemeOlmVM77KW6aoi5eIiFQ19wC/o+zVnA8D3nP3lR6s6v0ecHhlhRMRkZ2rsl28RESk+jGz4UChu39mZmUdlseOC6YuDreV9nwXARcBNGnShIKCgviFTaB169alRFbljK9UyQmpk1U5o6EKioiIpBQzex9oVsqu64HrCFYLjwt3fwh4CCA/P9+HDBkSr6dOqIKCAlIhq3LGV6rkhNTJqpzRUAVFRERSirsfXNp2M+sBtAO2t560BKaY2QB3/zbm0EJgSMzjlkBBQsKKiEiFaQyKiIhUCe4+3d1z3b2tu7cl6LrVp0TlBIIB9IeaWQMza0DQ4vJOJccVEZEyqAUlQqOnFnLnO3MpXL2RvHEfcM1h+YzoXWo3aBER2QNm1g+4xN0vcPeVZvYnYGK4+xZ3XxlhvLg48t6PmbV0zU8b3n4DgK7N6/LmlYMjSiUiUnGqoERk9NRCrn15Ohu3bgOgcPVGrn15OoAqKSIicRC2omy/Pwm4IObxSGBkBLESpk/r+nyxfC1bt/00eVlmutGnTYMIU4mIVJy6eEXkznfm/lg52W7j1m3c+c7ciBKJiEgqu2JYR9JKzFyWbsYVw1JjcUkRke1UQYnIktUbK7RdRERkZ3Lr5nBgp58WaM5MN07o14rcOjkRphIRqThVUCLSon6NCm0XERHZlVtHdCczPWhFKSp2LhzcLuJEIiIVpwpKRK45LJ8amek7bMtMN645LD+iRCIikupy6+Zwcr9WALjDtS9PZ1OJ7sQiIslOFZSIjOidx1+O70Fe2GKSk5HGtmKnVcOaEScTEZFUdsWwjnRqkMZNx3Tl0wXfc8nTk9lcpEqKiKQOVVAiNKJ3Hv/7w0E8fngtxl93MC0b1OSyZ6awYt3mqKOJiEiKyq2bw3UDa3DOfu3483E9KJj7HZc/O5Wt24qjjiYiUi6qoCSJejUz+dcZfVi1YQtXPDeVIhUkIiKyh04d0Jqbj+3Ge7OWcdWoaSpbRCQlqIKSRLq1qMetI7rzyZffc9d786KOIyIiVcDZ+7bl+iO78Mb0pfzupc8pLvZdnyQiEqFKraCY2eFmNtfM5pvZH0rZf4mZTTezaWY21sy6xuy7NjxvrpkdVpm5K9OJ/Vpx6oBWvD3jWzZsKYo6joiIVAEXHrAXvz20Ey9PLeS6V6arkiIiSa3SVpI3s3TgfuAQYDEw0cxec/dZMYc96+4PhMcfC9wNHB5WVE4BugEtgPfNrJO7V8lRfzce040t24qpmVVpPx4REaniLj+oI5u2FvOPMfPJzkjjpmO7YSUWdhQRSQaV2YIyAJjv7gvcfQswChgee4C7r4l5WAvYfolnODDK3Te7+0Jgfvh8VVJOZjp1czLZtHUb977/BRu3VMl6mIiIVLKrD+3EhYPb8cSnX/PnN2fjrpYUEUk+lXmJPg/4JubxYmBgyYPM7DLgN0AWcFDMueNKnJtXyrkXARcBNGnShIKCgnjkTrh169aVmnXuym38bcImtq74mn7Nom9NKStnskmVnJA6WZUzvlIlp1Q9ZsZ1R3Zhc1ExD3+8kJzMdK4+VOtviUhyif6v3hLc/X7gfjM7DfgjcHYFzn0IeAggPz/fhwwZkpCM8VZQUEBpWYcAhx2wnraNa1V2pFKVlTPZpEpOSJ2syhlfqZJTqiYz46ZjurGlqJi/fxB097r8oI5RxxIR+VFlVlAKgVYxj1uG28oyCvjXbp5bZWyvnExYuJLsjDT2blU/2kAiIpLy0tKM247rweaiYv767jyyM9K58IC9oo4lIgJU7hiUiUBHM2tnZlkEg95fiz3AzGIv4RwFfBHefw04xcyyzawd0BGYUAmZk0LRtmJ+99JnXPr0ZFau3xJ1HBERqQLS04w7T+jJUT2ac9ubs3ny06+ijiQiAlRiBcXdi4DLgXeA2cAL7j7TzG4JZ+wCuNzMZprZNIJxKGeH584EXgBmAW8Dl1XVGbxKk5Gext9P7cOK9Vu4ctRUtml6SBERiYOM9DT+dkovDunalBtencmoCYuijiQiUrnroLj7m+7eyd3bu/tt4bYb3P218P6V7t7N3Xu5+9CwYrL93NvC8/Ld/a3KzJ0MerSsxy3HduPjL1bwt/e1iKOIiMRHZnoa/zitNwd2asK1r0znlamLo44kItWcVpJPIacMaM1J/Vry9w/m88GcZVHHERGRKiI7I50Hz+zLoL0acfULn/HG50ujjiQi1ZgqKCnmluHd6daiLleNmsai7zdEHUdERKqInMx0Hjm7H33bNODKUVN5d+a3UUcSkWpKFZQUk5OZzr9O7wvAJU9PZtPWajMUR0REEqxmVgYjz+lPt7x6XPbsFMbMXR51JBGphlRBSUGtG9Xkb6f0YtbSNdzw6oyo44iISBVSJyeTJ88dQKemdbjkqcl8Mn9F1JFEpJpRBSVFHdS5KX84ojNH9GgedRQREali6tXM5KnzB9K2US3Of2ISE79aGXUkEalGVEFJYZcc2J6h+bkA6uolIiJx1bBWFk9fMJDm9XM497GJTF20KupIIlJNqIJSBTw7fhGH/e0jVm/QIo4iIhI/Tepk8+wF+9CwVhZnjZzAjMIfoo4kItWAKihVQNcWdenTugEZ6fpxiohIfDWrl8OzFw6kbk4mZz46njnfrok6kohUcfqLtgro1ao+95zci9rZGVplXkRE4q5lg5o8e+FAsjLSOOOR8cxfvi7qSCJShamCUoUs/WEjx/x9LAWaFlJEROKsTaNaPHPBPgCc/sg4vv5+fcSJRKSqUgWlCqlfI4tid656fhrfrNQijiIiEl8dcmvzzAX7sKWomNMeHs/iVSprRCT+VEGpQmpkpfOvM/qybZvzy2emaGYvEam2zOxqM3Mza1zG/m1mNi28vVbZ+VJZfrM6PHX+QNZu2sppD4/n2x82RR1JRKoYVVCqmHaNa3HXSXszvfAHbv7PrKjjiIhUOjNrBRwKLNrJYRvdvVd4O7aSolUZ3fPq8cR5A1i5fgunPTyO5WtVSRGR+FEFpQo6tFszLh3SnucmLOLFSd9EHUdEpLLdA/wO0KwhCdS7dQMeO7c/S3/YxBmPjGflek11LyLxkRF1AEmMqw/pxGffrOaPo2fQtUVdurWoF3UkEZGEM7PhQKG7f2ZmOzs0x8wmAUXA7e4+uoznuwi4CKBJkyYUFBTEN3CCrFu3rtKy/qpXJvdMXsdx9/6X3/XPoVbmTj/3HVRmzj2hnPGXKlmVMxqqoFRRGelp3Hdqb46+byyXPj2F/1y+P/VqZkYdS0Rkj5nZ+0CzUnZdD1xH0L1rV9q4e6GZ7QV8YGbT3f3Lkge5+0PAQwD5+fk+ZMiQ3Q9eiQoKCqisrEOArt2Xc9GTk3loXhZPnz+AOjnlK28qM+eeUM74S5WsyhkNdfGqwhrXzub+0/uw9IeNvDRlcdRxRETiwt0PdvfuJW/AAqAd8JmZfQW0BKaY2c8qM+5eGP67ACgAelfaG6iChuTn8o/TejOz8AfOfWwi6zcXRR1JRFKYKihVXN82DfjPr/bnvP3aRh1FRCSh3H26u+e6e1t3bwssBvq4+7exx5lZAzPLDu83BvYDNKvIHjq0WzPuPaU3Uxat4oInJmkmSRHZbaqgVAOdm9XFzPjyu3VMWLgy6jgiIpXOzPqZ2SPhwy7AJDP7DBhDMAZFFZQ4OKpnc+46aW/GLfyei5+azOYiVVJEpOI0BqWacHeuefEz1mwq4t2rDiAtrfyDGEVEUlHYirL9/iTggvD+J0CPiGJVecf1bsnmrcX84eXpXPbMVP51Rh8y03U9VETKTxWUasLMuPukXmRlpKlyIiIiCXXKgNZs2VbMDa/O5KpR07j3lF5kqJIiIuWkCko10rZxLQCKi50P533H0M65EScSEZGq6qxBbdlSVMytb8wmM92466RepOsCmYiUgy5nVEMvTv6Gcx+fyCtTNbOXiIgkzgWD9+Kaw/IZPW0J1708neJirZ0pIrumFpRq6Bd9WvLylEKufXk6XZrXpXOzulFHEhGRKuqyoR3YtHUbf/9gPtmZadx8bDd2sYimiFRzakGphjLS0/j7ab2pm5PJJU9NZs2mrVFHEhGRKuw3h3TiogP24slPv+a2N2bjrpYUESmbKijVVG6dHO4/vQ+LV23kty98psJCREQSxsy49ojOnD2oDY+MXchd786LOpKIJDF18arG+rdtyLVHduFPr8/iwY8WcMmB7aOOJCIiVZSZceMx3diyrZh/jJlPdkYaPdKjTiUiyUgtKNXcefu15aiezbnj7Tl88uWKqOOIiEgVlpZm3DaiB8f3zuOu9+bx1kJ1MRaRn1MFpZozM/7vFz1p17gWVzw3lW9/2BR1JBERqcLS0ow7TujJUT2b8/zcLTzxyVdRRxKRJKMKilA7O4MHz+xL1xb10MQqIiKSaBnpafzt5F70zk3nxtdm8tyERVFHEpEkojEoAkCH3Do8ed4AANxdU0CKiEhCZaan8cte2TzzdS2ue2U6Welp/KJvy6hjiUgSUAuK7GDNpq2cNXICr04rjDqKiIhUcZlpxgNn9GXf9o245qXP+M9nS6KOJCJJQBUU2UGNzHSK3dlcVBx1FBERqQZyMtN5+Kx+9GvTkKuen8Y7M7+NOpKIREwVFNlBZnoaT58/kJP6tYo6ioiIVBM1szJ49Jx+9Mirx+XPTmHMnOVRRxKRCKmCIj+zffzJq9MKuVqLOIqISCWok5PJE+cNIL9ZHS5+ejL/m6+p70Wqq0qtoJjZ4WY218zmm9kfStn/GzObZWafm9l/zaxNzL5tZjYtvL1Wmbmrq2VrNvHvKYt5dOzCqKOIiEg1UK9GJk+dN5C9Gtfi/CcmMn7B91FHEpEIVFoFxczSgfuBI4CuwKlm1rXEYVOBfu7eE3gJuCNm30Z37xXejq2U0NXchYP34vBuzfjLW3NUSIiISKVoUCuLp84fSF79Gpz3+ESmLFoVdSQRqWSV2YIyAJjv7gvcfQswChgee4C7j3H3DeHDcYDmG4yQmXHniT1p07Amlz83ldWbNHBeRPacBc4wsxvCx63NbEDUuSR5NKmTzTMX7EPjOtmcPXICMwp/iDqSiFSiylwHJQ/4JubxYmDgTo4/H3gr5nGOmU0CioDb3X10yRPM7CLgIoAmTZpQUFCwh5Erx7p165I663n5xdwybjN/n+LUzhpDRlpyr5GS7J9nrFTJqpzxlSo5E+ifQDFwEHALsBb4N9A/ylCSXJrVy+HZC/fhpAc+5YxHxzPqon3o3Kxu1LFEpBIk5UKNZnYG0A84MGZzG3cvNLO9gA/MbLq7fxl7nrs/BDwEkJ+f70OGDKmsyHukoKCAZM9ap1UhV46axrgNTfnj0SV75iWXVPg8t0uVrMoZX6mSM4EGunsfM5sK4O6rzCwr6lCSfPLq1+DZCwdy8oPjOP3h8Tx/8T50yK0TdSwRSbDK7OJVCMTOXdsy3LYDMzsYuB441t03b9/u7oXhvwuAAqB3IsPKjob3ymNY6wweGbuQNz5fGnUcEUltW8NxiQ5gZk0IWlREfqZNo1o8c+FAzIzTHh7PVyvWRx1JRBKsMisoE4GOZtYuvFJ2CrDDbFxm1ht4kKBysjxmewMzyw7vNwb2A2ZVWnIB4NTOWfRuXZ8bXp3Bxi3boo4jIqnrPuAVINfMbgPGAn+ONpIks/ZNavPMBQPZuq2Y0x4exzcrN+z6JBFJWZVWQXH3IuBy4B1gNvCCu880s1vMbPusXHcCtYEXS0wn3AWYZGafAWMIxqCoglLJMtKMf57ehyfPH0CNrPSo44hIinL3Z4DfAX8BlgIj3P3FaFNJsstvVoenzh/Ius1FnP7IeJb+sDHqSCKSIJU6BsXd3wTeLLHthpj7B5dx3idAj8Smk/JoXq8GzevVAGDcgu8Z2K7hjws7ioiUl7vPAeZEnUNSS/e8ejx5/kDOeGQ8pz88nlEX70NunZyoY4lInGkledktBXOXc8pD43hjusajiEjFmNkTZlY/5nEDMxsZYSRJIb1a1efxc/vz7ZpNnP7weL5ft3nXJ4lISlEFRXbLAR2b8NcT9+bwbs2ijiIiqaenu6/e/sDdV6GJT6QC+rVtyCNn92PRyg2c+egEftiwNepIIhJH5a6gmFm2mZ1mZteZ2Q3bb4kMJ8krLc04oW9LMtLT+G7tZr5bqytYIlJuaWbWYPsDM2tIkk57L8lr3/aNefDMvsxfvo6zRo5n7SZVUkSqioq0oLxKsPJ7EbA+5ibV2NZtxZz4wCf86rkpFG3TLKEiUi53AePM7E9mdivwCcEkKSIVMiQ/l/tP78PMJWs497GJrN9cFHUkEYmDilRQWrr7ye5+h7vftf2WsGSSEjLT0/jVQR0Zt2Ald747N+o4IpIC3P1J4DhgGcEsXseH2/aYmd1kZoXhTJDTzOzIMo473Mzmmtl8M/tDPF5bonFI16bcd2pvpixaxflPTNQ0+CJVQEUqKJ+YmWbSkp/5Rd+WnDawNQ9+uIC3Z3wbdRwRSXLhula9gLpAI+CEOHcZvsfde4W3N0vuDBeJvB84AugKnGpmXeP4+lLJjuzRnLtP6sX4hSu56KlJbNqqSopIKqtIBWV/YHJ4xelzM5tuZp8nKpiklhuP6creLevx2xc/Y8F366KOIyLJLeouwwOA+e6+wN23AKPCPJLCRvTO4/bje/DxFyu4/NkpbClSt2ORVFWRQYlHJCyFpLzsjHT+eUZfjr7vYy59egqvXLYvNbM05lVEStXS3Q9P4PNfbmZnAZOAq8NZwmLlAd/EPF4MDExgHqkkJ/dvzZaiYv7fqzO56vmp3HdKbzLSNWGpSKop91+Q7v51OOtKRyB2VaSv455KUlJe/Rrce0pvzn5sAte/MoO7T9pbiziKSGk+MbMe7j59d042s/eB0uY4vx74F/AnwMN/7wLO292gZnYRcBFAkyZNKCgo2N2nqlTr1q1LiayJyNkKOLVzFs9N/5aVK97lop7ZpO1hWVSdP89ESZWsyhmNcldQzOwC4EqgJTAN2Af4FDgoIckkJR3QqQm/PrgTd783jz6t63PmoLZRRxKR5LM/cI6ZLQQ2Awa4u/csz8nufnB5jjOzh4HXS9lVSPB37HYtw22lvdZDwEMA+fn5PmTIkPK8dOQKCgpIhayJyjkEaDlmPne+M5fWeQ25/fiepKXtfiWlun+eiZAqWZUzGhXpg3Ml0B8Y5+5Dzawz8OfExJJUdvnQDnz2zWpWrtec9CJSqoR1GTaz5u6+NHx4HDCjlMMmAh3NrB1BxeQU4LREZZJoXDa0A5u3buO+D+aTlZHGn4Z3V6u+SIqoSAVlk7tvMjPMLNvd55hZfsKSScpKSzMeOqsf6XtwtUpEqq4Edxm+w8x6EXTx+gq4GMDMWgCPuPuR7l5kZpcD7wDpwEh3nxmH15Yk8+tDOrG5qJgHP1pAdkY6fzyqiyopIimgIhWUxWZWHxgNvGdmq9D4EynD9srJ+AXf89yERdx1Ui9VWEQESGyXYXc/s4ztS4AjYx6/CfxsCmKpWsyMPxzRmc1FxTw6diHZGWlcc1i+KikiSa4ig+SPC+/eZGZjgHrA2wlJJVXG199v4PPFP7Bi3Waa1s3Z9QkiUh2oy7BUGjPjxmO6srmomH8WfElOZjpXDOsYdSwR2YmKDJI34HRgL3e/xcxaEyy0NSFB2aQKOKl/K47t1YKczPSoo4hI8lCXYalUZsZtI7qzuWgbd783j6yMNC45sH3UsUSkDBWZHPyfwCDg1PDxWoKVeEV2KicznU1bt3HjqzP4+vvKXItNRJJUyS7Dr6Iuw5JgaWnGHb/oydE9m3P7W3N47H8Lo44kImWoyBiUge7ex8ymArj7KjPLSlAuqWJWrNvM6GlLmPDVKl6+dF9qZKlFRaS6UpdhiUpGehr3nNyLLUXF3PyfWWRnpHPawNZRxxKREirSgrLVzNIJZkbBzJoAxQlJJVVOywY1+dvJvZjz7Rr+OHoG7h51JBFJAu7+obu/5u5bos4i1UNmehp/P603Q/ObcP3o6bw0eXHUkUSkhIpUUO4DXgFyzew2YCwa1CgVMLRzLr86qCP/nrKY5yZ8E3UcEalkZjY2/Hetma2Jua01szVR55PqIzsjnX+d0Zd92zfidy99xmufLYk6kojEqMgsXs+Y2WRgGMGqvyPcfXbCkkmVdOWwjkz7ZjU3vTaTbi3qsner+lFHEpFK4u77hxOudHP3RVHnkeotJzOdh8/qxzkjJ/Lr56eRlZ7G4d2bRR1LRKhYCwruPsfd73f3f6hyIrsjPc249+ReNKmTzS+fmcKq9erVIVKdeNC/842oc4gA1MzKYOS5/enZsh6/em4KY+YsjzqSiFCOCoqZvbazW2WElKqlQa0s/nl6H75bu5krn5/GtmKNRxGpZqaYWf+oQ4gA1M7O4PFzB5DfrA4XPz2ZsV+siDqSSLVXnhaUQQSr/X4M/BW4q8RNpML2blWfm47txkfzvuOJT76KOo6IVK6BwKdm9qWZfW5m083s86hDSfVVr0YmT503kL0a1+KCJycyfsH3UUcSqdbKMwalGXAIwfonpxE0zT/n7jMTGUyqvlMHtAJgeK8WEScRkUp2WNQBREpqUCuLpy8YyMkPfsp5j0/kyfMH0rdNg6hjiVRLu2xBcfdt7v62u58N7APMBwrM7PKEp5Mqzcw4bWBramVnsHHLNpat2RR1JBGpBO7+NbAGaAq0ibmJRKpx7WyevXAfGtfJ5pyRE5i++IeoI4lUS+WaxcvMsoGjCFpR2vLTlMMie8zdOfuxCWzeuo1XfrkfaWkWdSQRSSAzuwC4kqD78DSCi1+fAgdFGEsEgKZ1c3j2wn048I4xHPOPsT/teDuY26Fr87q8eeXgiNKJVA+7rKCY2ZNAd+BN4GZ3n5HwVFKtmBmXHtietDRT5USkergS6A+Mc/ehZtYZraslSSSvfg2O6tmcV6ftuD5KZrrRR92+RBKuPIPkzwA6EhQon2hhLUmEoZ1zObBTEwBWrNsccRoRSbBN7r4JghZ6d58D5EecSWQH1x/Zhaz0n/+ZdOHgdhGkEaleyjMGJc3d64S3ujG3Ou5etzJCSvXx2mdLGPx/Y5hRqH6/IlXYYjOrD4wG3jOzV4GvI00kUkJu3RxO6teSzPSfWva3bnOOuPdjfv38NArmLqdoW3GECUWqrnKvJC9SGfZr34j6NTO55OnJvP6r/alfMyvqSCISZ+5+XHj3JjMbA9QD3o4wkkiprhjWkRcnLwacnIw07jm5Fx998R1vfL6UV6YW0qhWFkf3bM7w3nn0blUfM3VTFomHCq0kL5JojWpn88/T+7BszSZ+/fw0irWIo0iVYWb3m9l+sdvc/UN3f83dt0SVS6QsuXVzOLFvSww4oV8rjujRnL8c35OJfzyYB8/sy8C9GvLcxG84/p+fMOSvBdz97ly+/G5d1LFFUp4qKJJ0erduwA1Hd2XM3O+4f8z8qOOISPzMA/5qZl+Z2R1m1jvqQCK7csWwjnRskMYVwzr8uC07I53DujXjn6f3ZdIfD+aOE3rSskEN/j5mPsPu+pBj/j6WRz5ewHJNny+yW9TFS5LSGfu0YfLXq7j7/Xns3ao+B4QD6EUkdbn7vcC9ZtYGOAUYaWY1gOcIFgCeF2lAkVLk1s3huoE1yK2TU+r+ujmZnNSvFSf1a8WyNZv4z2dLGD2tkFvfmM2f35zNvu0bM7xXCw7r3oy6OZmVnF4kNZWrBcXMGpjZWWb2ipnNNLPXzexCM8tNdECpnsyMPx/fg065dbhy1FQKV2+MOpKIxIm7f+3u/+fuvQnW1xoBzI42lciea1o3hwsG78XrvxrM+785kMuGdmDRyg1c89Ln9Lv1fX75zGTemfktm4u2RR1VJKntsoJiZi8DLwO5wO/dvRvwSyAHeNrMChKaUKqtmlkZPHBmX4q2Ob98erK+0EWqCDPLMLNjzOwZ4C1gLnB8xLFE4qpDbm2uPjSfD68Zwsu/3JdT+7di/IKVXPzUZAbc9l+ufflzxi34XmMtRUpRni5e57n76tgN7r4I+Dvw93CqSJGEaNe4FneeuDfXvzKdr1ZsIL9ZnagjichuMrNDCFpMjgQmAKOAi9x9faTBRBLIzOjTugF9Wjfgj0d3Zez8Fbw6tZBXpy3huQnf0KJeDsf0asGIXnl0aa7VG0SgHBUUd18drvI7HMgLNxcCr7n77JKVl50xs8OBe4F04BF3v73E/t8AFwBFwHcElaOvw31nA38MD73V3Z8o7+tKaju8ezP279iY2tkaMiWS4q4FngWudvdVUYcRqWyZ6WkMzc9laH4uG7YU8d6sZYyeWsgjHy/kwQ8XkN+0DsN7t+DYvVvQskHNqOOKRGaXf/GZ2e8JrniNIrjiBdASeM7MRpWsZOzkedKB+4FDgMXARDN7zd1nxRw2Fejn7hvM7FLgDuBkM2sI3Aj0AxyYHJ6rAq6aqJ2dQXGxc/+Y+Qzr0pSuLXSVSSTVuPtBUWcQSRY1szIY3iuP4b3y+H7dZt6YvpTRUwu54+253PH2XAa0bcixvVpwVI/mNKilNcGkeinPJenzgW7uvjV2o5ndDcwEylVBAQYA8919QXj+KIJWmR8rKO4+Jub4ccAZ4f3DgPfcfWV47nvA4QQzv0g18cPGrTw9/ms2FW1TBUVERKqMRrWzOWtQW84a1JZF32/g1WmFjJ5WyB9Hz+Dm/8zkwE5NGN4rj4O7NKVGVnrUcUUSrjwVlGKgBfB1ie3Nw33llQd8E/N4MTBwJ8efTzB4sqxz80qeYGYXARcBNGnShIKCggrEi866detSImsy5Ly2bxr1spZSUPBtmcckQ87ySpWsyhlfqZJTRCpf60Y1+dWwjlx+UAdmLlnDq9MKee2zJbw/ezm1stI5rHszRvTKY9/2jchI13J2UjWVp4JyFfBfM/uCnyoJrYEOwOWJCGVmZxB05zqwIue5+0PAQwD5+fk+ZMiQ+IdLgIKCAlIhazLlnL98LVO+Xs1J/Vv9bF8y5dyVVMmqnPGVKjlFJDpmRve8enTPq8cfjujC+AXfM3paIW9N/5aXpxTSuHY2x+zdnBG98ujZsh5mFnVkkbgpzyD5t82sE0EXrdhB8hPdvSLzvhYCsX9Ntgy37cDMDgauBw50980x5w4pcW5BBV5bqpiHPlrAS5MXk9egBvt1aBx1HBEpJzNrABwDHAd0AhYCrwKvuvvyODz/TcCFBBOtAFzn7m+WctxXwFpgG1Dk7v329LVFEiU9zdi3Q2P27dCYW4Z3Z8yc5YyeVsgz4xbx2P++ol3jWgzv1YJmmyvSsUUkeZVrWiR3LyYYE7InJgIdzawdQYXjFOC02APMrDfwIHB4iYLqHeDPYcEGcCjBbDBSTd14TDemLlrNFc9N5fUr9qd5vRpRRxKRXQjX1WoAvEGwrtY8M2tNMB7xaTPLcvchcXipe9z9r+U4bqi7r4jD64lUmpzMdI7o0ZwjejTnhw1beWvGUkZPK+Te/36BOzy3cCwjeudxdM8WNKmTHXVckd1Snlm8WpfzuVa7+5qydrp7kZldTlDZSAdGuvtMM7sFmOTurwF3ArWBF8OmykXufqy7rzSzPxFUcgBu2T5gXqqnWtkZ/OuMvgz/x1h++cwUnr9oEFkZ6osrkuS0rpZIHNWrmckpA1pzyoDWLP1hI/e8/DHT1zg3/2cWf3p9Fvt1aMyIXnkc1r2ZpuqXlFKe39byrDfiwOPAkzs9KGhmf7PEthti7h+8k3NHAiPLkUWqiQ65tbnzxL355TNTuO2NWdw8vHvUkURkJ+K5rtYuXG5mZwGTKHvNFQfeNTMHHgzHMIqkrOb1anBkuyzuGDKYecvW8uq0YDHIq1/8jOtHT+fgLk0Z0SuPAzo10QU9SXrlqaBcAsxzd090GJGKOrJHcy7Yvx2PjF1I79YNGNH7Z5O7iUiSiOO6Wu8DzUrZdT3wL+BPBBWQPwF3AeeVcuz+7l5oZrnAe2Y2x90/KuW1NDtkAilnfMXm7J8N/QYY81fn8OmSIgpmL+X1z5dSKxMGNMtgUIsMOtRPIy2iwfWp+Jkms1TJWV7lqaC8BLQxs3nA58D07f/GY0CjyJ76/RGd+Wzxaq558TP+/OZslq/dTN64D7jmsHxVWESSS1zW1dpZa3uJ530YeL2M5ygM/11uZq8QTATzswqKZodMLOWMr9JyDiWYNWJLUTEff/Edo6ct4b1Z3zLmm03k1a/B8F7NGd4rj/xmdSLPmoyUMxrlmcWrh5llAz0JumetB44GupkZ7l7aVSyRSpOZnsYxPZsz8atVLF8bTPxWuHoj1748HUCVFJHkEa91tcpkZs3dfWn48DhgRinH1ALS3H1teP9Q4JZ4vL5IssrKSGNYl6YM69KUdZuLeHfmt4yetoQHPvySfxZ8SedmdRjRO49j925Bi/qaeEaiVd5ZvDYDE81snbv/avv2mFm1RCL14EcLf7Zt49Zt3PnOXFVQRJLHVSR+Xa07zKwXQRevr4CLAcysBfCIux8JNAVeCSdjyQCedfe34/T6IkmvdnYGx/dpyfF9WvLd2s28/vkSRk9bwu1vzeH/3p7DgLYNGdE7jyO7N6dezcyo40o1VNEpHXYYh1LGwEORSrdk9cadbnd3LWIlErE4rqu1s9c4s4ztS4Ajw/sLgL3j8Xoiqa5JnWzO3a8d5+7Xjq9WrOfVaUt4dVoh1748nRtfncmQ/CaM6J3HQZ1zyclMjzquVBPlmWb4fmBKeNNfeJKUWtSvQWEplZTtzdSXPTuFTVuLObhLU4Z1yaVp3ZzKjigixG1dLRFJgLaNa3HlwR25YlgHphf+wOipS/jP50t4d9Yy6mRncHj3Zozoncc+ezUiPU1/EkrilKcF5TOgF3AWUMfMZhEMZpwFzHL35xMXT6R8rjksn2tfns7GrT9dhK2Rmc41h+UD0LphLd6YvoQP5iyHV6Bny3oc3KUpB3dpSpfmddS6IlIJ4rWulogklpnRs2V9erasz/VHdeGTL1cweuoS3prxLS9OXkxunWyO2bsFI3rl0T2vrspQibvyDJLfYW54M2sJ9CAYNH80oAqKRG77OJM735lL4eqN5NWvscMsXn84ojO/PzyfecvW8f7sZbw/exn3vD+Pu9+bR4t6ORzctSkn9G1Jz5b1I3wXIlVe3NbVEpHKkZ5mDO7YhMEdm3Db1u68P3sZo6cu4clPv+LRsQvZq0ktRvTKY0SvPFo3qhl1XKkiKrysqLsvBhYDb8U/jsjuG9E7jxG988qcas/MyG9Wh/xmdbhsaAe+W7uZMXOW897sZbww6Rs65NamZ8v6rFy/hTFzlnNIt6bUzdHgQJE40rpaIiksJzOdo3u24OieLVi9YQtvTF/Kq9OWcPd7wQW/3q3rM6JXHkf3bE6j2tlRx5UUVp4xKGqSlyqpSZ1sTurfipP6t2LT1m0Uh38zfThvOVe/+BmvN9uf7nn1WLhiPcXutG9SO+LEIilP62qJVBH1a2Zx+sA2nD6wDYWrN/JaOLj+xtdmcsvrsxjcsTEjeuVxSNem1Mqu8PVwqebK8xujJnmp8mJnJhm+dx4dmtShW4u6ADz44ZeMmvgN7RrX4uAuuQzr0pR+bRqQkZ4WVVyRlKR1tUSqprz6Nbh0SHsuHdKeOd+uYfTUJbw2rZCrnp9Gjcx0Du3WlBG98rjjnTnMXrr2pxPffgOArs3r8uaVgyNKL8moPGNQhlZGEJFkkZZm9GhZ78fHvxrWka4t6vLerGU8/slXPPzxQurVyOSgzrkM65LLgZ2aUEddwUTKRetqiVRtnZvV5Q9H1OV3h+Uz8auVjJ62hDfDrmDZGWmkGRTHdPLMTDf6tNF/f9lRudrczKwzMJwd561/1d3nJCqYSLLIq1+Dswa15axBbVm7aSsff7GC92ctY8zc5bwytZDMdOPk/q24dUSPqKOKpBKtqyVShaWlGQP3asTAvRpx07Fd+XDudzw/8Rv+O2fH3pzpZlwxrENEKSVZlWcMyu+BU4FRwIRwc0tglJmNcvfbE5hPJKnUycnkyB7NObJHc4q2FTNl0Wr+O3vZj+utbC7axqkPjePSIR04pGvTiNOKJBetqyVSPWVnpHNot2Yc2q0Zv3vpM16avJhihzSDX/RtSW4drU0mOypPC8r5QDd33xq70czuJlgPRRUUqZYy0tMY0K4hA9o1/HHbinVbyExPIzM9+Ntr1pI1PPnpVxzcpSn7dWhMjSytwivVmtbVEqnmfntoPq9OW8LmomKKHZas2sjmom1kZ6h8lJ+Up4JSDLQAvi6xvXm4T0RCefVr8PzFg358/OV363j986WMmvgNOZlp7N+hMQd3acpBXXJ1xUiqHa2rJSK5dXM4sW9Lnhm/iD5tGjBm3ndc9ORkHjijry7iyY/KU0G5CvivmX0BfBNuaw10AC5PUC6RKuGYvVtwWLdmjF/4Pf+dvZz3Zi3j/dlB/9u9W9Wnfc4WmnVeQ35TrWYv1Y/W1RKpnq4Y1pEJ8xbzrzP68MHs5Vz7ynTOfmwCj57dT5POCFC+WbzeNrNOwAB2HCQ/0d23JTKcSFWQlZH24yq8Nx7TlbnL1vL+rGW8N3s5L3+xlQ8fHs+E6w8m3WDBd+to2aAmWRmawliqHq2rJSIQtKJcN7AGuXVyOGVAa2pmZ/Cb56dxxiPjeeK8AdSvmRV1RIlYeQbJp7l7MTBuF/tFZBfMjM7N6tK5WV0uP6gjo9/+gGad9iY9zXB3znx0Ar1a1ef+0/sAsHbTVl1NkqpE62qJyM8cu3cLamSmc9kzUzjloXE8df5AmtTRSvTVWXm6eL1nZiuA0cAb7r7GzGoChwPHEfQf7pWwhCJVWP2cNPbZqxEA7nDzsd2oWyOokCz9YSOD/28Mfds04JCuTRnWpSntGteKMq7IHtG6WiJSlkO6NmXkOf258MlJnPTgpzx9wUDywhkypfopTxevYWbWlWAdlDfMLItgcPw7wD3uPiXBGUWqhbQ04+CYqYnT04xLh7TnvVnLuPWN2dz6xmzaN6nFwV2acnDXpvRp3YD0NI1bkdSidbVEpCz7d2zMU+cP4NzHJnLSA5/yzAUDaasLc9VSuRZqdPdZBNNA/sXMarj7xsTGEpHcOjlcfWg+Vx+az+JVG/jv7OW8P3sZI/+3kAc/WkCDmpkM7ZzL7w7rTLN6mhFMkp/W1RKRXenXtiHPXbQPZz46nhMf/JSnzx9IfrM6UceSSlauCkoJ15pZBjANmObu8+IbSURKatmgJmfv25az9w1Ws/9o3gren72MsV+s4JbhwX/j1z9fwqr1WzhjnzaaEUySldbVEpFd6p5XjxcuHsTpj4zn5Ic+5anzBtKjZb2oY0klqvBUQe5+A3Av8ANwnJk9HPdUIlKmOjmZHNWzOfec3Itx1w6jdnZQQXlrxre8OHnxj5WTV6Yu5vPFqyku9ijjisTavq5WSVpXS0R20LFpHV68ZBC1sjI47eFxTPxqZdSRpBKVZxavtsBlQHtgJUHLyX/c/R2CcSgiEpG0mDEo95/WhzWbggvTm4u2cf0rM9iwZRtN62ZzUOemHNI1l33bNyYnUwthSWSuQutqiUg5tWlUixcvGcQZj4znzEfH8/BZ/RjcsUnUsaQSlKeL16vAfcDbwEiCKSCvMbPXgd+4++YE5hORCqgbTkmcnZHO2N8fRMHcYNzKa9MKeW7CImpkprN/x8Yc0qUpQzvnahpHqVRaV0tEKqpF/Ro8f/Egznx0POc/Pom/n9abw7o1izqWJFh5Kijp7v4ogJmtdPcLwzEovwYeAs5OZEAR2T0Na2VxfJ+WHN+nJZuLtjF+wUren73sxxXtzeC+U3pzzN4t2FbspBkauyIJpXW1RGR3NKmTzaiL9uGcxybyy2emcPdJezO8V96uT5SUVZ4xKO+b2famdwdw9yJ3vxMYlLBkIhI32RnpHNCpCbcM787Y3w/lzSsG8+uDO9G3TQMA/j1lMQfcOYZlazbtcN7oqYXsd/sHnPP2eva7/QNGTy2MIr5UHe+Z2fNmdqqZ1QUws5pmdryZPQVo2noRKVX9mlk8fcFA+rdtwFXPT+PZ8YuijiQJVJ4WlN8QzNw1Ccgzs4uADQSVk+8TGU5E4s/M6NqiLl1b1P1xW/N6OfRv25DcsMvXbW/MYuJXK5m5ZA1btwWD7AtXb+Tal6cDMKK3rlxJxWldLRHZE7WzM3j83AFc8vRkrntlOhu2FHHB4L2ijiUJUJ6FGouB28zsHuBgglXj6wMzgOsTGU5EKsfgjk12GHiYnpbG54t/oOQEYBu3buPOd+aqgiK7TetqicieyMlM56Ez+3HV81O59Y3ZrN+8jSuGdVAX5SqmXOugmFk2cDWwL7COoBn+XXdfnbhoIhKVPxzRmQc//LLUfUtW6+9JiRutqyUiFZaVkcZ9p/SmRuZ07nl/Huu3FHHtEZ1VSalCyrsOyp1AG+APwGKgETDSzM5IVDARiVaL+jVK3V6/ZmYlJ5GqSutqicjuykhP484TenLWoDY89NEC/jh6htb9qkLKu5L83sBwd19tZgPcfb+wVaUAeDph6UQkMtccls+1L09n49afZn9NM1i1YSvXvjydPx/XXVerpEK0rpaIxFNamnHzsd2omZXBAx9+yYYt27jzhJ5kpFd4HXJJMuWtoNzJT60tK8zsbmAOoDVQRKqo7eNM7nxnLoWrN5JXvwZXH9KRL1esJzsjXZUT2R2Vsq6Wmf2KoCK0DXjD3X9XyjGHE7TepAOPuPvt8XhtEalcZsYfjuhMnZwM7nxnLhu2FHHfqb3JztCixKmsXBUUd3895uGJwAlAM+C0RIQSkeQwonceI3rnUVBQwJAhQ362f+wXK1i2ZhO/6Nuy8sNJKkr4ulpmNpRglrC93X2zmeWWckw6cD9wCEG35Ylm9lo4gF9EUtBlQztQIzOdW16fxQVPTOKhM/tRI0uVlFRV4TYwd9/i7s+6+93uvqQi55rZ4WY218zmm9kfStl/gJlNMbMiMzuhxL5tZjYtvL1W0dwiEn/PTVzEAx9+yeYiLQIu5VIZ62pdCty+vTXG3ZeXcswAYL67L3D3LcAogkqNiKSw8/Zvxx2/6MnY+Ss4e+QE1m7aGnUk2U2V1kkv5orVEUBX4NRwPvxYi4BzgGdLeYqN7t4rvB2b0LAiUi73ndKbZy4YSHZGOus3F/HFsrVRR5Lk9hugXuy6WmZ2hpndT/zW1eoEDDaz8Wb2oZn1L+WYPOCbmMeLw20ikuJO6t+K+07pzZRFqzj9kfGsWr8l6kiyG8o7BiUefrxiBWBm269Y/dik7u5fhfuKKzGXiOym9DQjt24OEIxVGTVxETcf242T+rXSGBX5mXitq2Vm7xN0My7peoJyrSGwD9AfeMHM9nL33ZreJ1yc+CKAJk2aUFBQsDtPU+nWrVuXElmVM75SJSckNmsd4LJeWdw/7QeOued9fts/h/rZu3dNPlU+01TJWV6VWUEp7YrVwAqcnxNedSsiaL4fHcdsIrKHfjm0PV8sX8vv/z2dT7/8ntuO60Gt7Mr8ipFUEI91tdz94J08/6XAy2GFZEJ4wasx8F3MYYVAq5jHLcNtpb3WQwTjY8jPz/fSxmIlo7LGjSUb5YyvVMkJic86BBjQZwUXPjmJv31uPHPhQPLKmD5/Z1LlM02VnOWVSn89tHH3QjPbC/jAzKa7+w4ryelKV2IpZ/ylStby5jy/vZNLJqOnLWHcvKVc1juHVnUqb7rHqvZ5VlF3AjUJ1tU6h5/W1XrY3eMxbf1oYCgwxsw6AVnAihLHTAQ6mlk7gorJKWjSF5EqZ78OjXnq/AGc89hETnrgU56+YCDtGteKOpaUQ2VWUMp9xao07l4Y/rvAzAqA3sCXJY7Rla4EUs74S5WsFcl50FA46cvvuXLUVP40fjM3HdONUwdUTpevqvh5VkGJXldrJEGFZwawBTjb3d3MWhBMJ3ykuxeFg/XfIZhmeKS7z4zDa4tIkunbpiHPXbgPZ42cwIkPfMozFwwkv1mdqGPJLlTmSjY/XrEysyyCK1blmo3LzBqEBRhm1hjYj5ixKyKSXAa1b8SbVw5mYLuGXPfKdK4YNU2zqch2pa2rdTZxWlcrnGnyDHfv7u593P2DcPsSdz8y5rg33b2Tu7d399vi8doikpy659Xj+Yv2IT0NTn7oUz5fvDrqSLILlVZBcfciYPsVq9nAC+4+08xuMbNjAcysv5ktJlhr5UEz235Fqwswycw+A8YQjEFRBUUkiTWunc0T5w7gmsPyeePzJfyz4MtdnyRVnru/7u4rw4cnApOA2qiLlYgkUMemdXjx4n2pnZ3BaQ+PZ8LClbs+SSJTqWNQ3P1N4M0S226IuT+RoOtXyfM+AXokPKCIxFVamnHZ0A7ss1cjujQPmtRXrt9Cg5qZmuVLCNcgKW1aeRGRuGvdqCYvXjKI0x8Zz1kjx/PQmf04oFOTqGNJKSqzi5eIVFN92zSgZlYGG7ds48QHPuGGV9XdX0REKl/zejV44eJBtGtcmwuemMTbM76NOpKUQhUUEak02RlpnNivFYd3L20JCxERkcRrXDubURfuQ7e8ulz27BRembo46khSgiooIlJp0tKMSw5sz34dGgNw33+/YOTYhezmGnoiIiK7pV7NTJ46fyAD2jbkNy98xjPjv446ksRQBUVEIlFc7Ewv/IFbXp/FxU9N5ocNmuVLREQqT+3sDB47tz9D83O5/pUZPPzRgqgjSUgVFBGJRFqa8dCZffnjUV34YM5yjrzvY6YuWhV1LBERqUZyMtN54Iy+HNWjObe9OZt73punVv0koAqKiETGzLhg8F68eMkgAE584FMe+XiBCgcREak0WRlp3Hdqb07o25J7//sFt70xW+VQxFRBEZHI9W7dgDevGMxBnXO59Y3ZXPjkJFZv2BJ1LBERqSbS04w7ftGTswe14ZGxC7nulRlsK1YlJSqqoIhIUqhXM5MHz+zLjcd05cN533HkvR8zc8kPUccSEZFqIi3NuOnYbvxySHuem7CIq1+YpkpKRCp1oUYRkZ0xM87drx192zTg5v/MIrdOTtSRRESkGjEzfnd4Z2plZ3DnO3NZlJvO/gdsIzsjPepo1YpaUEQk6fRsWZ+XLhlEkzrZbCt27nxnDt+v2xx1LBERqSYuG9qBm47pypTl27jgiUls2FIUdaRqRRUUEUlKZgbA9MIfePijhYydvyLiRCIiUp2cs187zu+exf/mr+DskRNYs0nT4VcWVVBEJKn1alWfD357IMN75QEwc8kPFKtPsIiIVILBLTO579TeTF20mtMfHs+q9ZrApTKogiIiSa9lg5oAFK7eyC/+9QlnPzaBFeryJSIileDoni146Ky+zF22lpMf+pTlazZFHanKUwVFRFJGi3o53HhMNyYsXMmR937Mp19+H3UkERGpBg7q3JTHz+nP4lUbOenBT1m8akPUkao0VVBEJGWYGacOaM3oy/ajdk4Gpz8yjnvf/0LTQIqISMLt26ExT50/kO/Xb+GkBz5lwXfroo5UZamCIiIpp0vzuvzn8v0Z3iuPe96fx5mPjmf5WjW5i4hIYvVt04BRF+3D5qJiTnpwHHO+XRN1pCpJFRQRSUm1sjO4+6S9ueMXPZmyaBVH3juWWd9vizqWiIhUcd1a1OP5iweRngYnPziOz75ZHXWkKkcVFBFJWWbGSf1b8drl+1O/Zib3TdnE6g2aYUVERBKrQ25tXrx4X+rWyOD0R8YzfoHGRMaTKigikvI6Na3Da5fvx6/75lC/Zhbuzg8bNF+9iIgkTutGNXnx4n1pWjebsx+bwIfzvos6UpWhCoqIVAk1szLIb5gOwIuTF3PQXQUsXLE+4lQiIlKVNauXwwsXD2KvxrW54ImJvD1jadSRqgRVUESkyunTugFH9mhO64Y1o44iIiJVXKPa2Tx30T70yKvHZc9O5eUpi6OOlPJUQRGRKqdDbm3+NKI76WnGsjWbuPipSSz9YWPUsUREpIqqVyOTp84fyMB2DfnNC5/x9Livo46U0lRBEZEqbd6ytYz9YgVH3vsxY+YsjzqOiIhUUbWyMxh5Tn+Gdc7lj6Nn8OCHX0YdKWWpgiIiVdrgjk34z6/2p1m9Gpz7+ET+8uZstm4rjjqWiIhUQTmZ6TxwZl+O6tmcv7w1h7vfm4e7FhOuKFVQRKTK26tJbV755b6cPrA1D360gJMf/JTC1eryJSIi8ZeZnsZ9p/TmpH4tue+/X3DrG7NVSakgVVBEpFrIyUzntuN68I/TejNv2TqOvPdj3pu1LOpYIiJSBaWnGbcf35Nz9m3Lo2MXct0r09lWrEpKeamCIiLVytE9W/D6r/anVcMaXPjkJP785uyoI0mcmdmvzGyOmc00szvKOOYrM5tuZtPMbFJlZxSRqi8tzbjxmK5cNrQ9z034ht+8ME1djMspI+oAIiKVrW3jWvz70n358xuzqZWlr8GqxMyGAsOBvd19s5nl7uTwoe6+opKiiUg1ZGZcc1hnamVncMfbc9mwZRt/P7U3OZnpUUdLaiqZRaRays5I5+bh3X/sF/y/+StYu2krh3dvHnEy2UOXAre7+2YAd9fUbSISuV8O6UDt7AxueHUmFz45iQfP7EtNXSArk7p4iUi1ZmYAjBy7kLvfm6fm99TXCRhsZuPN7EMz61/GcQ68a2aTzeyiSswnItXUWYPacucJPfnf/BWc9egE1mzaGnWkpKWqm4gI8K8z+vL9+s1kpqexfnMR36/bQutGWok+GZnZ+0CzUnZdT1CuNQT2AfoDL5jZXv7zKXT2d/fCsAvYe2Y2x90/KuW1LgIuAmjSpAkFBQVxfCeJs27dupTIqpzxlSo5IXWyxjtnE+CSvbN58LNVHHP3+/y2Xw51smyPnzdVPs/yUgVFRATIykijeb0aAPzlrdm8OnUJt/+iJ0f1VJevZOPuB5e1z8wuBV4OKyQTzKwYaAx8V+I5CsN/l5vZK8AA4GcVFHd/CHgIID8/34cMGRKvt5FQBQUFpEJW5YyvVMkJqZM1ETmHAP17LeeSpydz34w0nrlgILl1c/boOVPl8ywvdfESESnhkgPb0z63Npc9O4X/N3oGm7ZuizqSlN9oYCiAmXUCsoAdBsKbWS0zq7P9PnAoMKNyY4pIdTa0cy6PndufwtUbOfHBT1m8akPUkZKKKigiIiW0bFCTFy4exIWD2/HUuK85/p+fsHDF+qhjSfmMBPYysxnAKOBsd3cza2Fmb4bHNAXGmtlnwATgDXd/O6K8IlJN7du+MU9fMJBV67dw4gOfsuC7dVFHShqqoIiIlCIrI43rj+rKo2f3Y8kPGzn6vo95dVph1LFkF9x9i7uf4e7d3b2Pu38Qbl/i7keG9xe4+97hrZu73xZtahGprvq0bsCoiwaxpaiYkx78lNlL10QdKSmogiIishPDujTlzSsG06V5Xa4cNY1rX/5cXb5ERCRuuraoy/MXDyIjLY1THhrHtG9WRx0pcpVaQTGzw81srpnNN7M/lLL/ADObYmZFZnZCiX1nm9kX4e3sykstItVdi/o1eO6ifbh0SLAa8D8Lvow6koiIVCEdcmvz4iWDqFcjk9MfHse4Bd9HHSlSlVZBMbN04H7gCKArcKqZdS1x2CLgHODZEuc2BG4EBhLMtHKjmTVIdGYRke0y09P4/eGdefaCgVxy4F4AmsNeRETiplXDmrx4ySCa16/B2SMnUDC3+q4zW5ktKAOA+WHf3y0EgxeHxx7g7l+5++dAyZXSDgPec/eV7r4KeA84vDJCi4jE2rdDY2pmZbBhSxHH3f8//vLW7KgjiYhIFdG0bg7PX7QPHXJrc+GTk3hr+tKoI0WiMtdByQO+iXm8mKBFZHfPzSt5kBbUSizljL9UyaqcP7et2Oladyv1NiyhoGBZhc5Nlc9TREQqX6Pa2Tx74T6c9/hELnt2CneesDe/6Nsy6liVqkot1KgFtRJLOeMvVbIqZ+mGHfTT/fvHzCe3TjYn9mu1y/NS5fMUEZFo1KuRyZPnDeCipyZx9YufsWFLEWcOaht1rEpTmV28CoHYkrtluC3R54qIJNS2YufTL7/nmpc+5zcvTGP95qKoI4mISIqrlZ3Bo2f35+Auufy/V2fywIfVZ4KWyqygTAQ6mlk7M8sCTgFeK+e57wCHmlmDcHD8oeE2EZHIpacZT5w3gCuHdeSVqYUc+4+xzPlWc9mLiMieyclM519n9OXons25/a053PXuXNw96lgJV2kVFHcvAi4nqFjMBl5w95lmdouZHQtgZv3NbDFwIvCgmc0Mz10J/ImgkjMRuCXcJiKSFNLTjF8f0olnzh/Imk1FDP/H/xg1YVG1KEhERCRxMtPTuPeU3pzcrxV//2A+f3p9dpUvWyp1DIq7vwm8WWLbDTH3JxJ03yrt3JHAyIQGFBHZQ/t2aMybVwzm189P4w8vT+fTBd9z23E9qJ1dpYb8iYhIJUpPM/5yfA9qZqcz8n8L2bCliNuO60F6mkUdLSG0kryISJw1qZPNE+cN4OpDOvGfz5Zw7N/HMn/52qhjiYhICktLM244uiu/OqgDoyZ+w1XPT2PrtpIrc1QNuqQnIpIA6WnGr4Z1pH+7htz6xizq1chi9NRC7nxnLoWrN5I37gOuOSyfEb1/NmO6iIhIqcyMqw/Np1Z2Bre/NYf/fLbkp51vvwFA1+Z1efPKwREljA+1oIiIJNA+ezXiP5fvz//mr+Dalz+ncPVGAApXb+Tal6czeqomJBQRkYq55MD29G/b4GfbM9ONPm1+vj3VqIIiIpJgZsad78xl49Ydm+I3bt3Gne/MjSiViIiksvtP60NGiTEo6WZcMaxDRIniRxUUEZFKsCRsOSnvdhERkZ3JrZvDKf1b/ThQPjPdOKFfK3Lr5EScbM+pgiIiUgla1K9Roe0iIiK7csWwjj+2olSV1hNQBUVEpFJcc1g+NTLTd9hWIzOdaw7LjyiRiIikuty6OZzYtyUGVab1BFRBERGpFCN65/GX43uQF7aY5NWvwV+O76FZvEREZI9cMawjHRukVZnWE9A0wyIilWZE7zxG9M6joKCAIUOGRB1HRESqgNy6OVw3sEaVaT0BtaCIiIiIiEgSUQVFRERERESShiooIiIiIiKSNFRBERERERGRpKEKioiIiIiIJA1z96gzJISZrQXmRp2jnBoDK6IOUQ7KGX+pklU54ytVcgLku3udqEMkA5UrCaGc8ZUqOSF1sipnfJWrTKnK0wzPdfd+UYcoDzOblApZlTP+UiWrcsZXquSEIGvUGZKIypU4U874SpWckDpZlTO+ylumqIuXiIiIiIgkDVVQREREREQkaVTlCspDUQeogFTJqpzxlypZlTO+UiUnpFbWREulzyJVsipnfKVKTkidrMoZX+XKWWUHyYuIiIiISOqpyi0oIiIiIiKSYlRBERERERGRpFHlKihmNtLMlpvZjKiz7IyZtTKzMWY2y8xmmtmVUWcqi5nlmNkEM/sszHpz1Jl2xszSzWyqmb0edZaymNlXZjbdzKYl8zSuZlbfzF4yszlmNtvMBkWdqTRmlh9+lttva8zsqqhzlcbMfh3+P5phZs+ZWU7UmUpjZleGGWcm62dZWVSuxJfKlMRQuRJfKlfiryLlSpUbg2JmBwDrgCfdvXvUecpiZs2B5u4+xczqAJOBEe4+K+JoP2NmBtRy93VmlgmMBa5093ERRyuVmf0G6AfUdfejo85TGjP7Cujn7km9qJKZPQF87O6PmFkWUNPdV0cca6fMLB0oBAa6+9dR54llZnkE/3+6uvtGM3sBeNPdH4822Y7MrDswChgAbAHeBi5x9/mRBouIypX4UpmSGCpXEkflyp6raLlS5VpQ3P0jYGXUOXbF3Ze6+5Tw/lpgNpAXbarSeWBd+DAzvCVlzdbMWgJHAY9EnSXVmVk94ADgUQB335LshUhoGPBlshUiMTKAGmaWAdQElkScpzRdgPHuvsHdi4APgeMjzhQZlSvxpTKl+lK5kjBVrlypchWUVGRmbYHewPiIo5QpbOKeBiwH3nP3ZM36N+B3QHHEOXbFgXfNbLKZXRR1mDK0A74DHgu7NzxiZrWiDlUOpwDPRR2iNO5eCPwVWAQsBX5w93ejTVWqGcBgM2tkZjWBI4FWEWeSCkj2ckVlSkKoXEkclSt7rkLliiooETOz2sC/gavcfU3Uecri7tvcvRfQEhgQNtUlFTM7Glju7pOjzlIO+7t7H+AI4LKwC0myyQD6AP9y997AeuAP0UbaubC7wLHAi1FnKY2ZNQCGExTSLYBaZnZGtKl+zt1nA/8HvEvQDD8N2BZlJim/VChXVKYkhMqVBFC5Eh8VLVdUQYlQ2Pf238Az7v5y1HnKI2yKHQMcHnGU0uwHHBv2wx0FHGRmT0cbqXThFQ/cfTnwCkGfzGSzGFgcc2XzJYKCJZkdAUxx92VRBynDwcBCd//O3bcCLwP7RpypVO7+qLv3dfcDgFXAvKgzya6lWrmiMiV+VK4kjMqVOKlIuaIKSkTCQYKPArPd/e6o8+yMmTUxs/rh/RrAIcCcSEOVwt2vdfeW7t6WoDn2A3dPuqsIZlYrHMBK2LR9KEHTZ1Jx92+Bb8wsP9w0DEiqwbalOJUkbYYPLQL2MbOa4XfAMIJxAknHzHLDf1sT9BN+NtpEsiupUq6oTIk/lSsJpXIlTipSrmRUVqjKYmbPAUOAxma2GLjR3R+NNlWp9gPOBKaH/XABrnP3N6OLVKbmwBPhLBZpwAvuntTTLSa5psArwfcIGcCz7v52tJHK9CvgmbCJewFwbsR5yhQWyocAF0edpSzuPt7MXgKmAEXAVOChaFOV6d9m1gjYClyWIgNZE0LlStypTIk/lSsJoHIl7spdrlS5aYZFRERERCR1qYuXiIiIiIgkDVVQREREREQkaaiCIiIiIiIiSUMVFBERERERSRqqoIiIiIiISNJQBUWkgsyspZm9amZfmNkCM/uHmWWX47x1ZWy/xcwODu9fZWY1d/E8h5nZzWbW0Mze2r13ISIiyULlisiOVEERqYBwEaSXgdHu3hHoCNQA7tjd53T3G9z9/fDhVcBOCxJgMPBR+O/Y3X1dERGJnsoVkZ/TOigiFWBmwwgWaTsgZltd4GugFXAC0M/dLw/3vQ781d0LwitdDxOs8PstcIq7f2dmjwOvAy2AvwJzgRXuPrTEa58MXAvsFb5eU2ANMMvdj03cuxYRkURRuSLyc2pBEamYbsDk2A3uvgb4Cuiwi3NrAZPcvRvwIXBjiee5D1gCDC1ZiIT7nwd6AzPcvQcwHeitQkREJKWpXBEpQRUUkcpTDDwf3n8a2H83nqMTsCC8X8vd18YjmIiIpCSVK1IlqYIiUjGzgL6xG8Km+GYETehF7Pj/Kmcnz1Wh/pVmNgl4BxhiZrOAfDObZmaDK/I8IiKSVFSuiJSgCopIxfwXqGlmZwGYWTpwF/APd99I0CTfy8zSzKwVMCDm3DSCvsQAp1H6QMS1QJ3SXtjd+wFvAMMJBk9e7+693P3jPX5XIiISFZUrIiWogiJSAR7MKnEccIKZfQF8DxS7+23hIf8DFhJcEbsPmBJz+npggJnNAA4CbinlJR4C3jazMWVE6ANMI5hp5cM9ezciIhI1lSsiP6dZvET2gJntCzwHHOfuU3Z1vIiIyM6oXBFRBUVERERERJKIuniJiIiIiEjSUAVFRERERESShiooIiIiIiKSNFRBERERERGRpKEKioiIiIiIJA1VUEREREREJGn8f8pM5/Sowfe5AAAAAElFTkSuQmCC" + }, + "metadata": { + "needs_background": "light" + } + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "It can be seen that as the number of qubits increases, the maximum value of the gradient of all parameters obtained by multiple sampling is constantly close to 0, and the variance is also decreasing." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "To further see how the gradient changes as the number of quantum bits increases, we might as well visualize the influence of choosing different qubits on the optimization landscape:\n", + "\n", + "![BP-fig-qubit_landscape_compare](./figures/BP-fig-qubit_landscape_compare.png \"(a) Optimization landscape sampled for 2,4,and 6 qubits from left to right in different z-axis scale. (b) Same landscape in a fixed z-axis scale.\")\n", + "\n", + "$\\theta_1$ and $\\theta_2$ are the first two circuit parameters, and the remaining parameters are all fixed to $\\pi$. This way, it helps us visualize the shape of this high-dimensional manifold. Unsurprisingly, the landscape becomes more flatter as $n$ increases. **Notice the rapidly decreasing scale in the $z$-axis**. Compared with the 2-qubit case, the optimized landscape of 6 qubits is very flat.\n", + "\n", + "Note that only when the network structure and loss function meet certain conditions, i.e. unitary 2-design (see paper [1]), this effect will appear.\n" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### Application II: Quantum encoded classical data\n", + "\n", + "Supervised learning is one of the important applications of quantum neural networks. However, the barren plateau phenomenon limits the performance of quantum variational algorithms in such problems. Therefore, how to design more efficient circuits and loss functions to avoid the barren plateau phenomenon is one of the important research directions of quantum neural networks at present.\n", + "\n", + "In fact, it has been shown that using Renyi divergence as a loss function in the training of generative training can effectively avoid the barren plateau phenomenon [[3]](https://arxiv.org/abs/2106.09567). \n", + "The gradient analysis tools allow us to quickly analyze the information related to the gradient in a supervised learning model, which can facilitate researchers to try to explore different quantum circuits and loss functions." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Here, we present an example using the dataset provided by [Encoding Classical Data into Quantum States](./tutorial/machine_learning/DataEncoding_EN.ipynb)." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "#### Paddle Quantum Implement\n", + "\n", + "Firstly, import the packages needed for the problem." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 14, + "source": [ + "from paddle_quantum.circuit import UAnsatz\n", + "from paddle import matmul, transpose, reshape\n", + "from paddle_quantum.utils import pauli_str_to_matrix\n", + "import paddle.fluid as fluid\n", + "import paddle.fluid.layers as layers\n", + "\n", + "from paddle_quantum.dataset import Iris\n", + "from paddle_quantum.gradtool import random_sample_supervised, plot_supervised_loss_grad" + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "#### Define Quantum Circuits\n", + "\n", + "Next, construct the parameterized quantum circuit $U(\\theta)$." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 15, + "source": [ + "def U_theta(theta, n, depth):\n", + " \"\"\"\n", + " :param theta: dimension: [n, depth + 3]\n", + " :param n: the number of qubits\n", + " :param depth: circuit depth\n", + " :return: U_theta\n", + " \"\"\"\n", + " # Initialize the quantum circuit\n", + " cir = UAnsatz(n)\n", + "\n", + " # rotation gates \n", + " for i in range(n):\n", + " cir.rz(theta[i][0], i)\n", + " cir.ry(theta[i][1], i)\n", + " cir.rz(theta[i][2], i)\n", + "\n", + " # default depth = 1\n", + " # Build adjacent CNOT gates and RY rotation gates \n", + " for d in range(3, depth + 3):\n", + " for i in range(n - 1):\n", + " cir.cnot([i, i + 1])\n", + " cir.cnot([n - 1, 0])\n", + " for i in range(n):\n", + " cir.ry(theta[i][d], i)\n", + " return cir" + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "#### Define Objective Function\n", + "\n", + "Here the objective function ``loss_fun`` is defined, and the second parameter is still the variable ``*args``." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 16, + "source": [ + "def loss_func(cir,*args):\n", + " # input the quantum states and training labels\n", + " state_in = args[0]\n", + " label = args[1]\n", + " # Convert Numpy array to tensor\n", + " label_pp = reshape(paddle.to_tensor(label),(-1,1))\n", + " \n", + " Utheta = cir.U\n", + " \n", + " # Since Utheta is learned, we use row vector operations here to speed up the training without affecting the results\n", + " state_out = matmul(state_in,Utheta)\n", + " \n", + " # Measure the expected value of the Pauli Z operator \n", + " Ob = paddle.to_tensor(pauli_str_to_matrix([[1.0, 'z0']], qubit_num))\n", + " E_Z = matmul(matmul(state_out, Ob), transpose(paddle.conj(state_out), perm=[0, 2, 1]))\n", + "\n", + " # Mapping into label \n", + " state_predict = paddle.real(E_Z)[:, 0] * 0.5 + 0.5\n", + " loss = paddle.mean((state_predict - label_pp) ** 2) # mean-squared error\n", + " \n", + " return loss\n", + " " + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "#### Define the dataset\n", + "\n", + "Here, we use [Iris dataset](./tutorial/machine_learning/DataEncoding_EN.ipynb) to do the experiment." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 17, + "source": [ + "time_start = time.time()\n", + "# Hyper parameter settings\n", + "test_rate = 0.2\n", + "qubit_num = 2 # Don't give too many qubits, otherwise it will be seriously overfitted\n", + "depth = 1\n", + "lr = 0.1\n", + "BATCH = 4\n", + "EPOCH = 4\n", + "SAMPLE = 300\n", + "\n", + "# dataset\n", + "iris = Iris(encoding='amplitude_encoding', num_qubits=qubit_num, test_rate=test_rate,classes=[0,1], return_state=True)\n", + "\n", + "# Get inputs and labels for the dataset\n", + "train_x, train_y = iris.train_x, iris.train_y # train_x, test_x here is paddle.tensor type, train_y，test_y here is ndarray type.\n", + "test_x, test_y = iris.test_x, iris.test_y\n", + "testing_data_num = len(test_y)\n", + "training_data_num = len(train_y)\n", + "\n", + "\n", + "# Creating trainable parameters for circuits\n", + "theta = layers.create_parameter(shape=[qubit_num,depth+3], default_initializer=paddle.nn.initializer.Uniform(low=0.0, high=2 * np.pi),\n", + " dtype='float64',is_bias=False)\n", + "# Creating Circuits\n", + "circuit = U_theta(theta, qubit_num, depth)\n", + "\n", + "print(circuit)" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "--Rz(3.338)----Ry(2.554)----Rz(1.318)----*----x----Ry(4.679)--\n", + " | | \n", + "--Rz(0.246)----Ry(3.961)----Rz(5.514)----x----*----Ry(3.248)--\n", + " \n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Let's look at the variation of the loss function values and gradients during training with EPOCH=4 and BATCH=4." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 18, + "source": [ + "loss,grad = plot_supervised_loss_grad(circuit, loss_func, N=qubit_num, EPOCH = EPOCH, LR = lr,BATCH = BATCH, TRAIN_X=train_x, TRAIN_Y=train_y)" + ], + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
    " + ], + "image/png": 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" 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" + }, + "metadata": { + "needs_background": "light" + } + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "We can see that after ten steps of iteration, the value of the loss function only fluctuates in a small range, indicating that the training process is stable." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Then we randomly sample the initial parameters of the model 300 times, and here we choose the ``max`` mode to see the mean and variance of the maximum gradient for all parameters." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 19, + "source": [ + "mean, variance = random_sample_supervised(circuit,loss_func, N=qubit_num, sample_num=SAMPLE, BATCH=BATCH, TRAIN_X=train_x, TRAIN_Y=train_y, mode='max')" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + "Sampling: 100%|###################################################| 300/300 [00:21<00:00, 13.65it/s]\n" + ] + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Mean of max gradient\n", + "0.19336918419398885\n", + "Variance of max gradient\n", + "0.011469917351120164\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
    " + ], + "image/png": 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+ }, + "metadata": { + "needs_background": "light" + } + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "## Summary\n", + "\n", + "The trainability problem is a core direction of current research in quantum neural networks, and the gradient analysis tool provided by Quantum Paddle supports users to diagnose the trainability of the model, facilitating the study of subsequent problems such as barren plateaus." + ], + "metadata": {} + }, + { + "cell_type": "markdown", "source": [ "_______\n", "\n", @@ -573,15 +1197,17 @@ "\n", "[1] McClean, J. R., Boixo, S., Smelyanskiy, V. N., Babbush, R. & Neven, H. Barren plateaus in quantum neural network training landscapes. [Nat. Commun. 9, 4812 (2018).](https://www.nature.com/articles/s41467-018-07090-4)\n", "\n", - "[2] Cerezo, M., Sone, A., Volkoff, T., Cincio, L. & Coles, P. J. Cost-Function-Dependent Barren Plateaus in Shallow Quantum Neural Networks. [arXiv:2001.00550 (2020).](https://arxiv.org/abs/2001.00550)" - ] + "[2] Cerezo, M., Sone, A., Volkoff, T., Cincio, L. & Coles, P. J. Cost-Function-Dependent Barren Plateaus in Shallow Quantum Neural Networks. [arXiv:2001.00550 (2020).](https://arxiv.org/abs/2001.00550)\n", + "\n", + "[3] Kieferova, Maria, Ortiz Marrero Carlos, and Nathan Wiebe. \"Quantum Generative Training Using R\\'enyi Divergences.\" arXiv preprint [arXiv:2106.09567 (2021).](https://arxiv.org/abs/2106.09567)" + ], + "metadata": {} } ], "metadata": { "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" + "name": "python3", + "display_name": "Python 3.7.11 64-bit" }, "language_info": { "codemirror_mode": { @@ -593,7 +1219,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.10" + "version": "3.7.11" }, "toc": { "base_numbering": 1, @@ -636,8 +1262,11 @@ "_Feature" ], "window_display": false + }, + "interpreter": { + "hash": "3b61f83e8397e1c9fcea57a3d9915794102e67724879b24295f8014f41a14d85" } }, "nbformat": 4, "nbformat_minor": 4 -} +} \ No newline at end of file diff --git a/tutorial/qnn_research/Fisher_CN.ipynb b/tutorial/qnn_research/Fisher_CN.ipynb new file mode 100644 index 0000000..8ed323d --- /dev/null +++ b/tutorial/qnn_research/Fisher_CN.ipynb @@ -0,0 +1,987 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# 量子费舍信息\n", + "\n", + " Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. " + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "## 概览\n", + "\n", + "本教程简要介绍经典费舍信息（classical Fisher information, CFI）和量子费舍信息（quantum Fisher information, QFI）的概念及其在量子机器学习中的应用，并展示如何调用量桨来计算它们。" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "## 背景\n", + "\n", + "量子费舍信息这一概念源自量子传感领域，现已逐渐成为研究参数化量子系统的通用工具 [[1]](https://arxiv.org/abs/2103.15191)，例如描述过参数化现象 [[2]](https://arxiv.org/abs/2102.01659)，量子自然梯度下降 [[3]](https://arxiv.org/abs/1909.02108) 等。量子费舍信息是经典费舍信息在量子系统中的自然类比。经典费舍信息刻画了一个参数化的『概率分布』对其参数变化的灵敏度，而量子费舍信息刻画了一个参数化的『量子态』对其参数变化的灵敏度。\n", + "\n", + "按照传统的介绍方式，经典费舍信息会作为数理统计中参数估计的一部分内容出现，但对于初学者来说可能是复杂且不直观的。本教程将从几何的角度出发来介绍经典费舍信息，这不仅有助于直观理解，且更容易由此看出其与量子费舍信息之间的联系。" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### 经典费舍信息\n", + "\n", + "首先介绍经典费舍信息。对于一个参数化的概率分布 $p(\\boldsymbol{x};\\boldsymbol{\\theta})$，考虑如下问题\n", + "\n", + "- 一个轻微的参数改变会在多大程度上造成概率分布的改变？\n", + "\n", + "这是个关于微扰的问题，所以自然地想到做类似泰勒展开的操作。但在此之前，我们需要知道展开哪个函数，即我们需要量化『概率分布的改变』。更正式的说法是，我们需要定义任意两个概率分布之间的『距离』，记为 $d(p(\\boldsymbol{x};\\boldsymbol{\\theta}),p(\\boldsymbol{x};\\boldsymbol{\\theta}'))$，或简记为 $d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}')$。\n", + "\n", + "一般地，一个合法的距离定义应该是非负的，当且仅当两点重合时为零，即\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "&d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}')\\geq 0,\\\\\n", + "&d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}')=0~\\Leftrightarrow~\\boldsymbol{\\theta}=\\boldsymbol{\\theta}'.\n", + "\\end{aligned}\n", + "\\tag{1}\n", + "$$\n", + "\n", + "考虑一个很短的距离函数的展开 $d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})$，以上条件会导致\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "&d(\\boldsymbol{\\theta},\\boldsymbol{\\theta})=0~\\Rightarrow~\\text{零阶项}=0,\\\\\n", + "&d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})\\geq 0~\\Rightarrow~\\boldsymbol{\\delta}=0~\\text{取极小值}\n", + "~\\Rightarrow~\\text{一阶项}=0.\n", + "\\end{aligned}\n", + "\\tag{2}\n", + "$$\n", + "\n", + "因此，在这个展开中最低阶的非零贡献来自二阶。因此它可被写为\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})\n", + "=\\frac{1}{2}\\sum_{ij}\\delta_iM_{ij}\\delta_j+O(\\|\\boldsymbol{\\delta}\\|^3) \n", + "=\\frac{1}{2} \\boldsymbol{\\delta}^T M \\boldsymbol{\\delta} + O(\\|\\boldsymbol{\\delta}\\|^3),\n", + "\\end{aligned}\n", + "\\tag{3}\n", + "$$\n", + "\n", + "此处\n", + "\n", + "$$\n", + "M_{ij}(\\boldsymbol{\\theta})=\\left.\\frac{\\partial^2}{\\partial\\delta_i\\partial\\delta_j}d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})\\right|_{\\boldsymbol{\\delta}=0},\n", + "\\tag{4}\n", + "$$\n", + "\n", + "正是这个距离函数展开的海森矩阵。在微分几何的框架下，这称作流形的[度规](http://en.wikipedia.org/wiki/Metric_tensor)。以上简单的推导说明，我们总是可以用参数的一个二次型来近似表示一小段距离（如图1）。而二次型的系数矩阵，除了有一个 $1/2$ 因子的差别外，正是距离函数展开的海森矩阵。\n", + "\n", + "![feature map](./figures/FIM-fig-Sphere-metric.png \"Figure 1. Approximate a small distance on the 2-sphere as a quadratic form\")\n", + "
    图 1. 将一小段距离近似为二次型，此处以二维球面为例绘制
    \n", + "\n", + "如果我们定义概率分布之间的距离为相对熵或称 KL 散度\n", + "\n", + "$$\n", + "d_{\\mathrm{KL}}(\\boldsymbol{\\theta}, \\boldsymbol{\\theta}^{\\prime})=\\sum_{\\boldsymbol{x}} p(\\boldsymbol{x};\\boldsymbol{\\theta}) \\log \\frac{p(\\boldsymbol{x};\\boldsymbol{\\theta})}{p(\\boldsymbol{x};\\boldsymbol{\\theta}^{\\prime})}.\n", + "\\tag{5}\n", + "$$\n", + "\n", + "对应的海森矩阵为\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mathcal{I}_{ij}(\\boldsymbol{\\theta})&= \\left.\\frac{\\partial^2}{\\partial\\delta_i\\partial\\delta_j}d_{\\mathrm{KL}}(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})\\right|_{\\boldsymbol{\\delta}=0}\\\\\n", + "&=-\\sum_{\\boldsymbol{x}} p(\\boldsymbol{x};\\boldsymbol{\\theta}) \\partial_{i} \\partial_{j} \\log p(\\boldsymbol{x};\\boldsymbol{\\theta})\n", + "=\\mathbb{E}_{\\boldsymbol{x}}[-\\partial_{i} \\partial_{j} \\log p(\\boldsymbol{x};\\boldsymbol{\\theta})] \\\\\n", + "&=\\sum_{\\boldsymbol{x}} \\frac{1}{p(\\boldsymbol{x};\\boldsymbol{\\theta})} \\partial_i p(\\boldsymbol{x};\\boldsymbol{\\theta}) \\cdot \\partial_j p(\\boldsymbol{x};\\boldsymbol{\\theta})\n", + "=\\mathbb{E}_{\\boldsymbol{x}}[\\partial_i\\log p(\\boldsymbol{x};\\boldsymbol{\\theta})\\cdot \\partial_j \\log p(\\boldsymbol{x};\\boldsymbol{\\theta})].\n", + "\\end{aligned}\n", + "\\tag{6}\n", + "$$\n", + "\n", + "这就是所谓的经典费舍信息矩阵（classical Fisher information matrix, CFIM），矩阵元越大说明概率分布对相应的参数变化越灵敏。上式中我们使用了偏导数符号的简记 $\\partial_i=\\partial/\\partial \\theta_i$。\n", + "\n", + "为什么 $\\mathcal{I}(\\boldsymbol{\\theta})$ 称为『信息』？这是因为，CFIM 刻画了概率分布在对应参数一个领域内的灵敏度，或称锐度。对参数变化越灵敏，说明我们越容易将其同其它概率分布区分开来，进一步地，说明我们需要越少的样本就可以完成这种区分，那么每个样本中平均所含的信息量就越多。\n", + "\n", + "参数化量子电路（parameterized quantum circuit, PQC）的测量结果会形成一个概率分布，因此可以对不同的测量基定义不同的 CFIM。目前在 NISQ 设备上计算 CFIM 的主要挑战是，可能出现的测量结果的数量会随着量子比特数的增加而指数地增加，这意味着可能有很多小概率的测量结果从未出现过，导致 CFIM 的计算出现发散。一些可能的解决方案包括直接忽略小的概率事件，以及贝叶斯更新等 [[1]](https://arxiv.org/abs/2103.15191)。" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### 量子费舍信息\n", + "\n", + "量子费舍信息是经典费舍信息的自然类比，只是距离函数不再定义在两个概率分布之间，而是定义在两个量子态之间。我们通常选用保真度距离\n", + "\n", + "$$\n", + "d_f(\\boldsymbol{\\theta},\\boldsymbol{\\theta}')=2-2|\\langle\\psi(\\boldsymbol{\\theta})|\\psi(\\boldsymbol{\\theta}')\\rangle|^2.\n", + "\\tag{7}\n", + "$$\n", + "\n", + "此处因子 $2$ 是人为乘上去的，为的是让后续的结果与 CFIM 对应上。一个参数化量子纯态 $|\\psi(\\boldsymbol{\\theta})\\rangle, \\boldsymbol{\\theta}\\in\\mathbb{R}^m$ 的量子费舍信息矩阵（quantum Fisher information matrix, QFIM）就是保真度距离展开的海森矩阵，即\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mathcal{F}_{ij}(\\boldsymbol{\\theta})\n", + "&= \\left.\\frac{\\partial^2}{\\partial\\delta_i\\partial\\delta_j}d_{f}(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})\\right|_{\\boldsymbol{\\delta}=0} \\\\\n", + "&=4 \\operatorname{Re}\\left[\\left\\langle\\partial_{i} \\psi \\mid \\partial_{j} \\psi\\right\\rangle - \\left\\langle\\partial_{i} \\psi \\mid \\psi\\right\\rangle\\left\\langle\\psi \\mid \\partial_{j} \\psi\\right\\rangle\\right],\n", + "\\end{aligned}\n", + "\\tag{8}\n", + "$$\n", + "\n", + "上式中简洁起见我们略写了自变量 $\\boldsymbol{\\theta}$。与 CFIM 类似，QFIM 刻画了参数化量子态对参数微小变化的灵敏度。此外值得一提的是，QFIM 可以被视为另一个被称作量子几何张量的复数矩阵的实部，或称为 Fubini-Study 度规 [[1]](https://arxiv.org/abs/2103.15191)。\n", + "\n", + "目前，人们已经提出了一些在 NISQ 设备上计算纯态 QFIM 的方法，其中最直接的两个方法是\n", + "\n", + "- 利用二阶参数平移规则计算每个矩阵元 [[4]](https://arxiv.org/abs/2008.06517)\n", + "$$\n", + "\\begin{aligned}\n", + "\\mathcal{F}_{i j}=-\\frac{1}{2} \\Big(&|\\langle\\psi(\\boldsymbol{\\theta}) \\mid \\psi(\\boldsymbol{\\theta}+(\\boldsymbol{e}_{i}+\\boldsymbol{e}_{j}) \\frac{\\pi}{2})\\rangle|^{2}\n", + "-|\\langle\\psi(\\boldsymbol{\\theta}) \\mid \\psi(\\boldsymbol{\\theta}+(\\boldsymbol{e}_{i}-\\boldsymbol{e}_{j}) \\frac{\\pi}{2})\\rangle|^{2}\\\\\n", + "-&|\\langle\\psi(\\boldsymbol{\\theta}) \\mid \\psi(\\boldsymbol{\\theta}-(\\boldsymbol{e}_{i}-\\boldsymbol{e}_{j}) \\frac{\\pi}{2})\\rangle|^{2}\n", + "+|\\langle\\psi(\\boldsymbol{\\theta}) \\mid \\psi(\\boldsymbol{\\theta}-(\\boldsymbol{e}_{i}+\\boldsymbol{e}_{j}) \\frac{\\pi}{2})\\rangle|^{2}\\Big),\n", + "\\end{aligned}\n", + "\\tag{9}\n", + "$$\n", + "其中 $\\boldsymbol{e}_{i}$ 是 $\\theta_i$ 对应方向的单位向量。\n", + "\n", + "- 利用有限差分计算 QFIM 沿一个确定方向的投影 [[1]](https://arxiv.org/abs/2103.15191)\n", + "$$\n", + "\\boldsymbol{v}^{T} \\mathcal{F} \\boldsymbol{v} \\approx \\frac{4 d_{f}(\\boldsymbol{\\theta}, \\boldsymbol{\\theta}+\\epsilon \\boldsymbol{v})}{\\epsilon^{2}}.\n", + "\\tag{10}\n", + "$$\n", + "这个量可以被视为著名的 Fisher-Rao 模在量子态空间的类比。\n", + "\n", + "对于混态，QFIM 可以类似地通过 Bures 保真度距离的展开来定义\n", + "\n", + "$$\n", + "d_B(\\boldsymbol{\\theta},\\boldsymbol{\\theta}')\\equiv \n", + "2-2\\left[\\text{Tr}\\left([\\sqrt{\\rho(\\boldsymbol{\\theta})} \\rho(\\boldsymbol{\\theta}')\\sqrt{\\rho(\\boldsymbol{\\theta})}]^{1/2}\\right)\\right]^2,\n", + "\\tag{11}\n", + "$$\n", + "\n", + "或者等价地（$\\log x\\sim x-1$），通过如下形式的 $\\alpha=1/2$ 的 Rényi 相对熵的展开来定义 [[5]](https://arxiv.org/abs/1308.5961)\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "d_R(\\boldsymbol{\\theta},\\boldsymbol{\\theta}') &\\equiv 2\\widetilde{D}_{\\alpha=1/2}(\\rho(\\boldsymbol{\\theta'}) \\| \\rho(\\boldsymbol{\\theta})), \\\\\n", + "\\widetilde{D}_{\\alpha}(\\rho \\| \\sigma) \n", + "&\\equiv \n", + "\\frac{1}{\\alpha-1} \\log \\operatorname{Tr}\\left[\\left(\\sigma^{\\frac{1-\\alpha}{2 \\alpha}} \\rho \\sigma^{\\frac{1-\\alpha}{2 \\alpha}}\\right)^{\\alpha}\\right].\\\\\n", + "\\end{aligned}\n", + "\\tag{12}\n", + "$$\n", + "\n", + "更多细节请参考这篇综述 [[1]](https://arxiv.org/abs/2103.15191) 。" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### 经典与量子费舍信息的关系\n", + "\n", + "根据定义，对于一个参数化的量子电路，CFIM 依赖于测量基，而 QFIM 不依赖。事实上可以证明，一个量子态 $\\rho(\\boldsymbol{\\theta})$ 的 QFIM 是其在任意测量基下对应 CFIM 的一个上限，即\n", + "\n", + "$$\n", + "\\mathcal{I}[\\mathcal{E}[\\rho(\\boldsymbol{\\theta})]]\\leq \\mathcal{F}[\\rho(\\boldsymbol{\\theta})],~\\forall\\mathcal{E},\n", + "\\tag{13}\n", + "$$\n", + "\n", + "此处 $\\mathcal{E}$ 表示测量对应的量子操作。正定矩阵间不等式的含义是，大的减去小的结果仍然是一个正定矩阵。由于对量子态的测量永远无法提取出比量子态本身更多的信息，因此上式的成立是很自然的。数学上这根源于保真度距离对于保迹量子操作的单调性 [[1]](https://arxiv.org/abs/2103.15191)。" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### 应用：有效维数\n", + "\n", + "经典/量子费舍信息矩阵的秩在参数空间的最大值可以用来衡量神经网络表达能力，称为经典/量子有效维数\n", + "\n", + "$$\n", + "d_{\\text{eff}}=\\underset{\\boldsymbol{\\theta}\\in\\Theta} {\\max}\n", + "\\operatorname{rank}{\\mathcal{F}}(\\boldsymbol{\\theta}).\n", + "\\tag{14}\n", + "$$\n", + "\n", + "秩的大小刻画了参数变化会造成概率分布/量子态变化的方向的数量。非满秩意味着有一些特定方向的参数变化不能实际地导致概率分布/量子态发生变化，或者说有一些参数自由度是冗余的，可以把它们从模型中投影掉，因此这种现象被称作过参数化。另一方面，有效维数越大，对应着更多可以延伸的方向，这意味着模型对应的函数空间更大，即表达能力更强。\n", + "\n", + "在机器学习的语境下，『经验费舍信息矩阵』[[6]](https://arxiv.org/abs/2011.00027) 的使用更为广泛，它与 CFIM 的区别是用对样本的求和代替了求期望\n", + "\n", + "$$\n", + "\\tilde{\\mathcal{I}}_{ij}(\\boldsymbol{\\theta})\n", + "=\\frac{1}{n}\\sum_{k=1}^{n}\n", + "\\partial_i\\log p(x_k,y_k;\\boldsymbol{\\theta})\n", + "\\partial_j\\log p(x_k,y_k;\\boldsymbol{\\theta}),\n", + "\\tag{15}\n", + "$$\n", + "\n", + "此处 $(x_k,y_k)^{n}_{k=1}$ 是独立同分布的样本，分布为 $p(x,y;\\boldsymbol{\\theta})=p(y|x;\\boldsymbol{\\theta})p(x)$。显然，经验费舍信息矩阵在无限样本的极限下可以回到 CFIM，只要满足（1）模型被训练到全局最优；（2）模型拥有足够的表达能力来表达底层的数据分布。使用经验费舍信息矩阵的优势在于，它可以利用现成的样本直接计算，而不是为了计算公式中的积分而生成新的样本。\n", + "\n", + "利用经验费舍信息矩阵，我们可以定义有效维数的一个变体 \n", + "\n", + "$$\n", + "d_{\\text{eff}}(\\gamma, n)=\n", + "2 \\frac{\\log \\left(\\frac{1}{V_{\\Theta}} \\int_{\\Theta} \\sqrt{\\operatorname{det}\\left( 1 + \\frac{\\gamma n}{2 \\pi \\log n} \\hat{\\mathcal{I}}( \\boldsymbol{\\theta})\\right)} \\mathrm{d} \\boldsymbol{\\theta} \\right)}\n", + "{\\log \\left(\\frac{\\gamma n}{2 \\pi \\log n}\\right)},\n", + "\\tag{16}\n", + "$$\n", + "\n", + "其中 $V_{\\Theta}:=\\int_{\\Theta} \\mathrm{d} \\boldsymbol{\\theta} \\in \\mathbb{R}_{+}$ 是参数空间的体积。$\\gamma\\in(0,1]$ 是一个人为可调参数。$\\hat{\\mathcal{I}} (\\boldsymbol{\\theta}) \\in \\mathbb{R}^{d\\times d}$ 是归一化的经验费舍信息矩阵\n", + "\n", + "$$\n", + "\\hat{\\mathcal{I}}_{i j}(\\boldsymbol{\\theta}):= \\frac{V_{\\Theta} d }{\\int_{\\Theta} \\operatorname{Tr}(F( \\boldsymbol{\\theta} ) \\mathrm{d} \\theta} \\tilde{\\mathcal{I}}_{i j}(\\boldsymbol{\\theta}).\n", + "\\tag{17}\n", + "$$\n", + "\n", + "这个定义乍看起来可能很迷惑，因为它比上文通过秩来定义要复杂得多。然而，它实际上可以在无限样本的极限下 $n\\rightarrow \\infty$ 回到 CFIM 最大秩的定义 [[6]](https://arxiv.org/abs/2011.00027)。若忽略定义中的一些系数和取对数的操作，此处定义的有效维数可以粗略地看作归一化 CFIM 加上一个单位矩阵的本征谱的几何平均。依据几何平均与算术平均间的不等式关系，可知本征谱分布越均匀，有效维数越大。这和我们的直觉是一致的。在这个意义上，它可以看作是一个软化版本的有效维数。\n", + "\n", + "另外，费舍信息不仅可以用来计算模型的表达能力，还可以用来表征模型的可训练性。如果费舍信息矩阵的矩阵元在参数空间的平均随体系规模的增大而指数地趋于零，即概率分布/量子态对参数变化的灵敏度指数地趋于零，那么我们将无法高效地区分它们，也就意味着贫瘠高原现象的存在 [[6]](https://arxiv.org/abs/2011.00027)。" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "## 调用量桨计算费舍信息" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### 计算量子费舍信息\n", + "\n", + "利用量桨工具，通过以下步骤我们就可以方便地算出 QFIM。\n", + "\n", + "1. 调用 `UAnsatz` 类定义一个量子电路。\n", + "2. 调用 `QuantumFisher` 类定义一个 QFIM 计算器。\n", + "3. 调用 `get_qfisher_matrix()` 方法计算 QFIM。\n", + "\n", + "其中计算器 `QuantumFisher` 会追踪量子电路 `UAnsatz` 的实时变化。\n", + "\n", + "现在来着手写代码。首先导入一些必要的包。" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 1, + "source": [ + "import paddle\n", + "from paddle_quantum.circuit import UAnsatz\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from paddle_quantum.utils import QuantumFisher, ClassicalFisher\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\")" + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "然后定义量子电路。作为一个简单的例子，我们采用布洛赫角表示的单个量子比特\n", + "\n", + "$$\n", + "|\\psi(\\theta,\\phi)\\rangle=R_z(\\phi)R_y(\\theta)|0\\rangle=e^{-i\\phi/2}\\cos\\frac{\\theta}{2}|0\\rangle+e^{i\\phi/2}\\sin\\frac{\\theta}{2}|1\\rangle.\n", + "\\tag{18}\n", + "$$\n", + "\n", + "利用 (8) 式可以计算出对应 QFIM 的解析表达式为\n", + "\n", + "$$\n", + "\\mathcal{F}(\\theta,\\phi)=\\left(\\begin{matrix}\n", + "1&0\\\\\n", + "0&\\sin^2\\theta\n", + "\\end{matrix}\\right).\n", + "\\tag{19}\n", + "$$" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 2, + "source": [ + "def circuit_bloch():\n", + " cir = UAnsatz(1)\n", + " theta = 2 * np.pi * np.random.random(2)\n", + " theta = paddle.to_tensor(theta, stop_gradient=False, dtype='float64')\n", + " cir.ry(theta[0], which_qubit=0)\n", + " cir.rz(theta[1], which_qubit=0)\n", + " \n", + " return cir" + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 3, + "source": [ + "cir = circuit_bloch()\n", + "print(cir)" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "--Ry(1.888)----Rz(2.181)--\n", + " \n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "定义 QFIM 计算器然后计算不同 $\\theta$ 对应的 QFIM 矩阵元 $\\mathcal{F}_{\\phi\\phi}$ 。" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 4, + "source": [ + "qf = QuantumFisher(cir)\n", + "# 记录 QFIM 的矩阵元 F_{phi,phi}\n", + "list_qfisher_elements = []\n", + "num_thetas = 21\n", + "thetas = np.linspace(0, np.pi, num_thetas)\n", + "for theta in thetas:\n", + " list_param = cir.get_param().tolist()\n", + " list_param[0] = theta\n", + " cir.update_param(list_param)\n", + " # 计算 QFIM\n", + " qfim = qf.get_qfisher_matrix()\n", + " print(f'The QFIM at {np.array(list_param)} is \\n {qfim.round(14)}.')\n", + " list_qfisher_elements.append(qfim[1][1])" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "The QFIM at [0. 2.18107874] is \n", + " [[1. 0.]\n", + " [0. 0.]].\n", + "The QFIM at [0.15707963 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.02447174]].\n", + "The QFIM at [0.31415927 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.0954915]].\n", + "The QFIM at [0.4712389 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.20610737]].\n", + "The QFIM at [0.62831853 2.18107874] is \n", + " [[ 1. -0. ]\n", + " [-0. 0.3454915]].\n", + "The QFIM at [0.78539816 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.5]].\n", + "The QFIM at [0.9424778 2.18107874] is \n", + " [[ 1. -0. ]\n", + " [-0. 0.6545085]].\n", + "The QFIM at [1.09955743 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.79389263]].\n", + "The QFIM at [1.25663706 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.9045085]].\n", + "The QFIM at [1.41371669 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.97552826]].\n", + "The QFIM at [1.57079633 2.18107874] is \n", + " [[1. 0.]\n", + " [0. 1.]].\n", + "The QFIM at [1.72787596 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.97552826]].\n", + "The QFIM at [1.88495559 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.9045085]].\n", + "The QFIM at [2.04203522 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.79389263]].\n", + "The QFIM at [2.19911486 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.6545085]].\n", + "The QFIM at [2.35619449 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.5]].\n", + "The QFIM at [2.51327412 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.3454915]].\n", + "The QFIM at [2.67035376 2.18107874] is \n", + " [[ 1. -0. ]\n", + " [-0. 0.20610737]].\n", + "The QFIM at [2.82743339 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.0954915]].\n", + "The QFIM at [2.98451302 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.02447174]].\n", + "The QFIM at [3.14159265 2.18107874] is \n", + " [[1. 0.]\n", + " [0. 0.]].\n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "画出 $\\mathcal{F}_{\\phi\\phi}$ 随 $\\theta$ 变化的图像。" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 5, + "source": [ + "# 创建图像\n", + "fig = plt.figure(figsize=(9, 6))\n", + "ax = fig.add_subplot(111)\n", + "# 绘制 QFIM\n", + "ax.plot(thetas, list_qfisher_elements, 's', markersize=11, markerfacecolor='none')\n", + "# 绘制 sin^2 theta\n", + "ax.plot(thetas, np.sin(thetas) ** 2, linestyle=(0, (5, 3)))\n", + "# 设置图例，标签，刻度\n", + "label_font_size = 18\n", + "ax.legend(['get_qfisher_matrix()[1][1]', '$\\\\sin^2\\\\theta$'], \n", + " prop= {'size': label_font_size}, frameon=False) \n", + "ax.set_xlabel('$\\\\theta$', fontsize=label_font_size)\n", + "ax.set_ylabel('QFIM element $\\\\mathcal{F}_{\\\\phi\\\\phi}$', fontsize=label_font_size)\n", + "ax.tick_params(labelsize=label_font_size)" + ], + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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" + }, + "metadata": { + "needs_background": "light" + } + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "可以看到程序输出和解析结果是一致的。\n", + "\n", + "此外，我们还可以调用 `get_qfisher_norm()` 方法来计算式 (10) 中的量子费舍信息矩阵在某个方向的投影。\n", + "\n", + "举一个和上面不同的例子，两个量子比特上的一个典型的 hardware-efficient 拟设\n", + "\n", + "$$\n", + "|\\psi(\\boldsymbol{\\theta})\\rangle=\\left[R_{y}\\left( \\theta_{3}\\right) \\otimes R_{y}\\left( \\theta_{4}\\right)\\right] \\text{CNOT}_{0,1}\\left[ R_{y}\\left( \\theta_{1}\\right) \\otimes R_{y}\\left( \\theta_{2}\\right)\\right]|00\\rangle.\n", + "\\tag{20}\n", + "$$\n", + "\n", + "对应的 QFIM 为\n", + "\n", + "$$\n", + "\\mathcal{F}(\\theta_1,\\theta_2,\\theta_3,\\theta_4)=\\left(\\begin{array}{cc|cc}\n", + "1 & 0 & \\sin \\theta_{2} & 0 \\\\\n", + "0 & 1 & 0 & \\cos \\theta_{1} \\\\\n", + "\\hline \n", + "\\sin \\theta_{2} & 0 & 1 & -\\sin\\theta_1\\cos\\theta_2 \\\\\n", + "0 & \\cos \\theta_{1} & -\\sin\\theta_1\\cos\\theta_2 & 1\n", + "\\end{array}\\right).\n", + "\\tag{21}\n", + "$$\n", + "\n", + "定义相应的量子电路。" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 6, + "source": [ + "def circuit_hardeff_2qubit():\n", + " cir = UAnsatz(2)\n", + " theta = 2 * np.pi * np.random.random(4)\n", + " theta = paddle.to_tensor(theta, stop_gradient=False, dtype='float64')\n", + " cir.ry(theta[0], which_qubit=0)\n", + " cir.ry(theta[1], which_qubit=1)\n", + " cir.cnot(control=[0, 1])\n", + " cir.ry(theta[2], which_qubit=0)\n", + " cir.ry(theta[3], which_qubit=1)\n", + "\n", + " return cir" + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 7, + "source": [ + "cir = circuit_hardeff_2qubit()\n", + "print(cir)" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "--Ry(2.614)----*----Ry(3.253)--\n", + " | \n", + "--Ry(2.906)----x----Ry(5.027)--\n", + " \n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "定义 QFIM 计算器并计算不同 $\\theta$ 对应的 QFIM 在 $\\boldsymbol{v}=(1,1,1,1)$ 方向上的投影 $\\boldsymbol{v}^T\\mathcal{F}\\boldsymbol{v}$ （固定 $\\theta_1=\\theta_2=\\theta$）。" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 8, + "source": [ + "qf = QuantumFisher(cir)\n", + "v = [1, 1, 1, 1]\n", + "# 记录 QFIM 投影\n", + "list_qfisher_norm = []\n", + "num_thetas = 41\n", + "thetas = np.linspace(0, np.pi * 4, num_thetas)\n", + "for theta in thetas:\n", + " list_param = cir.get_param().tolist()\n", + " list_param[0] = theta\n", + " list_param[1] = theta\n", + " cir.update_param(list_param)\n", + " # 计算 QFIM 投影\n", + " qfisher_norm = qf.get_qfisher_norm(v)\n", + " print(\n", + " f'The QFI norm along {v} at {np.array(list_param)} is {qfisher_norm:.8f}.'\n", + " )\n", + " list_qfisher_norm.append(qfisher_norm)" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "The QFI norm along [1, 1, 1, 1] at [0. 0. 3.2533421 5.02652273] is 5.99962501.\n", + "The QFI norm along [1, 1, 1, 1] at [0.31415927 0.31415927 3.2533421 5.02652273] is 5.93033916.\n", + "The QFI norm along [1, 1, 1, 1] at [0.62831853 0.62831853 3.2533421 5.02652273] is 5.84133590.\n", + "The QFI norm along [1, 1, 1, 1] at [0.9424778 0.9424778 3.2533421 5.02652273] is 5.84309143.\n", + "The QFI norm along [1, 1, 1, 1] at [1.25663706 1.25663706 3.2533421 5.02652273] is 5.93367838.\n", + "The QFI norm along [1, 1, 1, 1] at [1.57079633 1.57079633 3.2533421 5.02652273] is 5.99962501.\n", + "The QFI norm along [1, 1, 1, 1] at [1.88495559 1.88495559 3.2533421 5.02652273] is 5.86697827.\n", + "The QFI norm along [1, 1, 1, 1] at [2.19911486 2.19911486 3.2533421 5.02652273] is 5.38230779.\n", + "The QFI norm along [1, 1, 1, 1] at [2.51327412 2.51327412 3.2533421 5.02652273] is 4.49128513.\n", + "The QFI norm along [1, 1, 1, 1] at [2.82743339 2.82743339 3.2533421 5.02652273] is 3.28287364.\n", + "The QFI norm along [1, 1, 1, 1] at [3.14159265 3.14159265 3.2533421 5.02652273] is 1.97995933.\n", + "The QFI norm along [1, 1, 1, 1] at [3.45575192 3.45575192 3.2533421 5.02652273] is 0.87758767.\n", + "The QFI norm along [1, 1, 1, 1] at [3.76991118 3.76991118 3.2533421 5.02652273] is 0.25010151.\n", + "The QFI norm along [1, 1, 1, 1] at [4.08407045 4.08407045 3.2533421 5.02652273] is 0.26070618.\n", + "The QFI norm along [1, 1, 1, 1] at [4.39822972 4.39822972 3.2533421 5.02652273] is 0.90660775.\n", + "The QFI norm along [1, 1, 1, 1] at [4.71238898 4.71238898 3.2533421 5.02652273] is 2.01995733.\n", + "The QFI norm along [1, 1, 1, 1] at [5.02654825 5.02654825 3.2533421 5.02652273] is 3.32425271.\n", + "The QFI norm along [1, 1, 1, 1] at [5.34070751 5.34070751 3.2533421 5.02652273] is 4.52539873.\n", + "The QFI norm along [1, 1, 1, 1] at [5.65486678 5.65486678 3.2533421 5.02652273] is 5.40406149.\n", + "The QFI norm along [1, 1, 1, 1] at [5.96902604 5.96902604 3.2533421 5.02652273] is 5.87599852.\n", + "The QFI norm along [1, 1, 1, 1] at [6.28318531 6.28318531 3.2533421 5.02652273] is 5.99962501.\n", + "The QFI norm along [1, 1, 1, 1] at [6.59734457 6.59734457 3.2533421 5.02652273] is 5.93033916.\n", + "The QFI norm along [1, 1, 1, 1] at [6.91150384 6.91150384 3.2533421 5.02652273] is 5.84133590.\n", + "The QFI norm along [1, 1, 1, 1] at [7.2256631 7.2256631 3.2533421 5.02652273] is 5.84309143.\n", + "The QFI norm along [1, 1, 1, 1] at [7.53982237 7.53982237 3.2533421 5.02652273] is 5.93367838.\n", + "The QFI norm along [1, 1, 1, 1] at [7.85398163 7.85398163 3.2533421 5.02652273] is 5.99962501.\n", + "The QFI norm along [1, 1, 1, 1] at [8.1681409 8.1681409 3.2533421 5.02652273] is 5.86697827.\n", + "The QFI norm along [1, 1, 1, 1] at [8.48230016 8.48230016 3.2533421 5.02652273] is 5.38230779.\n", + "The QFI norm along [1, 1, 1, 1] at [8.79645943 8.79645943 3.2533421 5.02652273] is 4.49128513.\n", + "The QFI norm along [1, 1, 1, 1] at [9.1106187 9.1106187 3.2533421 5.02652273] is 3.28287364.\n", + "The QFI norm along [1, 1, 1, 1] at [9.42477796 9.42477796 3.2533421 5.02652273] is 1.97995933.\n", + "The QFI norm along [1, 1, 1, 1] at [9.73893723 9.73893723 3.2533421 5.02652273] is 0.87758767.\n", + "The QFI norm along [1, 1, 1, 1] at [10.05309649 10.05309649 3.2533421 5.02652273] is 0.25010151.\n", + "The QFI norm along [1, 1, 1, 1] at [10.36725576 10.36725576 3.2533421 5.02652273] is 0.26070618.\n", + "The QFI norm along [1, 1, 1, 1] at [10.68141502 10.68141502 3.2533421 5.02652273] is 0.90660775.\n", + "The QFI norm along [1, 1, 1, 1] at [10.99557429 10.99557429 3.2533421 5.02652273] is 2.01995733.\n", + "The QFI norm along [1, 1, 1, 1] at [11.30973355 11.30973355 3.2533421 5.02652273] is 3.32425271.\n", + "The QFI norm along [1, 1, 1, 1] at [11.62389282 11.62389282 3.2533421 5.02652273] is 4.52539873.\n", + "The QFI norm along [1, 1, 1, 1] at [11.93805208 11.93805208 3.2533421 5.02652273] is 5.40406149.\n", + "The QFI norm along [1, 1, 1, 1] at [12.25221135 12.25221135 3.2533421 5.02652273] is 5.87599852.\n", + "The QFI norm along [1, 1, 1, 1] at [12.56637061 12.56637061 3.2533421 5.02652273] is 5.99962501.\n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 9, + "source": [ + "# 创建图像\n", + "fig = plt.figure(figsize=(9, 6))\n", + "ax = fig.add_subplot(111)\n", + "# 绘制 QFIM 投影\n", + "ax.plot(thetas, list_qfisher_norm, 's', markersize=11, markerfacecolor='none')\n", + "analytical_qfi_norm = 4 + 2 * np.sin(thetas) + 2 * np.cos(thetas) - 2 * np.cos(thetas) * np.sin(thetas)\n", + "ax.plot(thetas, analytical_qfi_norm, linestyle=(0, (5, 3)))\n", + "# 设置图例，标签，刻度\n", + "ax.legend(\n", + " ['get_qfisher_norm()', '$4+2\\\\sin\\\\theta+2\\\\cos\\\\theta-2\\\\sin\\\\theta\\\\cos\\\\theta$'], \n", + " loc='best', prop= {'size': label_font_size}, frameon=False,\n", + ")\n", + "ax.set_xlabel('$\\\\theta$', fontsize=label_font_size)\n", + "ax.set_ylabel('QFI norm along $v=(1,1,1,1)$', fontsize=label_font_size)\n", + "ax.set_ylim([-1, 9])\n", + "ax.tick_params(labelsize=label_font_size)" + ], + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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" + }, + "metadata": { + "needs_background": "light" + } + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "可以看到程序的输出和解析结果是一致的。" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### 计算有效量子维数\n", + "\n", + "利用量桨，我们可以通过调用 `get_eff_qdim()` 方法方便地计算有效量子维数（effective quantum dimension, EQD）。以下是上面提到的 hardware-efficient 拟设的 EQD 计算示例。" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 10, + "source": [ + "cir = circuit_hardeff_2qubit()\n", + "qf = QuantumFisher(cir)\n", + "print(cir)\n", + "print(f'The number of parameters is {len(cir.get_param().tolist())}.')\n", + "print(f'The EQD is {qf.get_eff_qdim()}. \\n')" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "--Ry(4.248)----*----Ry(1.233)--\n", + " | \n", + "--Ry(6.121)----x----Ry(4.717)--\n", + " \n", + "The number of parameters is 4.\n", + "The EQD is 3. \n", + "\n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "在这个例子中，EQD 比参数个数要少，这实际上可以通过控制电路上两个 $R_y$ 可以直接合并这一点上看出来。这可以通过替换其中一个 $R_y$ 门为 $R_x$ 门来修复，这会使得 EQD 增长 1。\n", + "\n", + "如果继续在电路上增加门，EQD 会无限增长吗？答案显然是不会，这是因为对于 $n$ 个量子比特，量子态的实数自由度为 $2\\cdot 2^n-2$，其中减 $2$ 是由于归一化和全局相位无关性这两条约束。这说明无论门的数量为多少，EQD 都不会超过 $2\\cdot 2^n-2$。我们可以通过下面的例子做一简单的验证。" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 11, + "source": [ + "def circuit_hardeff_overparam():\n", + " cir = UAnsatz(2)\n", + " theta = 2 * np.pi * np.random.random(8)\n", + " theta = paddle.to_tensor(theta, stop_gradient=False, dtype='float64')\n", + " cir.ry(theta[0], which_qubit=0)\n", + " cir.ry(theta[1], which_qubit=1)\n", + " cir.rx(theta[2], which_qubit=0)\n", + " cir.rx(theta[3], which_qubit=1)\n", + " cir.cnot(control=[0, 1])\n", + " cir.ry(theta[4], which_qubit=0)\n", + " cir.ry(theta[5], which_qubit=1)\n", + " cir.rx(theta[6], which_qubit=0)\n", + " cir.rx(theta[7], which_qubit=1)\n", + "\n", + " return cir\n", + "\n", + "\n", + "cir = circuit_hardeff_overparam()\n", + "qf = QuantumFisher(cir)\n", + "print(cir)\n", + "print(f'The number of parameters is {len(cir.get_param().tolist())}.')\n", + "print(f'The EQD is {qf.get_eff_qdim()}. \\n')" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "--Ry(0.173)----Rx(5.837)----*----Ry(3.082)----Rx(3.997)--\n", + " | \n", + "--Ry(1.354)----Rx(0.536)----x----Ry(5.267)----Rx(5.647)--\n", + " \n", + "The number of parameters is 8.\n", + "The EQD is 6. \n", + "\n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### 计算经典费舍信息和有效维数\n", + "\n", + "这里我们举一个简单的例子来展示如何利用量桨对于一个量子神经网络计算式 (16) 中的有效维数。\n", + "\n", + "首先，定义经典数据到量子数据的编码方式。" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 12, + "source": [ + "def U_theta(x, theta, num_qubits, depth, encoding):\n", + " cir = UAnsatz(num_qubits)\n", + " if encoding == 'IQP':\n", + " S = [[i, i + 1] for i in range(num_qubits - 1)]\n", + " cir.iqp_encoding(x, num_repeats=1, pattern=S)\n", + " cir.complex_entangled_layer(theta, depth)\n", + " elif encoding == 're-uploading':\n", + " for i in range(depth):\n", + " cir.complex_entangled_layer(theta[i:i + 1], depth=1)\n", + " for j in range(num_qubits):\n", + " cir.rx(x[j], which_qubit=j)\n", + " cir.complex_entangled_layer(theta[-1:], depth=1)\n", + " else:\n", + " raise RuntimeError('Non-existent encoding method')\n", + " return cir" + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "然后调用飞桨定义量子神经网络和相应的损失函数。" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 13, + "source": [ + "import paddle.nn as nn\n", + "\n", + "class QuantumNeuralNetwork(nn.Layer):\n", + " def __init__(self, num_qubits, depth, encoding):\n", + " super().__init__()\n", + " self.num_qubits, self.depth, self.encoding = num_qubits, depth, encoding\n", + " if self.encoding == 'IQP':\n", + " self.theta = self.create_parameter(\n", + " shape=[self.depth, self.num_qubits, 3],\n", + " default_initializer=paddle.nn.initializer.Uniform(low=0.0,\n", + " high=2 *\n", + " np.pi),\n", + " dtype='float64',\n", + " is_bias=False)\n", + " elif self.encoding == 're-uploading':\n", + " self.theta = self.create_parameter(\n", + " shape=[self.depth + 1, self.num_qubits, 3],\n", + " default_initializer=paddle.nn.initializer.Uniform(low=0.0,\n", + " high=2 *\n", + " np.pi),\n", + " dtype='float64',\n", + " is_bias=False)\n", + " else:\n", + " raise RuntimeError('Non-existent encoding method')\n", + "\n", + " def forward(self, x):\n", + " if not paddle.is_tensor(x):\n", + " x = paddle.to_tensor(x)\n", + " cir = U_theta(x, self.theta, self.num_qubits, self.depth,\n", + " self.encoding)\n", + " cir.run_state_vector()\n", + " return cir.expecval([[1.0, 'z0']]) * paddle.to_tensor(\n", + " [0.5], dtype='float64') + paddle.to_tensor([0.5], dtype='float64')" + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "最后，定义 CFIM 计算器并计算不同大小的训练集对应的有效维数。" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 17, + "source": [ + "# 配置模型参数\n", + "num_qubits = 4\n", + "depth = 2\n", + "num_inputs = 100\n", + "num_thetas = 10\n", + "# 定义 CFIM 计算器\n", + "cfim = ClassicalFisher(model=QuantumNeuralNetwork,\n", + " num_thetas=num_thetas,\n", + " num_inputs=num_inputs,\n", + " num_qubits=num_qubits,\n", + " depth=depth,\n", + " encoding='IQP')\n", + "# 计算归一化的 CFIM\n", + "fim, _ = cfim.get_normalized_cfisher()\n", + "# 计算不同样本大小对应的有效维数\n", + "n = [5000, 8000, 10000, 40000, 60000, 100000, 150000, 200000, 500000, 1000000]\n", + "effdim = cfim.get_eff_dim(fim, n)" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + "running in get_gradient: 100%|##################################| 1000/1000 [02:05<00:00, 7.94it/s]\n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "画出有效维数与参数个数之比随训练集大小的变化规律。" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 19, + "source": [ + "fig = plt.figure(figsize=(9, 6))\n", + "ax = fig.add_subplot(111)\n", + "print('the number of parameters：%s' % cfim.num_params)\n", + "ax.plot(n, np.array(effdim) / cfim.num_params)\n", + "label_font_size = 14\n", + "ax.set_xlabel('sample size', fontsize=label_font_size)\n", + "ax.set_ylabel('effective dimension / number of parameters', fontsize=label_font_size)\n", + "ax.tick_params(labelsize=label_font_size)" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "the number of parameters：24\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
    " + ], + "image/png": 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" + }, + "metadata": { + "needs_background": "light" + } + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "## 总结\n", + "\n", + "本教程从几何的角度简要介绍了经典费舍信息和量子费舍信息的概念及二者之间的关系，并以有效维数为例阐述了它们在量子机器学习中的应用，最后展示了如何调用量桨来具体地计算它们。" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "_______\n", + "\n", + "## 参考文献\n", + "\n", + "[1] Meyer, Johannes Jakob. \"Fisher information in noisy intermediate-scale quantum applications.\" [arXiv preprint arXiv:2103.15191 (2021).](https://arxiv.org/abs/2103.15191)\n", + "\n", + "[2] Haug, Tobias, Kishor Bharti, and M. S. Kim. \"Capacity and quantum geometry of parametrized quantum circuits.\" [arXiv preprint arXiv:2102.01659 (2021).](https://arxiv.org/abs/2102.01659)\n", + "\n", + "[3] Stokes, James, et al. \"Quantum natural gradient.\" [Quantum 4 (2020): 269.](https://quantum-journal.org/papers/q-2020-05-25-269/)\n", + "\n", + "[4] Mari, Andrea, Thomas R. Bromley, and Nathan Killoran. \"Estimating the gradient and higher-order derivatives on quantum hardware.\" [Physical Review A 103.1 (2021): 012405.](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.012405)\n", + "\n", + "[5] Datta, Nilanjana, and Felix Leditzky. \"A limit of the quantum Rényi divergence.\" [Journal of Physics A: Mathematical and Theoretical 47.4 (2014): 045304.](https://iopscience.iop.org/article/10.1088/1751-8113/47/4/045304)\n", + "\n", + "[6] Abbas, Amira, et al. \"The power of quantum neural networks.\" [Nature Computational Science 1.6 (2021): 403-409.](https://www.nature.com/articles/s43588-021-00084-1)" + ], + "metadata": {} + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file diff --git a/tutorial/qnn_research/Fisher_EN.ipynb b/tutorial/qnn_research/Fisher_EN.ipynb new file mode 100644 index 0000000..4593e26 --- /dev/null +++ b/tutorial/qnn_research/Fisher_EN.ipynb @@ -0,0 +1,986 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# Quantum Fisher Information\n", + "\n", + " Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. " + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "## Overview\n", + "\n", + "In this tutorial, we briefly introduce the concepts of the classical and quantum Fisher information, along with their applications in quantum machine learning, and show how to compute them with Paddle Quantum." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "## Background\n", + "\n", + "The quantum Fisher information (QFI) originates from the field of quantum sensing and have been versatile tools to study parameterized quantum systems [[1]](https://arxiv.org/abs/2103.15191), such as characterizing the overparameterization [[2]](https://arxiv.org/abs/2102.01659) and performing the quantum natural gradient descent [[3]](https://arxiv.org/abs/1909.02108). The QFI is a quantum analogue of the classical Fisher information (CFI). The CFI characterizes the sensibility of a parameterized **probability distribution** to parameter changes, while the QFI characterizes the sensibility of a parameterized **quantum state** to parameter changes.\n", + "\n", + "In a traditional introduction, the CFI will appear as a quantity of parameter estimation in mathematical statistics, which might be complicated and confusing for the beginners. This tutorial will introduce the CFI from a geometric point of view, which is not only helpful for intuitive understanding, but also easier to see the relationship between the CFI and QFI." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### Classical Fisher information\n", + "\n", + "Let's consider the classical Fisher information first. Suppose we now have a parameterized probability distribution $p(\\boldsymbol{x};\\boldsymbol{\\theta})$. Here comes a question:\n", + "\n", + "- How much does a small parameter change result in the probability distribution change ?\n", + "\n", + "Since the question sounds like a perturbation problem, an intuition is to perform something like the Taylor expansion. But before expansion, we need to know which function to expand, i.e. we need to quantify the probability distribution change first. More formally, we need to define a distance measure between any two probability distributions, denoted by $d(p(\\boldsymbol{x};\\boldsymbol{\\theta}),p(\\boldsymbol{x};\\boldsymbol{\\theta}'))$, or $d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}')$ for short.\n", + "\n", + "Generally, a legal distance measure is supposed to be non-negative and equal to zero if and only if two points are identical, i.e.\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "&d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}')\\geq 0,\\\\\n", + "&d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}')=0~\\Leftrightarrow~\\boldsymbol{\\theta}=\\boldsymbol{\\theta}'.\n", + "\\end{aligned}\n", + "\\tag{1}\n", + "$$\n", + "\n", + "Considering the expansion of a small distance $d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})$, the conditions above lead to\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "&d(\\boldsymbol{\\theta},\\boldsymbol{\\theta})=0~\\Rightarrow~\\text{the zero order}=0,\\\\\n", + "&d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})\\geq 0~\\Rightarrow~\\boldsymbol{\\delta}=0~\\text{takes minimum}\n", + "~\\Rightarrow~\\text{the first order}=0.\n", + "\\end{aligned}\n", + "\\tag{2}\n", + "$$\n", + "\n", + "Thus, the second order is the lowest order that does not vanish in the expansion. So the expansion can be written as\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})\n", + "=\\frac{1}{2}\\sum_{ij}\\delta_iM_{ij}\\delta_j+O(\\|\\boldsymbol{\\delta}\\|^3) \n", + "=\\frac{1}{2} \\boldsymbol{\\delta}^T M \\boldsymbol{\\delta} + O(\\|\\boldsymbol{\\delta}\\|^3),\n", + "\\end{aligned}\n", + "\\tag{3}\n", + "$$\n", + "\n", + "where\n", + "\n", + "$$\n", + "M_{ij}(\\boldsymbol{\\theta})=\\left.\\frac{\\partial^2}{\\partial\\delta_i\\partial\\delta_j}d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})\\right|_{\\boldsymbol{\\delta}=0},\n", + "\\tag{4}\n", + "$$\n", + "\n", + "is exactly the Hessian matrix of the distance expansion, which is called [metric](http://en.wikipedia.org/wiki/Metric_tensor) of manifold in the context of differentiable geometry. The brief derivation above tells us that we can approximate a small distance as a quadratic form of the corresponding parameters, as shown in Fig.1, and the coefficient matrix of the quadratic form is exactly the Hessian matrix from the distance expansion, up to a $1/2$ factor.\n", + "\n", + "![feature map](./figures/FIM-fig-Sphere-metric.png \"Figure 1. Approximate a small distance on the 2-sphere as a quadratic form\")\n", + "
    Figure 1. Approximate a small distance on the 2-sphere as a quadratic form
    \n", + "\n", + "If the distance measure is specified to be the relative entropy / KL divergence, i.e.\n", + "$$\n", + "d_{\\mathrm{KL}}(\\boldsymbol{\\theta}, \\boldsymbol{\\theta}^{\\prime})=\\sum_{\\boldsymbol{x}} p(\\boldsymbol{x};\\boldsymbol{\\theta}) \\log \\frac{p(\\boldsymbol{x};\\boldsymbol{\\theta})}{p(\\boldsymbol{x};\\boldsymbol{\\theta}^{\\prime})}.\n", + "\\tag{5}\n", + "$$\n", + "\n", + "The corresponding Hessian matrix\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mathcal{I}_{ij}(\\boldsymbol{\\theta})&= \\left.\\frac{\\partial^2}{\\partial\\delta_i\\partial\\delta_j}d_{\\mathrm{KL}}(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})\\right|_{\\boldsymbol{\\delta}=0}\\\\\n", + "&=-\\sum_{\\boldsymbol{x}} p(\\boldsymbol{x};\\boldsymbol{\\theta}) \\partial_{i} \\partial_{j} \\log p(\\boldsymbol{x};\\boldsymbol{\\theta})\n", + "=\\mathbb{E}_{\\boldsymbol{x}}[-\\partial_{i} \\partial_{j} \\log p(\\boldsymbol{x};\\boldsymbol{\\theta})] \\\\\n", + "&=\\sum_{\\boldsymbol{x}} \\frac{1}{p(\\boldsymbol{x};\\boldsymbol{\\theta})} \\partial_i p(\\boldsymbol{x};\\boldsymbol{\\theta}) \\cdot \\partial_j p(\\boldsymbol{x};\\boldsymbol{\\theta})\n", + "=\\mathbb{E}_{\\boldsymbol{x}}[\\partial_i\\log p(\\boldsymbol{x};\\boldsymbol{\\theta})\\cdot \\partial_j \\log p(\\boldsymbol{x};\\boldsymbol{\\theta})].\n", + "\\end{aligned}\n", + "\\tag{6}\n", + "$$\n", + "\n", + "is the so-called classical Fisher information matrix (CFIM), with large entries indicating large sensibility to the corresponding parameter changes. Here we use the notation $\\partial_i=\\partial/\\partial \\theta_i$.\n", + "\n", + "Why is $\\mathcal{I}(\\boldsymbol{\\theta})$ called \"information\"? Geometrically, the CFIM characterizes the sensitivity / sharpness of a probability distribution in the vicinity of $\\boldsymbol{\\theta}$. The more sensitive it is to a parameter change, the easier one can discriminate it from others, the fewer samples are needed to discriminate it, the more information per sample can give.\n", + "\n", + "The measurement outcomes from a parameterized quantum circuit (PQC) form a parameterized probability distribution. So one can define a CFIM for each kind of measurement on a PQC. Currently, the main challenge of calculating CFIM on NISQ devices is that the number of possible measurement outputs increases exponentially with the number of qubits, which means that there may be many measurement outputs with low probabilities that never appear, leading to divergence in CFIM calculations. Possible solutions includes neglecting small probabilities (cause diverge) and Bayesian updating [[1]](https://arxiv.org/abs/2103.15191)." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### Quantum Fisher information\n", + "\n", + "The quantum Fisher information is a natural quantum analogue of the classical notion above, where the expanded distance is not defined between two probability distributions, but two quantum states. A common choice is the fidelity distance \n", + "\n", + "$$\n", + "d_f(\\boldsymbol{\\theta},\\boldsymbol{\\theta}')=2-2|\\langle\\psi(\\boldsymbol{\\theta})|\\psi(\\boldsymbol{\\theta}')\\rangle|^2.\n", + "\\tag{7}\n", + "$$\n", + "\n", + "where an additional factor $2$ here is manually multiplied to make the subsequent results resemble the CFIM. Hence formally, the quantum Fisher information matrix (QFIM) at a parameterized pure quantum state $|\\psi(\\boldsymbol{\\theta})\\rangle, \\boldsymbol{\\theta}\\in\\mathbb{R}^m$ is the Hessian matrix of the fidelity distance expansion, i.e.\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mathcal{F}_{ij}(\\boldsymbol{\\theta})\n", + "&= \\left.\\frac{\\partial^2}{\\partial\\delta_i\\partial\\delta_j}d_{f}(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})\\right|_{\\boldsymbol{\\delta}=0} \\\\\n", + "&=4 \\operatorname{Re}\\left[\\left\\langle\\partial_{i} \\psi \\mid \\partial_{j} \\psi\\right\\rangle - \\left\\langle\\partial_{i} \\psi \\mid \\psi\\right\\rangle\\left\\langle\\psi \\mid \\partial_{j} \\psi\\right\\rangle\\right],\n", + "\\end{aligned}\n", + "\\tag{8}\n", + "$$\n", + "\n", + "where we have omitted the argument $\\boldsymbol{\\theta}$ for simplicity. Similar to the CFIM, the QFIM characterizes the sensibility of a parameterized quantum state to a small change of parameters. In addition, it is worth mentioning that the QFIM can be seen as the real part of a complex matrix called the quantum geometric tensor, or say the Fubini-Study metric [[1]](https://arxiv.org/abs/2103.15191).\n", + "\n", + "Currently, the community has developed some techniques to calculate the QFIM for pure states on NISQ devices, among which the two most straight methods are\n", + "\n", + "- applying the second order parameter shift rule [[4]](https://arxiv.org/abs/2008.06517)\n", + "$$\n", + "\\begin{aligned}\n", + "\\mathcal{F}_{i j}=-\\frac{1}{2} \\Big(&|\\langle\\psi(\\boldsymbol{\\theta}) \\mid \\psi(\\boldsymbol{\\theta}+(\\boldsymbol{e}_{i}+\\boldsymbol{e}_{j}) \\frac{\\pi}{2})\\rangle|^{2}\n", + "-|\\langle\\psi(\\boldsymbol{\\theta}) \\mid \\psi(\\boldsymbol{\\theta}+(\\boldsymbol{e}_{i}-\\boldsymbol{e}_{j}) \\frac{\\pi}{2})\\rangle|^{2}\\\\\n", + "-&|\\langle\\psi(\\boldsymbol{\\theta}) \\mid \\psi(\\boldsymbol{\\theta}-(\\boldsymbol{e}_{i}-\\boldsymbol{e}_{j}) \\frac{\\pi}{2})\\rangle|^{2}\n", + "+|\\langle\\psi(\\boldsymbol{\\theta}) \\mid \\psi(\\boldsymbol{\\theta}-(\\boldsymbol{e}_{i}+\\boldsymbol{e}_{j}) \\frac{\\pi}{2})\\rangle|^{2}\\Big),\n", + "\\end{aligned}\n", + "\\tag{9}\n", + "$$\n", + "where $\\boldsymbol{e}_{i}$ denotes the unit vector corresponding to $\\theta_i$.\n", + "\n", + "- applying the finite difference expression to calculate the projection along a certain direction [[1]](https://arxiv.org/abs/2103.15191)\n", + "$$\n", + "\\boldsymbol{v}^{T} \\mathcal{F} \\boldsymbol{v} \\approx \\frac{4 d_{f}(\\boldsymbol{\\theta}, \\boldsymbol{\\theta}+\\epsilon \\boldsymbol{v})}{\\epsilon^{2}}.\n", + "\\tag{10}\n", + "$$\n", + "which can be regarded as the quantum analogue of the famed Fisher-Rao norm.\n", + "\n", + "For mixed states, the QFIM can be defined by the expansion of the Bures fidelity distance\n", + "\n", + "$$\n", + "d_B(\\boldsymbol{\\theta},\\boldsymbol{\\theta}')\\equiv \n", + "2-2\\left[\\text{Tr}\\left([\\sqrt{\\rho(\\boldsymbol{\\theta})} \\rho(\\boldsymbol{\\theta}')\\sqrt{\\rho(\\boldsymbol{\\theta})}]^{1/2}\\right)\\right]^2,\n", + "\\tag{11}\n", + "$$\n", + "\n", + "or equivalently ($\\log x\\sim x-1$), the $\\alpha=1/2$ \"sandwiched\" Rényi relative entropy [[5]](https://arxiv.org/abs/1308.5961)\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "d_R(\\boldsymbol{\\theta},\\boldsymbol{\\theta}') &\\equiv 2\\widetilde{D}_{\\alpha=1/2}(\\rho(\\boldsymbol{\\theta'}) \\| \\rho(\\boldsymbol{\\theta})), \\\\\n", + "\\widetilde{D}_{\\alpha}(\\rho \\| \\sigma) \n", + "&\\equiv \n", + "\\frac{1}{\\alpha-1} \\log \\operatorname{Tr}\\left[\\left(\\sigma^{\\frac{1-\\alpha}{2 \\alpha}} \\rho \\sigma^{\\frac{1-\\alpha}{2 \\alpha}}\\right)^{\\alpha}\\right].\\\\\n", + "\\end{aligned}\n", + "\\tag{12}\n", + "$$\n", + "\n", + "Please see the review [[1]](https://arxiv.org/abs/2103.15191) for more details." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### The relation between CFIM and QFIM\n", + "\n", + "By definition, for a parameterized quantum circuit, the CFIM depends on the measurement bases while the QFIM does not. In fact, one can prove that the QFIM of a quantum state $\\rho(\\boldsymbol{\\theta})$ is an upper bound of the CFIM obtained by arbitrary measurement from the same quantum state, i.e.\n", + "\n", + "$$\n", + "\\mathcal{I}[\\mathcal{E}[\\rho(\\boldsymbol{\\theta})]]\\leq \\mathcal{F}[\\rho(\\boldsymbol{\\theta})],~\\forall\\mathcal{E},\n", + "\\tag{13}\n", + "$$\n", + "\n", + "where $\\mathcal{E}$ denotes the quantum operation corresponding to the measurement, and the inequality between two positive matrices means that the large minus the small is still a positive matrix. This is a natural result since measurements can not extract more information than the quantum state itself, which mathematically stems from the monotonicity of the fidelity distance with respect to trace-preserving quantum operations [[1]](https://arxiv.org/abs/2103.15191)." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### Application: effective dimension\n", + "\n", + "The maximal rank of the CFIM / QFIM over the parameter space $\\Theta$ is a quantity to characterize the **capacity** of a classical / quantum neural network, called effective classical / quantum dimension\n", + "\n", + "$$\n", + "d_{\\text{eff}}=\\underset{\\boldsymbol{\\theta}\\in\\Theta} {\\max}\n", + "\\operatorname{rank}{\\mathcal{F}}(\\boldsymbol{\\theta}).\n", + "\\tag{14}\n", + "$$\n", + "\n", + "The rank captures in how many directions parameter changes will result in the probability distribution / quantum state changes. A not-full rank means that some changes of parameters can not actually change the probability distribution / quantum state, or say there are redundant degrees of freedom of parameters that can be projected out and the model is therefore overparameterized. On the other hand, a larger effective dimension corresponds to more directions that can be extended, suggesting a more extensive space occupied by the model, i.e. a larger capacity.\n", + "\n", + "In the context of machine learning, the so-called empirical CFIM [[6]](https://arxiv.org/abs/2011.00027) is more widely used, which is defined by a summation over samples instead of the expectation in the original definition\n", + "\n", + "$$\n", + "\\tilde{\\mathcal{I}}_{ij}(\\boldsymbol{\\theta})\n", + "=\\frac{1}{n}\\sum_{k=1}^{n}\n", + "\\partial_i\\log p(x_k,y_k;\\boldsymbol{\\theta})\n", + "\\partial_j\\log p(x_k,y_k;\\boldsymbol{\\theta}),\n", + "\\tag{15}\n", + "$$\n", + "\n", + "where $(x_k,y_k)^{n}_{k=1}$ are identical independent distributed training data drawn from the distribution $p(x,y;\\boldsymbol{\\theta})=p(y|x;\\boldsymbol{\\theta})p(x)$. Clearly, the empirical CFIM can converge to the CFIM in the limit of infinite samples if (1) the model has been well-trained and (2) the model has enough capacity to cover the underlying data distribution. The advantage of the empirical CFIM is that it can be calculated directly using the training data at hand, instead of calculating the original integral by generating new samples. \n", + "\n", + "By use of the empirical CFIM, a variant of the effective dimension can be defined as\n", + "\n", + "$$\n", + "d_{\\text{eff}}(\\gamma, n)=\n", + "2 \\frac{\\log \\left(\\frac{1}{V_{\\Theta}} \\int_{\\Theta} \\sqrt{\\operatorname{det}\\left( 1 + \\frac{\\gamma n}{2 \\pi \\log n} \\hat{\\mathcal{I}}( \\boldsymbol{\\theta})\\right)} \\mathrm{d} \\boldsymbol{\\theta} \\right)}\n", + "{\\log \\left(\\frac{\\gamma n}{2 \\pi \\log n}\\right)},\n", + "\\tag{16}\n", + "$$\n", + "\n", + "where $V_{\\Theta}:=\\int_{\\Theta} \\mathrm{d} \\boldsymbol{\\theta} \\in \\mathbb{R}_{+}$ is the volume of the parameter space. $\\gamma\\in(0,1]$ is an artificial tunable parameter. $\\hat{\\mathcal{I}} (\\boldsymbol{\\theta}) \\in \\mathbb{R}^{d\\times d}$ is the normalized empirical CFIM\n", + "\n", + "$$\n", + "\\hat{\\mathcal{I}}_{i j}(\\boldsymbol{\\theta}):= \\frac{V_{\\Theta} d }{\\int_{\\Theta} \\operatorname{Tr}(F( \\boldsymbol{\\theta} ) \\mathrm{d} \\theta} \\tilde{\\mathcal{I}}_{i j}(\\boldsymbol{\\theta}).\n", + "\\tag{17}\n", + "$$\n", + "\n", + "This definition might be strange and confusing at first glance, which is far more complicated than the maximal rank of the CFIM. However, it can converge to the maximal rank of the CFIM in the limit of infinite samples $n\\rightarrow \\infty$ [[6]](https://arxiv.org/abs/2011.00027). Regardless of the coefficients and the logarithm, the effective dimension here can be seen roughly as the geometric mean of the spectrum of the normalized CFIM plus an identity, then averaging over the parameter space. Associated with the inequality between the geometric mean and the arithmetic mean, we may expect that a more uniform empirical CFIM spectrum leads to a larger effective dimension, which is consistent with our natural impression. In this sense, it is a \"soft\" version of the effective dimension.\n", + "\n", + "In addition, the Fisher information can not only provide an capacity measure, but also can serve as an indicator of trainability. If the entries of the Fisher information vanish exponentially with the system size averaging over the parameter space, i.e. the sensitivity becomes exponentially small, we can not distinguish them efficiently, which indicates the existence of barrens plateaus [[6]](https://arxiv.org/abs/2011.00027)." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "## Paddle Quantum Implementation" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### Calculate the QFIM\n", + "\n", + "With Paddle Quantum, one can obtain the QFIM conveniently by the following steps.\n", + "\n", + "1. Define a quantum circuit using `UAnsatz`.\n", + "2. Define a `QuantumFisher` class as a calculator of the QFIM.\n", + "3. Use the method `get_qfisher_matrix()` to calculate the QFIM.\n", + "\n", + "The calculator `QuantumFisher` will keep track of the change of the circuit `UAnsatz`.\n", + "\n", + "Now let's code. Firstly, import packages." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 1, + "source": [ + "import paddle\n", + "from paddle_quantum.circuit import UAnsatz\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from paddle_quantum.utils import QuantumFisher, ClassicalFisher\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\")" + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Then, define a quantum circuit. As a simple example, we exploit a single qubit parameterized by two Bloch angles\n", + "\n", + "$$\n", + "|\\psi(\\theta,\\phi)\\rangle=R_z(\\phi)R_y(\\theta)|0\\rangle=e^{-i\\phi/2}\\cos\\frac{\\theta}{2}|0\\rangle+e^{i\\phi/2}\\sin\\frac{\\theta}{2}|1\\rangle.\n", + "\\tag{18}\n", + "$$\n", + "\n", + "The corresponding QFIM can be directly calculated using Eq.(8). The analytical result reads\n", + "\n", + "$$\n", + "\\mathcal{F}(\\theta,\\phi)=\\left(\\begin{matrix}\n", + "1&0\\\\\n", + "0&\\sin^2\\theta\n", + "\\end{matrix}\\right).\n", + "\\tag{19}\n", + "$$" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 2, + "source": [ + "def circuit_bloch():\n", + " cir = UAnsatz(1)\n", + " theta = 2 * np.pi * np.random.random(2)\n", + " theta = paddle.to_tensor(theta, stop_gradient=False, dtype='float64')\n", + " cir.ry(theta[0], which_qubit=0)\n", + " cir.rz(theta[1], which_qubit=0)\n", + " \n", + " return cir" + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 3, + "source": [ + "cir = circuit_bloch()\n", + "print(cir)" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "--Ry(1.888)----Rz(2.181)--\n", + " \n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Define a QFIM calculator and calculate the QFIM element $\\mathcal{F}_{\\phi\\phi}$ corresponding to different $\\theta$." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 4, + "source": [ + "qf = QuantumFisher(cir)\n", + "# Record the QFIM element F_{phi,phi}\n", + "list_qfisher_elements = []\n", + "num_thetas = 21\n", + "thetas = np.linspace(0, np.pi, num_thetas)\n", + "for theta in thetas:\n", + " list_param = cir.get_param().tolist()\n", + " list_param[0] = theta\n", + " cir.update_param(list_param)\n", + " # Calculate the QFIM\n", + " qfim = qf.get_qfisher_matrix()\n", + " print(f'The QFIM at {np.array(list_param)} is \\n {qfim.round(14)}.')\n", + " list_qfisher_elements.append(qfim[1][1])" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "The QFIM at [0. 2.18107874] is \n", + " [[1. 0.]\n", + " [0. 0.]].\n", + "The QFIM at [0.15707963 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.02447174]].\n", + "The QFIM at [0.31415927 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.0954915]].\n", + "The QFIM at [0.4712389 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.20610737]].\n", + "The QFIM at [0.62831853 2.18107874] is \n", + " [[ 1. -0. ]\n", + " [-0. 0.3454915]].\n", + "The QFIM at [0.78539816 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.5]].\n", + "The QFIM at [0.9424778 2.18107874] is \n", + " [[ 1. -0. ]\n", + " [-0. 0.6545085]].\n", + "The QFIM at [1.09955743 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.79389263]].\n", + "The QFIM at [1.25663706 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.9045085]].\n", + "The QFIM at [1.41371669 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.97552826]].\n", + "The QFIM at [1.57079633 2.18107874] is \n", + " [[1. 0.]\n", + " [0. 1.]].\n", + "The QFIM at [1.72787596 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.97552826]].\n", + "The QFIM at [1.88495559 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.9045085]].\n", + "The QFIM at [2.04203522 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.79389263]].\n", + "The QFIM at [2.19911486 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.6545085]].\n", + "The QFIM at [2.35619449 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.5]].\n", + "The QFIM at [2.51327412 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.3454915]].\n", + "The QFIM at [2.67035376 2.18107874] is \n", + " [[ 1. -0. ]\n", + " [-0. 0.20610737]].\n", + "The QFIM at [2.82743339 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.0954915]].\n", + "The QFIM at [2.98451302 2.18107874] is \n", + " [[1. 0. ]\n", + " [0. 0.02447174]].\n", + "The QFIM at [3.14159265 2.18107874] is \n", + " [[1. 0.]\n", + " [0. 0.]].\n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Plot the outputs of the QFIM element $\\mathcal{F}_{\\phi\\phi}$ as function of $\\theta$." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 5, + "source": [ + "# Create a figure\n", + "fig = plt.figure(figsize=(9, 6))\n", + "ax = fig.add_subplot(111)\n", + "# Plot the QFIM\n", + "ax.plot(thetas, list_qfisher_elements, 's', markersize=11, markerfacecolor='none')\n", + "# Plot sin^2 theta\n", + "ax.plot(thetas, np.sin(thetas) ** 2, linestyle=(0, (5, 3)))\n", + "# Set legends, labels, ticks\n", + "label_font_size = 18\n", + "ax.legend(['get_qfisher_matrix()[1][1]', '$\\\\sin^2\\\\theta$'], \n", + " prop= {'size': label_font_size}, frameon=False) \n", + "ax.set_xlabel('$\\\\theta$', fontsize=label_font_size)\n", + "ax.set_ylabel('QFIM element $\\\\mathcal{F}_{\\\\phi\\\\phi}$', fontsize=label_font_size)\n", + "ax.tick_params(labelsize=label_font_size)" + ], + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
    " + ], + "image/png": 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" + }, + "metadata": { + "needs_background": "light" + } + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "We can see that the outputs are consistent with the analytical results.\n", + "\n", + "Moreover, one can use the method `get_qfisher_norm()` to calculate the quantum Fisher-Rao norm in Eq.(10), i.e. the QFIM projection along a certain direction.\n", + "\n", + "As a different example, we exploit two qubits with a typical hardware-efficient ansatz\n", + "\n", + "$$\n", + "|\\psi(\\boldsymbol{\\theta})\\rangle=\\left[R_{y}\\left( \\theta_{3}\\right) \\otimes R_{y}\\left( \\theta_{4}\\right)\\right] \\text{CNOT}_{0,1}\\left[ R_{y}\\left( \\theta_{1}\\right) \\otimes R_{y}\\left( \\theta_{2}\\right)\\right]|00\\rangle.\n", + "\\tag{20}\n", + "$$\n", + "\n", + "The corresponding QFIM reads\n", + "\n", + "$$\n", + "\\mathcal{F}(\\theta_1,\\theta_2,\\theta_3,\\theta_4)=\\left(\\begin{array}{cc|cc}\n", + "1 & 0 & \\sin \\theta_{2} & 0 \\\\\n", + "0 & 1 & 0 & \\cos \\theta_{1} \\\\\n", + "\\hline \n", + "\\sin \\theta_{2} & 0 & 1 & -\\sin\\theta_1\\cos\\theta_2 \\\\\n", + "0 & \\cos \\theta_{1} & -\\sin\\theta_1\\cos\\theta_2 & 1\n", + "\\end{array}\\right).\n", + "\\tag{21}\n", + "$$\n", + "\n", + "Define the corresponding quantum circuit." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 6, + "source": [ + "def circuit_hardeff_2qubit():\n", + " cir = UAnsatz(2)\n", + " theta = 2 * np.pi * np.random.random(4)\n", + " theta = paddle.to_tensor(theta, stop_gradient=False, dtype='float64')\n", + " cir.ry(theta[0], which_qubit=0)\n", + " cir.ry(theta[1], which_qubit=1)\n", + " cir.cnot(control=[0, 1])\n", + " cir.ry(theta[2], which_qubit=0)\n", + " cir.ry(theta[3], which_qubit=1)\n", + "\n", + " return cir" + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 7, + "source": [ + "cir = circuit_hardeff_2qubit()\n", + "print(cir)" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "--Ry(2.614)----*----Ry(3.253)--\n", + " | \n", + "--Ry(2.906)----x----Ry(5.027)--\n", + " \n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Define a QFIM calculator and calculate the quantum Fisher-Rao norm $\\boldsymbol{v}^T\\mathcal{F}\\boldsymbol{v}$ along the direction $\\boldsymbol{v}=(1,1,1,1)$ corresponding to different $\\theta$ (set $\\theta_1=\\theta_2=\\theta$)." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 8, + "source": [ + "qf = QuantumFisher(cir)\n", + "v = [1, 1, 1, 1]\n", + "# Record the QFI norm\n", + "list_qfisher_norm = []\n", + "num_thetas = 41\n", + "thetas = np.linspace(0, np.pi * 4, num_thetas)\n", + "for theta in thetas:\n", + " list_param = cir.get_param().tolist()\n", + " list_param[0] = theta\n", + " list_param[1] = theta\n", + " cir.update_param(list_param)\n", + " # Calculate the QFI norm\n", + " qfisher_norm = qf.get_qfisher_norm(v)\n", + " print(\n", + " f'The QFI norm along {v} at {np.array(list_param)} is {qfisher_norm:.8f}.'\n", + " )\n", + " list_qfisher_norm.append(qfisher_norm)" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "The QFI norm along [1, 1, 1, 1] at [0. 0. 3.2533421 5.02652273] is 5.99962501.\n", + "The QFI norm along [1, 1, 1, 1] at [0.31415927 0.31415927 3.2533421 5.02652273] is 5.93033916.\n", + "The QFI norm along [1, 1, 1, 1] at [0.62831853 0.62831853 3.2533421 5.02652273] is 5.84133590.\n", + "The QFI norm along [1, 1, 1, 1] at [0.9424778 0.9424778 3.2533421 5.02652273] is 5.84309143.\n", + "The QFI norm along [1, 1, 1, 1] at [1.25663706 1.25663706 3.2533421 5.02652273] is 5.93367838.\n", + "The QFI norm along [1, 1, 1, 1] at [1.57079633 1.57079633 3.2533421 5.02652273] is 5.99962501.\n", + "The QFI norm along [1, 1, 1, 1] at [1.88495559 1.88495559 3.2533421 5.02652273] is 5.86697827.\n", + "The QFI norm along [1, 1, 1, 1] at [2.19911486 2.19911486 3.2533421 5.02652273] is 5.38230779.\n", + "The QFI norm along [1, 1, 1, 1] at [2.51327412 2.51327412 3.2533421 5.02652273] is 4.49128513.\n", + "The QFI norm along [1, 1, 1, 1] at [2.82743339 2.82743339 3.2533421 5.02652273] is 3.28287364.\n", + "The QFI norm along [1, 1, 1, 1] at [3.14159265 3.14159265 3.2533421 5.02652273] is 1.97995933.\n", + "The QFI norm along [1, 1, 1, 1] at [3.45575192 3.45575192 3.2533421 5.02652273] is 0.87758767.\n", + "The QFI norm along [1, 1, 1, 1] at [3.76991118 3.76991118 3.2533421 5.02652273] is 0.25010151.\n", + "The QFI norm along [1, 1, 1, 1] at [4.08407045 4.08407045 3.2533421 5.02652273] is 0.26070618.\n", + "The QFI norm along [1, 1, 1, 1] at [4.39822972 4.39822972 3.2533421 5.02652273] is 0.90660775.\n", + "The QFI norm along [1, 1, 1, 1] at [4.71238898 4.71238898 3.2533421 5.02652273] is 2.01995733.\n", + "The QFI norm along [1, 1, 1, 1] at [5.02654825 5.02654825 3.2533421 5.02652273] is 3.32425271.\n", + "The QFI norm along [1, 1, 1, 1] at [5.34070751 5.34070751 3.2533421 5.02652273] is 4.52539873.\n", + "The QFI norm along [1, 1, 1, 1] at [5.65486678 5.65486678 3.2533421 5.02652273] is 5.40406149.\n", + "The QFI norm along [1, 1, 1, 1] at [5.96902604 5.96902604 3.2533421 5.02652273] is 5.87599852.\n", + "The QFI norm along [1, 1, 1, 1] at [6.28318531 6.28318531 3.2533421 5.02652273] is 5.99962501.\n", + "The QFI norm along [1, 1, 1, 1] at [6.59734457 6.59734457 3.2533421 5.02652273] is 5.93033916.\n", + "The QFI norm along [1, 1, 1, 1] at [6.91150384 6.91150384 3.2533421 5.02652273] is 5.84133590.\n", + "The QFI norm along [1, 1, 1, 1] at [7.2256631 7.2256631 3.2533421 5.02652273] is 5.84309143.\n", + "The QFI norm along [1, 1, 1, 1] at [7.53982237 7.53982237 3.2533421 5.02652273] is 5.93367838.\n", + "The QFI norm along [1, 1, 1, 1] at [7.85398163 7.85398163 3.2533421 5.02652273] is 5.99962501.\n", + "The QFI norm along [1, 1, 1, 1] at [8.1681409 8.1681409 3.2533421 5.02652273] is 5.86697827.\n", + "The QFI norm along [1, 1, 1, 1] at [8.48230016 8.48230016 3.2533421 5.02652273] is 5.38230779.\n", + "The QFI norm along [1, 1, 1, 1] at [8.79645943 8.79645943 3.2533421 5.02652273] is 4.49128513.\n", + "The QFI norm along [1, 1, 1, 1] at [9.1106187 9.1106187 3.2533421 5.02652273] is 3.28287364.\n", + "The QFI norm along [1, 1, 1, 1] at [9.42477796 9.42477796 3.2533421 5.02652273] is 1.97995933.\n", + "The QFI norm along [1, 1, 1, 1] at [9.73893723 9.73893723 3.2533421 5.02652273] is 0.87758767.\n", + "The QFI norm along [1, 1, 1, 1] at [10.05309649 10.05309649 3.2533421 5.02652273] is 0.25010151.\n", + "The QFI norm along [1, 1, 1, 1] at [10.36725576 10.36725576 3.2533421 5.02652273] is 0.26070618.\n", + "The QFI norm along [1, 1, 1, 1] at [10.68141502 10.68141502 3.2533421 5.02652273] is 0.90660775.\n", + "The QFI norm along [1, 1, 1, 1] at [10.99557429 10.99557429 3.2533421 5.02652273] is 2.01995733.\n", + "The QFI norm along [1, 1, 1, 1] at [11.30973355 11.30973355 3.2533421 5.02652273] is 3.32425271.\n", + "The QFI norm along [1, 1, 1, 1] at [11.62389282 11.62389282 3.2533421 5.02652273] is 4.52539873.\n", + "The QFI norm along [1, 1, 1, 1] at [11.93805208 11.93805208 3.2533421 5.02652273] is 5.40406149.\n", + "The QFI norm along [1, 1, 1, 1] at [12.25221135 12.25221135 3.2533421 5.02652273] is 5.87599852.\n", + "The QFI norm along [1, 1, 1, 1] at [12.56637061 12.56637061 3.2533421 5.02652273] is 5.99962501.\n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 9, + "source": [ + "# Create a figure\n", + "fig= plt.figure(figsize=(9, 6))\n", + "ax = fig.add_subplot(111)\n", + "# Plot the QFI norm\n", + "ax.plot(thetas, list_qfisher_norm, 's', markersize=11, markerfacecolor='none')\n", + "analytical_qfi_norm = 4 + 2 * np.sin(thetas) + 2 * np.cos(thetas) - 2 * np.cos(thetas) * np.sin(thetas)\n", + "ax.plot(thetas, analytical_qfi_norm, linestyle=(0, (5, 3)))\n", + "# Set legends, labels, ticks\n", + "ax.legend(\n", + " ['get_qfisher_norm()', '$4+2\\\\sin\\\\theta+2\\\\cos\\\\theta-2\\\\sin\\\\theta\\\\cos\\\\theta$'], \n", + " loc='best', prop= {'size': label_font_size}, frameon=False,\n", + ")\n", + "ax.set_xlabel('$\\\\theta$', fontsize=label_font_size)\n", + "ax.set_ylabel('QFI norm along $v=(1,1,1,1)$', fontsize=label_font_size)\n", + "ax.set_ylim([-1, 9])\n", + "ax.tick_params(labelsize=label_font_size)" + ], + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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" + }, + "metadata": { + "needs_background": "light" + } + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "We can see that the outputs are consistent with the analytical results." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### Calculate the effective quantum dimension\n", + "\n", + "With Paddle Quantum, one can obtain the effective quantum dimension (EQD) by simply using the method `get_eff_qdim()`. For example, the EQD of the hardware-efficient ansatz shown above can be calculated as follows." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 10, + "source": [ + "cir = circuit_hardeff_2qubit()\n", + "qf = QuantumFisher(cir)\n", + "print(cir)\n", + "print(f'The number of parameters is {len(cir.get_param().tolist())}.')\n", + "print(f'The EQD is {qf.get_eff_qdim()}. \\n')" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "--Ry(4.248)----*----Ry(1.233)--\n", + " | \n", + "--Ry(6.121)----x----Ry(4.717)--\n", + " \n", + "The number of parameters is 4.\n", + "The EQD is 3. \n", + "\n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "In this example, the EQD is smaller than the number of parameters, which can be easily seen from the fact that the two $R_y$ gates on the control wire can be merged without changing anything. This inefficiency can be fixed by simply replacing one of the $R_y$ gates with a $R_x$ gate, and then the EQD will increase by one.\n", + "\n", + "If we continue to add gates to the circuit, can we make the EQD grow indefinitely? The answer is clearly no. Provided $n$ qubits, an obvious upper bound can be given by the real number degrees of freedom in a general quantum state, which is equal to $2\\cdot 2^n-2$. The minus two reflect the two constraints of normalization and global phase independence. This can be verified by the following example." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 11, + "source": [ + "def circuit_hardeff_overparam():\n", + " cir = UAnsatz(2)\n", + " theta = 2 * np.pi * np.random.random(8)\n", + " theta = paddle.to_tensor(theta, stop_gradient=False, dtype='float64')\n", + " cir.ry(theta[0], which_qubit=0)\n", + " cir.ry(theta[1], which_qubit=1)\n", + " cir.rx(theta[2], which_qubit=0)\n", + " cir.rx(theta[3], which_qubit=1)\n", + " cir.cnot(control=[0, 1])\n", + " cir.ry(theta[4], which_qubit=0)\n", + " cir.ry(theta[5], which_qubit=1)\n", + " cir.rx(theta[6], which_qubit=0)\n", + " cir.rx(theta[7], which_qubit=1)\n", + "\n", + " return cir\n", + "\n", + "\n", + "cir = circuit_hardeff_overparam()\n", + "qf = QuantumFisher(cir)\n", + "print(cir)\n", + "print(f'The number of parameters is {len(cir.get_param().tolist())}.')\n", + "print(f'The EQD is {qf.get_eff_qdim()}. \\n')" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "--Ry(0.173)----Rx(5.837)----*----Ry(3.082)----Rx(3.997)--\n", + " | \n", + "--Ry(1.354)----Rx(0.536)----x----Ry(5.267)----Rx(5.647)--\n", + " \n", + "The number of parameters is 8.\n", + "The EQD is 6. \n", + "\n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### Calculate the CFIM and effective dimension\n", + "\n", + "Here we exploit a brief example to show how to calculate the effective dimension defined in Eq.(16) with respect to a quantum neural network with Paddle Quantum.\n", + "\n", + "Firstly, define the encoding method from classical data to quantum data." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 12, + "source": [ + "def U_theta(x, theta, num_qubits, depth, encoding):\n", + " cir = UAnsatz(num_qubits)\n", + " if encoding == 'IQP':\n", + " S = [[i, i + 1] for i in range(num_qubits - 1)]\n", + " cir.iqp_encoding(x, num_repeats=1, pattern=S)\n", + " cir.complex_entangled_layer(theta, depth)\n", + " elif encoding == 're-uploading':\n", + " for i in range(depth):\n", + " cir.complex_entangled_layer(theta[i:i + 1], depth=1)\n", + " for j in range(num_qubits):\n", + " cir.rx(x[j], which_qubit=j)\n", + " cir.complex_entangled_layer(theta[-1:], depth=1)\n", + " else:\n", + " raise RuntimeError('Non-existent encoding method')\n", + " return cir" + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Then, define our quantum neural network along with the loss function using PaddlePaddle." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 13, + "source": [ + "import paddle.nn as nn\n", + "\n", + "class QuantumNeuralNetwork(nn.Layer):\n", + " def __init__(self, num_qubits, depth, encoding):\n", + " super().__init__()\n", + " self.num_qubits, self.depth, self.encoding = num_qubits, depth, encoding\n", + " if self.encoding == 'IQP':\n", + " self.theta = self.create_parameter(\n", + " shape=[self.depth, self.num_qubits, 3],\n", + " default_initializer=paddle.nn.initializer.Uniform(low=0.0,\n", + " high=2 *\n", + " np.pi),\n", + " dtype='float64',\n", + " is_bias=False)\n", + " elif self.encoding == 're-uploading':\n", + " self.theta = self.create_parameter(\n", + " shape=[self.depth + 1, self.num_qubits, 3],\n", + " default_initializer=paddle.nn.initializer.Uniform(low=0.0,\n", + " high=2 *\n", + " np.pi),\n", + " dtype='float64',\n", + " is_bias=False)\n", + " else:\n", + " raise RuntimeError('Non-existent encoding method')\n", + "\n", + " def forward(self, x):\n", + " if not paddle.is_tensor(x):\n", + " x = paddle.to_tensor(x)\n", + " cir = U_theta(x, self.theta, self.num_qubits, self.depth,\n", + " self.encoding)\n", + " cir.run_state_vector()\n", + " return cir.expecval([[1.0, 'z0']]) * paddle.to_tensor(\n", + " [0.5], dtype='float64') + paddle.to_tensor([0.5], dtype='float64')" + ], + "outputs": [], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Finally, define a CFIM calculator and calculate the effective dimension corresponding to different size of training samples." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 17, + "source": [ + "# Configure model parameters\n", + "num_qubits = 4\n", + "depth = 2\n", + "num_inputs = 100\n", + "num_thetas = 10\n", + "# Define the CFIM calculator\n", + "cfim = ClassicalFisher(model=QuantumNeuralNetwork,\n", + " num_thetas=num_thetas,\n", + " num_inputs=num_inputs,\n", + " num_qubits=num_qubits,\n", + " depth=depth,\n", + " encoding='IQP')\n", + "# Compute the normalized classical Fisher information\n", + "fim, _ = cfim.get_normalized_cfisher()\n", + "# Compute the effective dimension for different size of samples\n", + "n = [5000, 8000, 10000, 40000, 60000, 100000, 150000, 200000, 500000, 1000000]\n", + "effdim = cfim.get_eff_dim(fim, n)" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + "running in get_gradient: 100%|##################################| 1000/1000 [02:05<00:00, 7.94it/s]\n" + ] + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Plot the ratio of the effective dimension over number of parameters vs. sample size." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 19, + "source": [ + "fig = plt.figure(figsize=(9, 6))\n", + "ax = fig.add_subplot(111)\n", + "print('the number of parameters：%s' % cfim.num_params)\n", + "ax.plot(n, np.array(effdim) / cfim.num_params)\n", + "label_font_size = 14\n", + "ax.set_xlabel('sample size', fontsize=label_font_size)\n", + "ax.set_ylabel('effective dimension / number of parameters', fontsize=label_font_size)\n", + "ax.tick_params(labelsize=label_font_size)" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "the number of parameters：24\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
    " + ], + "image/png": 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" + }, + "metadata": { + "needs_background": "light" + } + } + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "## Conclusion\n", + "\n", + "This tutorial briefly introduces the concept of classical and quantum Fisher information and their relationship from a geometric point of view. Then, we illustrates their applications in quantum machine learning by taking effective dimension as an example. Finally, we show how to actually perform calculations of these quantities with Paddle Quantum." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "_______\n", + "\n", + "## References\n", + "\n", + "[1] Meyer, Johannes Jakob. \"Fisher information in noisy intermediate-scale quantum applications.\" [arXiv preprint arXiv:2103.15191 (2021).](https://arxiv.org/abs/2103.15191)\n", + "\n", + "[2] Haug, Tobias, Kishor Bharti, and M. S. Kim. \"Capacity and quantum geometry of parametrized quantum circuits.\" [arXiv preprint arXiv:2102.01659 (2021).](https://arxiv.org/abs/2102.01659)\n", + "\n", + "[3] Stokes, James, et al. \"Quantum natural gradient.\" [Quantum 4 (2020): 269.](https://quantum-journal.org/papers/q-2020-05-25-269/)\n", + "\n", + "[4] Mari, Andrea, Thomas R. Bromley, and Nathan Killoran. \"Estimating the gradient and higher-order derivatives on quantum hardware.\" [Physical Review A 103.1 (2021): 012405.](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.012405)\n", + "\n", + "[5] Datta, Nilanjana, and Felix Leditzky. \"A limit of the quantum Rényi divergence.\" [Journal of Physics A: Mathematical and Theoretical 47.4 (2014): 045304.](https://iopscience.iop.org/article/10.1088/1751-8113/47/4/045304)\n", + "\n", + "[6] Abbas, Amira, et al. \"The power of quantum neural networks.\" [Nature Computational Science 1.6 (2021): 403-409.](https://www.nature.com/articles/s43588-021-00084-1)" + ], + "metadata": {} + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file diff --git a/tutorial/qnn_research/Noise_CN.ipynb b/tutorial/qnn_research/Noise_CN.ipynb index a6e8399..2ad5577 100644 --- a/tutorial/qnn_research/Noise_CN.ipynb +++ b/tutorial/qnn_research/Noise_CN.ipynb @@ -2,6 +2,7 @@ "cells": [ { "cell_type": "markdown", + "id": "dedicated-alexander", "metadata": {}, "source": [ "# 在 Paddle Quantum 中模拟含噪量子电路\n", @@ -11,6 +12,7 @@ }, { "cell_type": "markdown", + "id": "weird-functionality", "metadata": {}, "source": [ "## 噪声简介\n", @@ -54,7 +56,7 @@ "\\tag{4}\n", "$$\n", "\n", - "其中 $X,I$ 是泡利矩阵。 对应的 *Kruas* 算符为：\n", + "其中 $X,I$ 是泡利矩阵。 对应的 *Kraus* 算符为：\n", "\n", "$$\n", "E_0 = \\sqrt{1-p}\n", @@ -77,6 +79,7 @@ }, { "cell_type": "markdown", + "id": "transsexual-hayes", "metadata": {}, "source": [ "### Paddle Quantum 中添加信道的方式\n", @@ -87,6 +90,7 @@ { "cell_type": "code", "execution_count": 1, + "id": "scheduled-attraction", "metadata": { "ExecuteTime": { "end_time": "2021-04-08T05:16:08.247239Z", @@ -136,6 +140,7 @@ }, { "cell_type": "markdown", + "id": "indian-slave", "metadata": {}, "source": [ "之后，我们加上一个 $p=0.1$ 的比特反转噪声，并测量通过信道之后的量子比特。 \n", @@ -145,6 +150,7 @@ { "cell_type": "code", "execution_count": 2, + "id": "fiscal-literature", "metadata": { "ExecuteTime": { "end_time": "2021-04-08T05:16:09.221527Z", @@ -193,6 +199,7 @@ }, { "cell_type": "markdown", + "id": "bibliographic-undergraduate", "metadata": {}, "source": [ "可以看到，经过了比特反转信道（概率为 $p=0.1$）之后的量子态变成了混合态 $0.9 | 0 \\rangle \\langle 0 | + 0.1 | 1 \\rangle \\langle 1 |$。\n", @@ -201,6 +208,7 @@ }, { "cell_type": "markdown", + "id": "million-diagnosis", "metadata": {}, "source": [ "### 常用噪声信道\n", @@ -307,6 +315,7 @@ }, { "cell_type": "markdown", + "id": "alert-senator", "metadata": {}, "source": [ "### 自定义信道\n", @@ -317,6 +326,7 @@ { "cell_type": "code", "execution_count": 3, + "id": "mobile-death", "metadata": { "ExecuteTime": { "end_time": "2021-04-08T05:17:30.681411Z", @@ -375,6 +385,7 @@ }, { "cell_type": "markdown", + "id": "proper-director", "metadata": {}, "source": [ "按照上述例子，用户可以通过自定义 *Kraus* 算符的方式实现特定的信道。" @@ -382,6 +393,7 @@ }, { "cell_type": "markdown", + "id": "tested-elder", "metadata": {}, "source": [ "## 拓展：Paddle Quantum 模拟含噪纠缠资源\n", @@ -393,6 +405,7 @@ { "cell_type": "code", "execution_count": 4, + "id": "spread-monkey", "metadata": { "ExecuteTime": { "end_time": "2021-04-08T05:24:35.552425Z", @@ -450,6 +463,7 @@ }, { "cell_type": "markdown", + "id": "comparable-athletics", "metadata": {}, "source": [ "**注释：** 在 [纠缠蒸馏](../locc/EntanglementDistillation_LOCCNET_CN.ipynb) 的教程中我们介绍了如何利用 Paddle Quantm 中的 LoccNet 模块来研究纠缠蒸馏，即利用多个含噪声的纠缠对来提取高保真度的纠缠对，感兴趣的读者可以前往阅读。" @@ -457,6 +471,7 @@ }, { "cell_type": "markdown", + "id": "elegant-bikini", "metadata": {}, "source": [ "## 应用： Paddle Quantum 模拟含噪变分量子本征求解器（VQE）\n", @@ -477,6 +492,7 @@ { "cell_type": "code", "execution_count": 5, + "id": "unavailable-october", "metadata": { "ExecuteTime": { "end_time": "2021-04-08T05:34:47.301281Z", @@ -508,6 +524,7 @@ { "cell_type": "code", "execution_count": 6, + "id": "protected-difficulty", "metadata": { "ExecuteTime": { "end_time": "2021-04-08T05:34:51.742273Z", @@ -666,6 +683,7 @@ }, { "cell_type": "markdown", + "id": "important-testing", "metadata": {}, "source": [ "可以看到，含噪的变分量子本征求解器的效果要差于不含噪的版本，无法达到化学精度的要求 $\\varepsilon = 0.0016$ Ha。" @@ -673,6 +691,7 @@ }, { "cell_type": "markdown", + "id": "extensive-forge", "metadata": {}, "source": [ "## 总结\n", @@ -682,6 +701,7 @@ }, { "cell_type": "markdown", + "id": "inappropriate-board", "metadata": {}, "source": [ "---\n", @@ -716,7 +736,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.3" + "version": "3.7.10" }, "toc": { "base_numbering": 1, diff --git a/tutorial/qnn_research/figures/BP-fig-Barren_circuit.png b/tutorial/qnn_research/figures/BP-fig-Barren_circuit.png index 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a/tutorial/quantum_simulation/DistributedVQE_CN.ipynb b/tutorial/quantum_simulation/DistributedVQE_CN.ipynb new file mode 100644 index 0000000..8a70c91 --- /dev/null +++ b/tutorial/quantum_simulation/DistributedVQE_CN.ipynb @@ -0,0 +1,577 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "c1a5f1e6", + "metadata": {}, + "source": [ + "# 基于施密特分解的分布式变分量子本征求解器\n", + "\n", + "*Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved.*" + ] + }, + { + "cell_type": "markdown", + "id": "cf44390c", + "metadata": { + "tags": [] + }, + "source": [ + "## 概览\n", + "\n", + "在物理和化学等学科中，一个非常重要的问题就是提取分子、原子等物理系统的基态信息。系统的基态是由系统对应的哈密顿量决定的。目前普遍认为量子计算机在求解哈密顿量基态问题上具有优势。[变分量子本征求解器](https://qml.baidu.com/tutorials/quantum-simulation/variational-quantum-eigensolver.html)（variational quantum eigensolver, VQE），作为有望在近期展现量子优势的算法之一，为研究者们提供了可以在含噪的中等规模量子（NISQ）设备上研究量子化学的可能。然而，目前 NISQ 设备仍存在许多局限性，阻碍了大规模量子算法的运行。例如，受限于现有量子设备所能提供的量子比特数，研究者们无法利用 VQE 在 NISQ 设备上模拟真实的大分子。为了突破这一限制，许多分布式方案 [1-3] 相继被提出。\n", + "在本教程中，我们以 [4] 提出的基于施密特分解的 VQE 为例，向读者展示如何利用 Paddle Quantum 实现分布式量子算法。" + ] + }, + { + "cell_type": "markdown", + "id": "f3fcc1b4", + "metadata": {}, + "source": [ + "## 施密特分解\n", + "\n", + "对于任意处于复合系统 $AB$ 上的纯态 $|\\psi\\rangle$，我们有如下平凡分解:\n", + "\n", + "$$\n", + "|\\psi\\rangle=\\sum_{ij}a_{ij}|i\\rangle\\otimes|j\\rangle,\n", + "\\tag{1}\n", + "$$\n", + "\n", + "其中 $|i\\rangle$ 和 $|j\\rangle$ 分别是子系统 $A$、$B$ 上的计算基底，$a_{ij}$ 是某复矩阵 $a$ 的元素。接下来，我们对矩阵 $a$ 运用[奇异值分解](https://zh.wikipedia.org/wiki/奇异值分解)（singular value decomposition, SVD），即，$a = udv$，其中 $u,v$ 是酉矩阵，$d$ 是对角矩阵。那么，$a_{ij}=\\sum_ku_{ik}d_{kk}v_{kj}$。\n", + "\n", + "通过定义 \n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "|k_A\\rangle\\equiv & \\sum_iu_{ik}|i\\rangle=u|k\\rangle,\\\\\n", + "|k_B\\rangle\\equiv & \\sum_jv_{kj}|j\\rangle=v^T|k\\rangle,\\\\\n", + "\\lambda_k\\equiv & d_{kk},\\end{aligned}\n", + "\\tag{2}\n", + "$$\n", + "\n", + "我们可以把（1）式重写为\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + " |\\psi\\rangle &= \\sum_{ijk}u_{ik}d_{kk}v_{kj}|i\\rangle\\otimes|j\\rangle \\\\\n", + " &= \\sum_{k}\\lambda_{k}\\Big(\\sum_iu_{ik}|i\\rangle\\Big)\\otimes\\Big(\\sum_jv_{kj}|j\\rangle\\Big) \\\\\n", + " &=\\sum_{k}\\lambda_k(u|k\\rangle\\otimes v^T|k\\rangle)\\\\\n", + " &=\\sum_{k}\\lambda_k|k_A\\rangle\\otimes|k_B\\rangle.\n", + "\\end{aligned}\n", + "\\tag{3}\n", + "$$\n", + "\n", + "形如 $|\\psi\\rangle=\\sum_k\\lambda_k|k_A\\rangle\\otimes|k_B\\rangle$ 的分解方式就称为 **施密特分解** [5]。同时，$\\{\\lambda_k\\}_k$ 被称作施密特系数，非零 $\\lambda_k$ 的数量被称为 $|\\psi\\rangle$ 的施密特秩。事实上，奇异值分解的性质还保证了 $\\lambda_k\\in\\mathbb{R}^+$ 及 $\\sum_k\\lambda_k^2=1$。" + ] + }, + { + "cell_type": "markdown", + "id": "620e053c", + "metadata": { + "tags": [] + }, + "source": [ + "## 基于施密特分解的分布式 VQE\n", + "\n", + "作为标准 VQE [6] 的一个变种，分布式 VQE 同样试图寻找一个 $N$ 量子比特哈密顿量 $\\hat{H}=\\sum_tc_t\\hat{H}_t^{(A)}\\otimes\\hat{H}_t^{(B)}$ 的基态及其能量，其中 $\\hat{H}_t^{(A)},\\hat{H}_t^{(B)}$ 是分别作用于子系统 $A$、$B$ 上的哈密顿量分量（我们假设 $A$、$B$ 都包含 $N/2$ 量子比特）。\n", + "\n", + "我们从如下试探波函数开始：\n", + "\n", + "$$\n", + "|\\psi\\rangle\\equiv\\sum_{k=1}^S\\lambda_k\\Big(U(\\boldsymbol{\\theta})|k\\rangle\\Big)\\otimes\\Big(V(\\boldsymbol{\\phi})|k\\rangle\\Big)\n", + "\\tag{4},\n", + "$$\n", + "\n", + "其中 $\\boldsymbol{\\lambda}\\equiv(\\lambda_1, \\lambda_2,...,\\lambda_S)^T$，$1\\leq S\\leq 2^{N/2}$ 是一个用户定义的常数。根据施密特分解，目标基态同样可写成（4）式的形式。因此，通过寻找合适的参数向量 $\\boldsymbol{\\lambda}, \\boldsymbol{\\theta}$ 和 $\\boldsymbol{\\phi}$，我们可以在任意误差内近似目标基态。\n", + "\n", + "接下来，对于所有 $i,j=1,...,S$，我们在一台 $N/2$ 量子比特的量子计算机上计算如下项：\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "E_{ijt}^A(\\boldsymbol{\\theta}) &\\equiv \\langle i|U^\\dagger(\\boldsymbol{\\theta}) \\hat{H}_t^{(A)} U(\\boldsymbol{\\theta})|j\\rangle,\\\\\n", + "E_{ijt}^B(\\boldsymbol{\\phi}) &\\equiv \\langle i|V^\\dagger(\\boldsymbol{\\phi}) \\hat{H}_t^{(B)} V(\\boldsymbol{\\phi}))|j\\rangle.\n", + "\\end{aligned}\n", + "\\tag{5}\n", + "$$\n", + "\n", + "然后，在一台经典计算机上，我们根据如下定义构造一个 $S\\times S$ 维的矩阵 $M(\\boldsymbol{\\theta},\\boldsymbol{\\phi})$：\n", + "\n", + "$$\n", + "[M(\\boldsymbol{\\theta},\\boldsymbol{\\phi})]_{ij}\\equiv\\sum_tc_tE_{ijt}^A(\\boldsymbol{\\theta})E_{ijt}^B(\\boldsymbol{\\phi}).\n", + "\\tag{6}\n", + "$$\n", + "\n", + "这样，目标基态能量就可以写为 \n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "E_{tar} &= \\min_{\\boldsymbol{\\lambda}, \\boldsymbol{\\theta}, \\boldsymbol{\\phi}} \\langle{\\psi}|\\hat{H}|\\psi\\rangle \\\\\n", + " &= \\min_{\\boldsymbol{\\lambda}, \\boldsymbol{\\theta}, \\boldsymbol{\\phi}}\\Big(\\sum_{i,j=1}^S\\lambda_i\\lambda_j[M(\\boldsymbol{\\theta},\\boldsymbol{\\phi})]_{ij}\\Big)\\\\\n", + " &= \\min_{\\boldsymbol{\\theta}, \\boldsymbol{\\phi}} E(\\boldsymbol{\\theta},\\boldsymbol{\\phi}),\n", + "\\end{aligned}\n", + "\\tag{7}\n", + "$$\n", + "\n", + "其中 $E(\\boldsymbol{\\theta},\\boldsymbol{\\phi})\\equiv\\min_{\\boldsymbol{\\lambda}} \\boldsymbol{\\lambda}^T M(\\boldsymbol{\\theta},\\boldsymbol{\\phi})\\boldsymbol{\\lambda}$。根据线性代数的内容，不难发现，$E(\\boldsymbol{\\theta},\\boldsymbol{\\phi})$ 正是矩阵 $M(\\boldsymbol{\\theta},\\boldsymbol{\\phi})$ 的最小特征值，可以通过经典算法求得。\n", + "\n", + "最终，我们重复如上过程，并使用基于梯度下降的优化方法最小化 $E(\\boldsymbol{\\theta},\\boldsymbol{\\phi})$，使其趋近于 $E_{tar}$。\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "f79d3333", + "metadata": { + "tags": [] + }, + "source": [ + "## 量桨实现\n", + "\n", + "首先，我们导入必要的包。由于我们要使用飞桨和量桨的最新功能，请确保您的 *PaddlePaddle* >= 2.2.0 且 *Paddle Quantum* >= 2.1.3。" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "bb7c0db4", + "metadata": {}, + "outputs": [], + "source": [ + "import time\n", + "import numpy as np\n", + "from matplotlib import pyplot as plt\n", + "\n", + "import paddle\n", + "from paddle_quantum.circuit import UAnsatz\n", + "from paddle_quantum.utils import pauli_str_to_matrix, schmidt_decompose" + ] + }, + { + "cell_type": "markdown", + "id": "c84dd264", + "metadata": {}, + "source": [ + "定义一些全局常数：" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "27e4ce36", + "metadata": {}, + "outputs": [], + "source": [ + "N = 10 # 量子比特数\n", + "SEED = 16 # 固定随机种子\n", + "ITR = 100 # 设置迭代次数\n", + "LR = 0.1 # 设置学习率\n", + "D = 3 # 设置量子神经网络的层数" + ] + }, + { + "cell_type": "markdown", + "id": "3db38f56", + "metadata": {}, + "source": [ + "下面这一函数经典地计算出哈密顿量 $H$ 的基态信息（基态对能量和施密特秩），以作为后面量子模型的基准参照。" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "32b310ed", + "metadata": {}, + "outputs": [], + "source": [ + "def get_ground_state_info(H):\n", + "\n", + " # 计算 H 的特征值与特征向量\n", + " vals, vecs = paddle.linalg.eigh(H)\n", + " # 获取基态\n", + " ground_state = vecs[:, 0].numpy()\n", + " # 获取基态能量\n", + " ground_state_energy = vals.tolist()[0]\n", + " print(f'The ground state energy is {ground_state_energy:.5f} Ha.')\n", + " # 对基态运用施密特分解\n", + " l, _, _ = schmidt_decompose(ground_state)\n", + " print(f'Schmidt rank of the ground state is {l.size}.')\n", + "\n", + " return ground_state_energy" + ] + }, + { + "cell_type": "markdown", + "id": "8c2c88d3", + "metadata": {}, + "source": [ + "现在，我们生成一个哈密顿量并计算其基态信息。" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "6149b4d4", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The ground state energy is -0.99783 Ha.\n", + "Schmidt rank of the ground state is 3.\n" + ] + } + ], + "source": [ + "# 固定随机种子\n", + "np.random.seed(SEED)\n", + "\n", + "# 硬编码一个哈密顿量\n", + "coefs = [-0.8886258, 0.453882]\n", + "pauli_str = ['x0,z1,z2,z4,x5,y6,y7,x8,x9', 'y0,x1,x2,x3,y4,x5,z6,z7,y8,x9']\n", + "pauli_str_A = ['x0,z1,z2,z4', 'y0,x1,x2,x3,y4'] # 子系统 A 的泡利字符串\n", + "pauli_str_B = ['x0,y1,y2,x3,x4', 'x0,z1,z2,y3,x4'] # 子系统 B 的泡利字符串\n", + "\n", + "# 把相关对象转换为张量形式\n", + "H_mtr = paddle.to_tensor(pauli_str_to_matrix(zip(coefs, pauli_str), n=N))\n", + "coefs = paddle.to_tensor(coefs)\n", + "H_A = [pauli_str_to_matrix([[1., pstr]], n=N//2) for pstr in pauli_str_A]\n", + "H_A = paddle.to_tensor(np.stack(H_A))\n", + "H_B = [pauli_str_to_matrix([[1., pstr]], n=N-N//2) for pstr in pauli_str_B]\n", + "H_B = paddle.to_tensor(np.stack(H_B))\n", + "\n", + "# 计算该哈密顿量的基态信息\n", + "ground_state_energy = get_ground_state_info(H_mtr)" + ] + }, + { + "cell_type": "markdown", + "id": "9abf331c", + "metadata": {}, + "source": [ + "准备好一个哈密顿量后，我们可以构建一个分布式 VQE 来求解它。" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "32cacc67", + "metadata": {}, + "outputs": [], + "source": [ + "# 构造参数化量子电路\n", + "def U_theta(param, N, D):\n", + " \n", + " cir = UAnsatz(N) # 初始化一个宽度为 N 量子比特的电路\n", + " cir.complex_entangled_layer(param, D) # 添加量子门\n", + " return cir.U # 获取参数化电路的矩阵\n", + "\n", + "# 把参数化电路作用在计算基底上\n", + "# 并返回一个形状为 [2**N, num_states] 的张量\n", + "def output_states(theta, num_states, N, D):\n", + " # 创建 num_states 个计算基底\n", + " basis = paddle.eye(2**N, num_states)\n", + " \n", + " # 获得参数化电路\n", + " U = U_theta(theta, N, D)\n", + " \n", + " # 把参数化电路作用在这些基底上\n", + " vec = U @ basis \n", + " \n", + " return vec" + ] + }, + { + "cell_type": "markdown", + "id": "0ca5787c", + "metadata": {}, + "source": [ + "以下代码是本教程的核心。请读者仔细阅读，并与前文的公式叙述做比较。" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "6ebf5159", + "metadata": {}, + "outputs": [], + "source": [ + "# 构造分布式模型\n", + "class DistributedVQE(paddle.nn.Layer):\n", + " def __init__(self, N, D, S):\n", + " super().__init__()\n", + " paddle.seed(SEED)\n", + "\n", + " # 定义常数 S\n", + " self.S = S\n", + " self.N, self.D = N, D\n", + " # 初始化参数列表 theta, phi，并用 [0, 2*pi] 的均匀分布来填充初始值\n", + " self.theta = self.create_parameter(shape=[D, N//2, 3], dtype=\"float64\",\n", + " default_initializer=paddle.nn.initializer.Uniform(low=0.0, high=2*np.pi))\n", + " self.phi = self.create_parameter(shape=[D, N - N//2, 3], dtype=\"float64\",\n", + " default_initializer=paddle.nn.initializer.Uniform(low=0.0, high=2*np.pi))\n", + " \n", + " # 分布式 VQE 的核心逻辑\n", + " def forward(self):\n", + " # 分别获得子系统 A、B 上的 U|k> 和 V|k> \n", + " vec_A = output_states(self.theta, self.S, self.N//2, self.D)\n", + " vec_B = output_states(self.phi, self.S, self.N - self.N//2, self.D)\n", + " \n", + " # 计算由前文定义的 E_{ijt}^A 和 E_{ijt}^B 组成的张量 E_A, E_B\n", + " E_A = vec_A.conj().t() @ H_A @ vec_A\n", + " E_B = vec_B.conj().t() @ H_B @ vec_B\n", + " M = (coefs.reshape([-1, 1, 1]) * E_A * E_B).sum(0)\n", + "\n", + " # 计算矩阵 M 的最小特征值\n", + " eigval = paddle.linalg.eigvalsh(M)\n", + " loss = eigval[0]\n", + " \n", + " return loss" + ] + }, + { + "cell_type": "markdown", + "id": "d04669ff", + "metadata": {}, + "source": [ + "定义训练函数。" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "066f5e72", + "metadata": {}, + "outputs": [], + "source": [ + "def train(model):\n", + " start_time = time.time() # 用以计算该函数的运行时长\n", + " \n", + " # 我们使用基于梯度下降的优化器 Adam 来优化 theta 和 phi\n", + " opt = paddle.optimizer.Adam(learning_rate=LR, parameters=model.parameters())\n", + " summary_loss = [] # 记录损失历史\n", + "\n", + " # 迭代优化\n", + " for itr in range(ITR):\n", + "\n", + " # 前向传播，计算损失函数\n", + " loss = model()\n", + "\n", + " # 后向传播，优化损失函数\n", + " loss.backward()\n", + " opt.minimize(loss)\n", + " opt.clear_grad()\n", + "\n", + " # 更新优化结果\n", + " summary_loss.append(loss.numpy())\n", + "\n", + " # 打印中间结果\n", + " if (itr+1) % 20 == 0:\n", + " print(f\"iter: {itr+1}, loss: {loss.tolist()[0]: .4f} Ha\")\n", + "\n", + " print(f'Ground truth is {ground_state_energy:.4f} Ha')\n", + " print(f'Training took {time.time() - start_time:.2f}s')\n", + " \n", + " plt.plot(list(range(ITR)), summary_loss, color='r', label='loss')\n", + " plt.hlines(y=ground_state_energy, xmin=0, xmax=ITR, linestyle=':', label='ground truth')\n", + " plt.legend()\n", + " plt.title(f'Loss for {type(model).__name__} on a {N}-qubit Hamiltonian')\n", + " plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "c8770b19", + "metadata": {}, + "source": [ + "现在，我们实例化并训练分布式模型。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "78b46dcc", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "iter: 20, loss: -0.9244 Ha\n", + "iter: 40, loss: -0.9906 Ha\n", + "iter: 60, loss: -0.9968 Ha\n", + "iter: 80, loss: -0.9977 Ha\n", + "iter: 100, loss: -0.9978 Ha\n", + "Ground truth is -0.9978 Ha\n", + "Training took 13.01s\n" + ] + }, + { + "data": { + "image/png": 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", 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    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 注意，由于我们构造的哈密顿量在两子系统间相互作用较小，我们只需设置 S = 4.\n", + "#（更多解释请见总结部分）\n", + "vqe = DistributedVQE(N, D, S=4)\n", + "train(vqe)" + ] + }, + { + "cell_type": "markdown", + "id": "9eb85055", + "metadata": {}, + "source": [ + "在上图中，我们用虚线画出了真实的基态能量。可以看到，loss 曲线收敛至虚线，表明我们的分布式 VQE 成功找到了该哈密顿量的基态能量。然而，要妥当地评估我们的模型，我们还需将它与标准 VQE 做比较。因此，下面我们构建标准 VQE 模型：" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "2fff9166", + "metadata": {}, + "outputs": [], + "source": [ + "class StandardVQE(paddle.nn.Layer):\n", + " def __init__(self, N, D):\n", + " super().__init__()\n", + " paddle.seed(SEED)\n", + " self.N, self.D = N, D\n", + " self.theta = self.create_parameter(shape=[D, N, 3], dtype=\"float64\",\n", + " default_initializer=paddle.nn.initializer.Uniform(low=0.0, high=2*np.pi))\n", + " \n", + " def forward(self):\n", + " vec = output_states(self.theta, 1, self.N, self.D)\n", + " loss = vec.conj().t() @ H_mtr @ vec\n", + " return loss.cast('float64').flatten()" + ] + }, + { + "cell_type": "markdown", + "id": "8bc5dcfd", + "metadata": {}, + "source": [ + "实例化并训练标准 VQE。" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "a35f3eb4", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "iter: 20, loss: -0.8365 Ha\n", + "iter: 40, loss: -0.9852 Ha\n", + "iter: 60, loss: -0.9958 Ha\n", + "iter: 80, loss: -0.9975 Ha\n", + "iter: 100, loss: -0.9978 Ha\n", + "Ground truth is -0.9978 Ha\n", + "Training took 721.76s\n" + ] + }, + { + "data": { + "image/png": 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", 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    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "svqe = StandardVQE(N, D)\n", + "train(svqe) # 训练标准 VQE" + ] + }, + { + "cell_type": "markdown", + "id": "5688a618", + "metadata": {}, + "source": [ + "有趣的是，通过比较两个模型的运行时间，我们发现，分布式 VQE 的运行速度比标准 VQE 快了五十多倍！事实上，这很容易理解：在分布式模型中，我们只需模拟两个 $N/2$ 量子比特的酉变换，这无论在时间还是空间上，都比标准 VQE 中模拟一个 $N$ 量子比特的酉变换高效得多。" + ] + }, + { + "cell_type": "markdown", + "id": "94cda668", + "metadata": { + "tags": [] + }, + "source": [ + "## 总结\n", + "\n", + "在此教程中，我们构造了一个分布式 VQE 并展示了其部分优势：\n", + "- NISQ 设备的计算范围得以拓展。通过分布式策略，我们可以运行超过硬件量子比特数的量子算法。\n", + "- 计算效率得到提升。对于量子过程的经典模拟而言，分布式算法降低了酉矩阵的维度，因此降低了模拟这些矩阵所需的时间、空间消耗。\n", + "\n", + "同时，需要注意的是，用户定义的常数 $S$ 在训练准确度和效率上扮演了重要角色：\n", + "- 对于子系统间相互作用弱的哈密顿量而言，其基态在子系统间纠缠较弱 [7]。因此，其施密特秩较低，可以被一个较小的 $S$ 精确且高效地模拟。事实上，我们所给的演示及大多数物理、化学中有意义的哈密顿量都具有此性质。\n", + "- 相反的，对于子系统间相互作用强的哈密顿量而言，其基态在子系统间纠缠较强，因此需要一个较大的 $S$ 来模拟。但是，无论如何，$S$ 的上界是 $2^{N/2}$，因此矩阵 $M$ 的维度上界是 $2^{N/2}\\times2^{N/2}$，这仍然比初始哈密顿量的维度（$2^{N}\\times 2^{N}$）小。因此，该算法的效率总是优于纯经典模拟。" + ] + }, + { + "cell_type": "markdown", + "id": "922679aa", + "metadata": { + "jp-MarkdownHeadingCollapsed": true, + "tags": [] + }, + "source": [ + "_______\n", + "\n", + "# 参考文献\n", + "\n", + "[1] Fujii, Keisuke, et al. \"Deep Variational Quantum Eigensolver: a divide-and-conquer method for solving a larger problem with smaller size quantum computers.\" [arXiv preprint arXiv:2007.10917 (2020)](https://arxiv.org/abs/2007.10917).\n", + "\n", + "[2] Zhang, Yu, et al. \"Variational Quantum Eigensolver with Reduced Circuit Complexity.\" [arXiv preprint arXiv:2106.07619 (2021)](https://arxiv.org/abs/2106.07619).\n", + "\n", + "[3] Peng, Tianyi et al. \"Simulating Large Quantum Circuits On A Small Quantum Computer\". [Physical Review Letters 125.15, (2020): 150504](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.150504).\n", + "\n", + "[4] Eddins, Andrew, et al. \"Doubling the size of quantum simulators by entanglement forging.\" [arXiv preprint arXiv:2104.10220 (2021)](https://arxiv.org/abs/2104.10220).\n", + "\n", + "[5] Nielsen, Michael A., and Isaac L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2010.\n", + "\n", + "[6] Moll, Nikolaj, et al. \"Quantum optimization using variational algorithms on near-term quantum devices.\" [Quantum Science and Technology 3.3 (2018): 030503](https://iopscience.iop.org/article/10.1088/2058-9565/aab822).\n", + "\n", + "[7] Khatri, Sumeet, and Mark M. Wilde. \"Principles of quantum communication theory: A modern approach.\" [arXiv preprint arXiv:2011.04672 (2020)](https://arxiv.org/abs/2011.04672)." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/tutorial/quantum_simulation/DistributedVQE_EN.ipynb b/tutorial/quantum_simulation/DistributedVQE_EN.ipynb new file mode 100644 index 0000000..95f6080 --- /dev/null +++ b/tutorial/quantum_simulation/DistributedVQE_EN.ipynb @@ -0,0 +1,574 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "responsible-handle", + "metadata": {}, + "source": [ + "# Distributed Variational Quantum Eigensolver Based on Schmidt Decomposition\n", + "*Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved.*" + ] + }, + { + "cell_type": "markdown", + "id": "superb-sunrise", + "metadata": { + "tags": [] + }, + "source": [ + "## Overview\n", + "\n", + "Retrieving ground state information of a Hamiltonian in amongst the essential questions in physics and chemistry. Currently, it is widely believed that quantum computers are advantageous in solving this kind of problem. As one of the promising algorithms to demonstrate quantum supremacy in the near term, [Variational Quantum Eigensolver (VQE)](https://qml.baidu.com/tutorials/quantum-simulation/variational-quantum-eigensolver.html)\n", + "enables the study of quantum chemistry on Noisy Intermediate-Scale Quantum (NISQ) devices. However, various technical limitations still exist on current NISQ hardware, forbidding the deployment of large-scale quantum algorithms. For example, limited by the number of available qubits, researchers have not been able to simulate realistic large molecules with high precision. To overcome this barrier, researchers have proposed a wide range of distributed strategies [1-3]. In this tutorial, we take the distributed VQE based on Schmidt decomposition, proposed in [4], as an example to demonstrate how to implement distributed quantum algorithms using Paddle Quantum." + ] + }, + { + "cell_type": "markdown", + "id": "illegal-zealand", + "metadata": {}, + "source": [ + "## Schmidt Decomposition\n", + "We start with the following trivial decomposition for any pure state $|\\psi\\rangle$ of a composite system $AB$:\n", + "\n", + "$$\n", + "|\\psi\\rangle=\\sum_{ij}a_{ij}|i\\rangle\\otimes|j\\rangle,\n", + "\\tag{1}\n", + "$$\n", + "\n", + "where $|i\\rangle$ and $|j\\rangle$ are computational bases of subsystems $A$ and $B$ respectively, and $a_{ij}$ are elements of some complex matrix $a$. Then, we apply [singular value decomposition (SVD)](https://en.wikipedia.org/wiki/Singular_value_decomposition)\n", + "on $a$, i.e., $a = udv$ with $u,v$ being unitary and $d$ diagonal. Hence, $a_{ij}=\\sum_ku_{ik}d_{kk}v_{kj}$. \n", + "\n", + "By defining\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "|k_A\\rangle\\equiv & \\sum_iu_{ik}|i\\rangle=u|k\\rangle,\\\\\n", + "|k_B\\rangle\\equiv & \\sum_jv_{kj}|j\\rangle=v^T|k\\rangle,\\\\\n", + "\\lambda_k\\equiv & d_{kk},\n", + "\\end{aligned}\n", + "\\tag{2}\n", + "$$\n", + "\n", + "we may rewrite Eq. (1) as\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + " |\\psi\\rangle &= \\sum_{ijk}u_{ik}d_{kk}v_{kj}|i\\rangle\\otimes|j\\rangle \\\\\n", + " &= \\sum_{k}\\lambda_{k}\\Big(\\sum_iu_{ik}|i\\rangle\\Big)\\otimes\\Big(\\sum_jv_{kj}|j\\rangle\\Big) \\\\\n", + " &=\\sum_{k}\\lambda_k(u|k\\rangle\\otimes v^T|k\\rangle)\\\\\n", + " &=\\sum_{k}\\lambda_k|k_A\\rangle\\otimes|k_B\\rangle.\n", + "\\end{aligned}\n", + "\\tag{3}\n", + "$$\n", + "\n", + "The decomposition of $|\\psi\\rangle$ into the form of $\\sum_k\\lambda_k|k_A\\rangle\\otimes|k_B\\rangle$ is known as its ***Schmidt decomposition*** [5], with $\\{\\lambda_k\\}_k$ called the *Schmidt coefficients* and the number of non-zero $\\lambda_k$'s its *Schmidt rank*. In fact, the property of SVD also guarantees that $\\lambda_k\\in\\mathbb{R}^+$ and $\\sum_k\\lambda_k^2=1$. " + ] + }, + { + "cell_type": "markdown", + "id": "looking-detail", + "metadata": { + "tags": [] + }, + "source": [ + "## Distributed VQE Based on Schmidt Decomposition\n", + "\n", + "As a variation of the standard VQE [6], the distributed VQE also seeks to solve the ground state and its energy of an $N$-qubit Hamiltonian $\\hat{H}=\\sum_tc_t\\hat{H}_t^{(A)}\\otimes\\hat{H}_t^{(B)}$， where $\\hat{H}_t^{(A)},\\hat{H}_t^{(B)}$ are Hamiltonian terms on subsystems $A,B$ respectively (we have assumed that $A$, $B$ both have $N/2$ qubits).\n", + "\n", + "To start with, we write the trial wave function as\n", + "\n", + "$$\n", + "|\\psi\\rangle\\equiv\\sum_{k=1}^S\\lambda_k\\Big(U(\\boldsymbol{\\theta})|k\\rangle\\Big)\\otimes\\Big(V(\\boldsymbol{\\phi})|k\\rangle\\Big),\n", + "\\tag{4}\n", + "$$\n", + "\n", + "for some $\\boldsymbol{\\lambda}\\equiv(\\lambda_1, \\lambda_2,...,\\lambda_S)^T$ and $1\\leq S\\leq 2^{N/2}$ a user-defined constant. According to Schmidt decomposition, the target ground state also has the form of Eq. (4) and hence can be approximated with high precision by choosing appropriate parameters $\\boldsymbol{\\lambda}, \\boldsymbol{\\theta}$ and $\\boldsymbol{\\phi}$.\n", + "\n", + "Now, for all $i,j=1,...,S$, we evaluate the following terms on an $N/2$-qubit quantum computer:\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "E_{ijt}^A(\\boldsymbol{\\theta}) &\\equiv \\langle i|U^\\dagger(\\boldsymbol{\\theta}) \\hat{H}_t^{(A)} U(\\boldsymbol{\\theta})|j\\rangle,\\\\\n", + "E_{ijt}^B(\\boldsymbol{\\phi}) &\\equiv \\langle i|V^\\dagger(\\boldsymbol{\\phi}) \\hat{H}_t^{(B)} V(\\boldsymbol{\\phi}))|j\\rangle.\n", + "\\end{aligned}\n", + "\\tag{5}\n", + "$$\n", + "\n", + "Then, on a classical computer, we construct an $S\\times S$ dimensional matrix $M(\\boldsymbol{\\theta},\\boldsymbol{\\phi})$ according to\n", + "\n", + "$$\n", + "[M(\\boldsymbol{\\theta},\\boldsymbol{\\phi})]_{ij}\\equiv\\sum_tc_tE_{ijt}^A(\\boldsymbol{\\theta})E_{ijt}^B(\\boldsymbol{\\phi}).\n", + "\\tag{6}\n", + "$$\n", + "\n", + "In this way, the target ground state energy can be written as \n", + "$$\n", + "\\begin{aligned}\n", + "E_{tar} &= \\min_{\\boldsymbol{\\lambda}, \\boldsymbol{\\theta}, \\boldsymbol{\\phi}} \\langle{\\psi}|\\hat{H}|\\psi\\rangle \\\\\n", + " &= \\min_{\\boldsymbol{\\lambda}, \\boldsymbol{\\theta}, \\boldsymbol{\\phi}}\\Big(\\sum_{i,j=1}^S\\lambda_i\\lambda_j[M(\\boldsymbol{\\theta},\\boldsymbol{\\phi})]_{ij}\\Big)\\\\\n", + " &= \\min_{\\boldsymbol{\\theta}, \\boldsymbol{\\phi}} E(\\boldsymbol{\\theta},\\boldsymbol{\\phi}),\n", + "\\end{aligned}\n", + "\\tag{7}\n", + "$$\n", + "\n", + "where $E(\\boldsymbol{\\theta},\\boldsymbol{\\phi})\\equiv\\min_{\\boldsymbol{\\lambda}} \\boldsymbol{\\lambda}^T M(\\boldsymbol{\\theta},\\boldsymbol{\\phi})\\boldsymbol{\\lambda}$. By linear algebra, we see that $E(\\boldsymbol{\\theta},\\boldsymbol{\\phi})$ is exactly the minimal eigenvalue of $M(\\boldsymbol{\\theta},\\boldsymbol{\\phi})$, which can be solved using classical algorithms.\n", + "\n", + "Finally, we repeat the whole process and minimize $E(\\boldsymbol{\\theta},\\boldsymbol{\\phi})$ to approximate $E_{tar}$ using gradient-based optimization methods." + ] + }, + { + "cell_type": "markdown", + "id": "enabling-bulletin", + "metadata": { + "tags": [] + }, + "source": [ + "## Paddle Quantum implementation\n", + "\n", + "First of all, we import necessary packages. Please make sure that you have *PaddlePaddle* >= 2.2.0 and *Paddle Quantum* >= 2.1.3, as we will use some of their latest features." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "sized-girlfriend", + "metadata": {}, + "outputs": [], + "source": [ + "import time\n", + "import numpy as np\n", + "from matplotlib import pyplot as plt\n", + "\n", + "import paddle\n", + "from paddle_quantum.circuit import UAnsatz\n", + "from paddle_quantum.utils import pauli_str_to_matrix, schmidt_decompose" + ] + }, + { + "cell_type": "markdown", + "id": "central-internet", + "metadata": {}, + "source": [ + "Define some global constants:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "diverse-village", + "metadata": {}, + "outputs": [], + "source": [ + "N = 10 # Number of qubits\n", + "SEED = 16 # Fix a random seed\n", + "ITR = 100 # Set the number of learning iterations\n", + "LR = 0.1 # Set the learning rate\n", + "D = 3 # Set the depth for QNN" + ] + }, + { + "cell_type": "markdown", + "id": "strange-challenge", + "metadata": {}, + "source": [ + "The following function classically calculates the ground state information (the energy and the Schmidt rank of the ground state) of a Hamiltonian $H$, which we will use as the ground truth to benchmark our quantum models." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "musical-ultimate", + "metadata": {}, + "outputs": [], + "source": [ + "def get_ground_state_info(H):\n", + "\n", + " # Calculate the eigenvalues and eigenvectors of H\n", + " vals, vecs = paddle.linalg.eigh(H)\n", + " # Retrieve the ground state\n", + " ground_state = vecs[:, 0].numpy()\n", + " # Retrieve the ground state energy\n", + " ground_state_energy = vals.tolist()[0]\n", + " print(f'The ground state energy is {ground_state_energy:.5f} Ha.')\n", + " # Run Schmidt decomposition on the ground state.\n", + " l, _, _ = schmidt_decompose(ground_state)\n", + " print(f'Schmidt rank of the ground state is {l.size}.')\n", + "\n", + " return ground_state_energy" + ] + }, + { + "cell_type": "markdown", + "id": "lesbian-employment", + "metadata": {}, + "source": [ + "Now, we generate a Hamiltonian and calculate its ground state information." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "indie-detroit", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The ground state energy is -0.99783 Ha.\n", + "Schmidt rank of the ground state is 3.\n" + ] + } + ], + "source": [ + "# Fix a random seed\n", + "np.random.seed(SEED)\n", + "\n", + "# Hard code a random a Hamiltonian\n", + "coefs = [-0.8886258, 0.453882]\n", + "pauli_str = ['x0,z1,z2,z4,x5,y6,y7,x8,x9', 'y0,x1,x2,x3,y4,x5,z6,z7,y8,x9']\n", + "pauli_str_A = ['x0,z1,z2,z4', 'y0,x1,x2,x3,y4'] # pauli substring for system A\n", + "pauli_str_B = ['x0,y1,y2,x3,x4', 'x0,z1,z2,y3,x4'] # pauli substring for system B\n", + "\n", + "# Convert relavent object into Tensor form\n", + "H_mtr = paddle.to_tensor(pauli_str_to_matrix(zip(coefs, pauli_str), n=N))\n", + "coefs = paddle.to_tensor(coefs)\n", + "H_A = [pauli_str_to_matrix([[1., pstr]], n=N//2) for pstr in pauli_str_A]\n", + "H_A = paddle.to_tensor(np.stack(H_A))\n", + "H_B = [pauli_str_to_matrix([[1., pstr]], n=N-N//2) for pstr in pauli_str_B]\n", + "H_B = paddle.to_tensor(np.stack(H_B))\n", + "\n", + "# calculate the ground state information\n", + "ground_state_energy = get_ground_state_info(H_mtr)" + ] + }, + { + "cell_type": "markdown", + "id": "dietary-hotel", + "metadata": {}, + "source": [ + "Now that we have prepared a Hamiltonian, we may build a distributed VQE to solve it." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "international-wesley", + "metadata": {}, + "outputs": [], + "source": [ + "# Construct parameterized circuit\n", + "def U_theta(param, N, D):\n", + " \n", + " cir = UAnsatz(N) # Initialize an N-qubit-width circuit\n", + " cir.complex_entangled_layer(param, D) # Add quantum gates\n", + " return cir.U # Retrieve the unitary matrix for the parameterized circuit\n", + "\n", + "# Apply a parameterized circuit on the conputational bases\n", + "# and return a tensor of shape [2**N, num_states]\n", + "def output_states(theta, num_states, N, D):\n", + " # Create num_states-many computational bases\n", + " basis = paddle.eye(2**N, num_states)\n", + " \n", + " # Acquire a parameterized circuit\n", + " U = U_theta(theta, N, D)\n", + " \n", + " # Apply the parameterized circuit on these bases\n", + " vec = U @ basis \n", + " \n", + " return vec" + ] + }, + { + "cell_type": "markdown", + "id": "disturbed-strap", + "metadata": {}, + "source": [ + "The code below is core to this tutorial. Please compare them with the formulae given in the beginning section and make sure that they are well understood." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "normal-leader", + "metadata": {}, + "outputs": [], + "source": [ + "# Construct the distributed model\n", + "class DistributedVQE(paddle.nn.Layer):\n", + " def __init__(self, N, D, S):\n", + " super().__init__()\n", + " paddle.seed(SEED)\n", + "\n", + " # Define constant S\n", + " self.S = S\n", + " self.N, self.D = N, D\n", + " # Initialize the parameter lists theta, phi, filled by a uniform distribution in [0, 2*pi]\n", + " self.theta = self.create_parameter(shape=[D, N//2, 3], dtype=\"float64\",\n", + " default_initializer=paddle.nn.initializer.Uniform(low=0.0, high=2*np.pi))\n", + " self.phi = self.create_parameter(shape=[D, N - N//2, 3], dtype=\"float64\",\n", + " default_initializer=paddle.nn.initializer.Uniform(low=0.0, high=2*np.pi))\n", + " \n", + " # The core logic of distributed VQE\n", + " def forward(self):\n", + " # Obtain U|k> and V|k> for subsystems A and B respectively \n", + " vec_A = output_states(self.theta, self.S, self.N//2, self.D)\n", + " vec_B = output_states(self.phi, self.S, self.N - self.N//2, self.D)\n", + " \n", + " # Calculate tensor E_A, E_B, which have elements E_{ijt}^A and E_{ijt}^B, as per defined in above\n", + " E_A = vec_A.conj().t() @ H_A @ vec_A\n", + " E_B = vec_B.conj().t() @ H_B @ vec_B\n", + " M = (coefs.reshape([-1, 1, 1]) * E_A * E_B).sum(0)\n", + "\n", + " # Find the minimal eigenvalue of M\n", + " eigval = paddle.linalg.eigvalsh(M)\n", + " loss = eigval[0]\n", + " \n", + " return loss" + ] + }, + { + "cell_type": "markdown", + "id": "independent-undergraduate", + "metadata": {}, + "source": [ + "Define training function." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "liberal-mountain", + "metadata": {}, + "outputs": [], + "source": [ + "def train(model):\n", + " start_time = time.time() # To calculate the running time of this function\n", + " \n", + " # We will use Adam, a gradient-based optimizer to optimize theta and phi\n", + " opt = paddle.optimizer.Adam(learning_rate=LR, parameters=model.parameters())\n", + " summary_loss = [] # Save loss history\n", + "\n", + " # Optimization iteration\n", + " for itr in range(ITR):\n", + "\n", + " # Forward propagation to calculates the loss function\n", + " loss = model()\n", + "\n", + " # Backward propagation to optimize the loss function\n", + " loss.backward()\n", + " opt.minimize(loss)\n", + " opt.clear_grad()\n", + "\n", + " # Update optimization result\n", + " summary_loss.append(loss.numpy())\n", + "\n", + " # Print itermediary result\n", + " if (itr+1) % 20 == 0:\n", + " print(f\"iter: {itr+1}, loss: {loss.tolist()[0]: .4f} Ha\")\n", + "\n", + " print(f'Ground truth is {ground_state_energy:.4f} Ha')\n", + " print(f'Training took {time.time() - start_time:.2f}s')\n", + " \n", + " plt.plot(list(range(ITR)), summary_loss, color='r', label='loss')\n", + " plt.hlines(y=ground_state_energy, xmin=0, xmax=ITR, linestyle=':', label='ground truth')\n", + " plt.legend()\n", + " plt.title(f'Loss for {type(model).__name__} on a {N}-qubit Hamiltonian')\n", + " plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "civic-distance", + "metadata": {}, + "source": [ + "Now, we are ready to instantiate the model and train it!" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "compressed-reviewer", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "iter: 20, loss: -0.9244 Ha\n", + "iter: 40, loss: -0.9906 Ha\n", + "iter: 60, loss: -0.9968 Ha\n", + "iter: 80, loss: -0.9977 Ha\n", + "iter: 100, loss: -0.9978 Ha\n", + "Ground truth is -0.9978 Ha\n", + "Training took 13.01s\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Note that we manually set S = 4 as the Hamiltonian we just created interacts weakly across the subsystems.\n", + "# (See the Conclusion section for further description)\n", + "vqe = DistributedVQE(N, D, S=4)\n", + "train(vqe)" + ] + }, + { + "cell_type": "markdown", + "id": "convenient-receiver", + "metadata": {}, + "source": [ + "We have plotted the actual ground state energy as a dotted line in the figure above. We see that the loss curve converges to the dotted line, meaning that our distributed VQE successfully found the ground state energy of the Hamiltonian. However, to properly evaluate our model, we need to compare it with the standard VQE, which we build below:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "intensive-pickup", + "metadata": {}, + "outputs": [], + "source": [ + "class StandardVQE(paddle.nn.Layer):\n", + " def __init__(self, N, D):\n", + " super().__init__()\n", + " paddle.seed(SEED)\n", + " self.N, self.D = N, D\n", + " self.theta = self.create_parameter(shape=[D, N, 3], dtype=\"float64\",\n", + " default_initializer=paddle.nn.initializer.Uniform(low=0.0, high=2*np.pi))\n", + " \n", + " def forward(self):\n", + " vec = output_states(self.theta, 1, self.N, self.D)\n", + " loss = vec.conj().t() @ H_mtr @ vec\n", + " return loss.cast('float64').flatten()" + ] + }, + { + "cell_type": "markdown", + "id": "dress-vulnerability", + "metadata": {}, + "source": [ + "Instantiate and train the StandardVQE." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a35f3eb4", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "iter: 20, loss: -0.8365 Ha\n", + "iter: 40, loss: -0.9852 Ha\n", + "iter: 60, loss: -0.9958 Ha\n", + "iter: 80, loss: -0.9975 Ha\n", + "iter: 100, loss: -0.9978 Ha\n", + "Ground truth is -0.9978 Ha\n", + "Training took 721.76s\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "svqe = StandardVQE(N, D)\n", + "train(svqe) # Train the standard VQE " + ] + }, + { + "cell_type": "markdown", + "id": "centered-sheffield", + "metadata": {}, + "source": [ + "Interestingly, by comparing the running time of the two models, we find that the distributed model runs 50 times faster than the standard VQE! In fact, this is easy to understand: in a distributed model, we only need to simulate two $N/2$-qubit unitary transformations, which is, of course, much more time- and space-efficient than simulating an $N$-qubit unitary transformation in the standard VQE." + ] + }, + { + "cell_type": "markdown", + "id": "blocked-determination", + "metadata": { + "tags": [] + }, + "source": [ + "## Conclusion\n", + "\n", + "In this tutorial, we built a distributed VQE and demonstrated some of its advantages:\n", + "- The capability of NISQ devices is expanded. Distributed strategies enable the deployment of quantum algorithms which require qubits that exceed the capability of current hardware.\n", + "- The computation efficiency is improved. For classical simulation of quantum processes, distributed algorithms reduce the dimension of unitary matrices, hence reducing the space and time cost for simulating them.\n", + "\n", + "In the meantime, one must note that $S$, as a user-defined constant, plays a key role in the training accuracy and efficiency:\n", + "- For Hamiltonians which encode weak inter-subsystem interactions, their ground states are weakly entangled across the subsystems [7]. Hence, the Schmidt ranks are small and can be accurately and efficiently simulated by a small $S$. In fact, our example and most physically and chemically interesting Hamiltonians fall into this category.\n", + "- In contrast, for Hamiltonians which encode strong inter-subsystem interactions, their ground states are strongly entangled. Hence, a large $S$ may be required. But anyway, $S$ is upper-bounded by $2^{N/2}$ and thus the dimension of $M$ is upper-bounded by $2^{N/2}\\times2^{N/2}$, which is still much smaller than the dimension of the initial Hamiltonian ($2^{N}\\times 2^{N}$). Consequently, the efficiency of this algorithm is always better than the purely classical simulation." + ] + }, + { + "cell_type": "markdown", + "id": "suspended-monroe", + "metadata": { + "jp-MarkdownHeadingCollapsed": true, + "tags": [] + }, + "source": [ + "_______\n", + "\n", + "# References\n", + "\n", + "[1] Fujii, Keisuke, et al. \"Deep Variational Quantum Eigensolver: a divide-and-conquer method for solving a larger problem with smaller size quantum computers.\" [arXiv preprint arXiv:2007.10917 (2020)](https://arxiv.org/abs/2007.10917).\n", + "\n", + "[2] Zhang, Yu, et al. \"Variational Quantum Eigensolver with Reduced Circuit Complexity.\" [arXiv preprint arXiv:2106.07619(2021)](https://arxiv.org/abs/2106.07619).\n", + "\n", + "[3] Peng, Tianyi et al. \"Simulating Large Quantum Circuits On A Small Quantum Computer\". [Physical Review Letters 125.15, (2020): 150504](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.150504).\n", + "\n", + "[4] Eddins, Andrew, et al. \"Doubling the size of quantum simulators by entanglement forging.\" [arXiv preprint arXiv:2104.10220 (2021)](https://arxiv.org/abs/2104.10220).\n", + "\n", + "[5] Nielsen, Michael A., and Isaac L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2010.\n", + "\n", + "[6] Moll, Nikolaj, et al. \"Quantum optimization using variational algorithms on near-term quantum devices.\" [Quantum Science and Technology 3.3 (2018): 030503](https://iopscience.iop.org/article/10.1088/2058-9565/aab822).\n", + "\n", + "[7] Khatri, Sumeet, and Mark M. Wilde. \"Principles of quantum communication theory: A modern approach.\" [arXiv preprint arXiv:2011.04672 (2020)](https://arxiv.org/abs/2011.04672)." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/tutorial/quantum_simulation/GibbsState_CN.ipynb b/tutorial/quantum_simulation/GibbsState_CN.ipynb index 1d02a08..d49c0cd 100644 --- a/tutorial/quantum_simulation/GibbsState_CN.ipynb +++ b/tutorial/quantum_simulation/GibbsState_CN.ipynb @@ -430,7 +430,7 @@ "\n", "[3] Somma, R. D., Boixo, S., Barnum, H. & Knill, E. Quantum Simulations of Classical Annealing Processes. [Phys. Rev. Lett. 101, 130504 (2008).](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.130504)\n", "\n", - "[4] Wang, Y., Li, G. & Wang, X. Variational quantum Gibbs state preparation with a truncated Taylor series. [arXiv:2005.08797 (2020).](https://arxiv.org/pdf/2005.08797.pdf)" + "[4] Wang, Y., Li, G. & Wang, X. Variational quantum Gibbs state preparation with a truncated Taylor series. [Phys. Rev. A 16, 054035 (2021).](https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.16.054035)" ] } ], @@ -450,7 +450,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.3" + "version": "3.7.10" }, "toc": { "base_numbering": 1, diff --git a/tutorial/quantum_simulation/GibbsState_EN.ipynb b/tutorial/quantum_simulation/GibbsState_EN.ipynb index dae12ac..8271e58 100644 --- a/tutorial/quantum_simulation/GibbsState_EN.ipynb +++ b/tutorial/quantum_simulation/GibbsState_EN.ipynb @@ -411,7 +411,7 @@ "\n", "[3] Somma, R. D., Boixo, S., Barnum, H. & Knill, E. Quantum Simulations of Classical Annealing Processes. [Phys. Rev. Lett. 101, 130504 (2008).](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.130504)\n", "\n", - "[4] Wang, Y., Li, G. & Wang, X. Variational quantum Gibbs state preparation with a truncated Taylor series. [arXiv:2005.08797 (2020).](https://arxiv.org/pdf/2005.08797.pdf)" + "[4] Wang, Y., Li, G. & Wang, X. Variational quantum Gibbs state preparation with a truncated Taylor series. [Phys. Rev. A 16, 054035 (2021).](https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.16.054035)" ] } ], @@ -431,7 +431,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.3" + "version": "3.7.10" }, "toc": { "base_numbering": 1, diff --git a/tutorial/quantum_simulation/SSVQE_CN.ipynb b/tutorial/quantum_simulation/SSVQE_CN.ipynb index 136e939..a45237c 100644 --- a/tutorial/quantum_simulation/SSVQE_CN.ipynb +++ b/tutorial/quantum_simulation/SSVQE_CN.ipynb @@ -2,8 +2,9 @@ "cells": [ { "cell_type": "markdown", + "metadata": {}, "source": [ - "# 子空间搜索-量子变分本征求解器\n", + "# 子空间搜索-变分量子本征求解器\n", "\n", " Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. \n", "\n", @@ -12,12 +13,18 @@ "- 在本案例中，我们将展示如何通过 Paddle Quantum 训练量子神经网络来求解量子系统的整个能量谱。\n", "\n", "- 首先，让我们通过下面几行代码引入必要的 library 和 package。" - ], - "metadata": {} + ] }, { "cell_type": "code", "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2021-04-30T09:12:57.571029Z", + "start_time": "2021-04-30T09:12:54.960356Z" + } + }, + "outputs": [], "source": [ "import numpy\n", "from numpy import pi as PI\n", @@ -25,17 +32,11 @@ "from paddle import matmul\n", "from paddle_quantum.circuit import UAnsatz\n", "from paddle_quantum.utils import random_pauli_str_generator, pauli_str_to_matrix, dagger" - ], - "outputs": [], - "metadata": { - "ExecuteTime": { - "end_time": "2021-04-30T09:12:57.571029Z", - "start_time": "2021-04-30T09:12:54.960356Z" - } - } + ] }, { "cell_type": "markdown", + "metadata": {}, "source": [ "## 背景\n", "\n", @@ -47,67 +48,73 @@ "\n", "- 对于具体需要分析的分子，我们需要其几何构型（geometry）、电荷（charge）以及自旋多重度（spin multiplicity）等多项信息来建模获取描述系统的 Hamilton 量。具体的，通过我们内置的量子化学工具包可以利用 fermionic-to-qubit 映射的技术来输出目标分子的量子比特 Hamilton 量表示。\n", "- 作为简单的入门案例，我们在这里提供一个简单的随机双量子比特 Hamilton 量作为例子。" - ], - "metadata": {} + ] }, { "cell_type": "code", "execution_count": 3, - "source": [ - "N = 2 # 量子比特数/量子神经网络的宽度\n", - "SEED = 14 # 固定随机种子" - ], - "outputs": [], "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:12:57.580461Z", "start_time": "2021-04-30T09:12:57.574080Z" } - } + }, + "outputs": [], + "source": [ + "N = 2 # 量子比特数/量子神经网络的宽度\n", + "SEED = 14 # 固定随机种子" + ] }, { "cell_type": "code", "execution_count": 8, - "source": [ - "# 生成用泡利字符串表示的随机哈密顿量\n", - "numpy.random.seed(SEED)\n", - "hamiltonian = random_pauli_str_generator(N, terms=10)\n", - "print(\"Random Hamiltonian in Pauli string format = \\n\", hamiltonian)\n", - "\n", - "# 生成 Hamilton 量的矩阵信息\n", - "H = pauli_str_to_matrix(hamiltonian, N)" - ], + "metadata": { + "ExecuteTime": { + "end_time": "2021-04-30T09:12:57.604652Z", + "start_time": "2021-04-30T09:12:57.592553Z" + } + }, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ "Random Hamiltonian in Pauli string format = \n", " [[0.9152074787317819, 'x1,y0'], [-0.2717604556798945, 'z0'], [0.3628495008719168, 'x0'], [-0.5050129214094752, 'x1'], [-0.6971554357833791, 'y0,x1'], [0.8651151857574237, 'x0,y1'], [0.7409989105435002, 'y0'], [-0.39981603921243236, 'y0'], [0.06862640764702, 'z0'], [-0.7647553733438246, 'y1']]\n" ] } ], - "metadata": { - "ExecuteTime": { - "end_time": "2021-04-30T09:12:57.604652Z", - "start_time": "2021-04-30T09:12:57.592553Z" - } - } + "source": [ + "# 生成用泡利字符串表示的随机哈密顿量\n", + "numpy.random.seed(SEED)\n", + "hamiltonian = random_pauli_str_generator(N, terms=10)\n", + "print(\"Random Hamiltonian in Pauli string format = \\n\", hamiltonian)\n", + "\n", + "# 生成 Hamilton 量的矩阵信息\n", + "H = pauli_str_to_matrix(hamiltonian, N)" + ] }, { "cell_type": "markdown", + "metadata": {}, "source": [ "## 搭建量子神经网络\n", "\n", "- 在实现 SSVQE 的过程中，我们首先需要设计量子神经网络（quantum neural network, QNN），也即参数化量子电路。在本教程中，我们提供一个预设的适用于双量子比特的通用量子电路模板。理论上，该模板具有足够强大的表达能力可以表示任意的双量子比特逻辑运算 [5]。具体的实现方式是需要 3 个 $CNOT$ 门加上任意 15 个单比特旋转门 $\\in \\{R_y, R_z\\}$。\n", "\n", "- 初始化其中的变量参数，${\\bf{\\theta}}$ 代表我们量子神经网络中的参数组成的向量，一共有 15 个参数。" - ], - "metadata": {} + ] }, { "cell_type": "code", "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2021-04-30T09:12:57.673600Z", + "start_time": "2021-04-30T09:12:57.664882Z" + } + }, + "outputs": [], "source": [ "THETA_SIZE = 15 # 量子神经网络中参数的数量\n", "\n", @@ -123,17 +130,11 @@ "\n", " # 返回量子神经网络的电路\n", " return cir" - ], - "outputs": [], - "metadata": { - "ExecuteTime": { - "end_time": "2021-04-30T09:12:57.673600Z", - "start_time": "2021-04-30T09:12:57.664882Z" - } - } + ] }, { "cell_type": "markdown", + "metadata": {}, "source": [ "## 配置训练模型——损失函数\n", "\n", @@ -148,12 +149,18 @@ "$$\n", "\\mathcal{L}(\\boldsymbol{\\theta}) = \\sum_{k=1}^{2^n}w_k*\\left\\langle {\\psi_k \\left( {\\bf{\\theta }} \\right)} \\right|H\\left| {\\psi_k \\left( {\\bf{\\theta }} \\right)} \\right\\rangle. \\tag{1}\n", "$$" - ], - "metadata": {} + ] }, { "cell_type": "code", "execution_count": 10, + "metadata": { + "ExecuteTime": { + "end_time": "2021-04-30T09:12:58.591349Z", + "start_time": "2021-04-30T09:12:58.577120Z" + } + }, + "outputs": [], "source": [ "class Net(paddle.nn.Layer):\n", " def __init__(self, shape, dtype='float64'):\n", @@ -186,51 +193,74 @@ " loss += weight * loss_components[i]\n", " \n", " return loss, loss_components, cir" - ], - "outputs": [], - "metadata": { - "ExecuteTime": { - "end_time": "2021-04-30T09:12:58.591349Z", - "start_time": "2021-04-30T09:12:58.577120Z" - } - } + ] }, { "cell_type": "markdown", + "metadata": {}, "source": [ "## 配置训练模型——模型参数\n", "在进行量子神经网络的训练之前，我们还需要进行一些训练的超参数设置，主要是学习速率（learning rate, LR）、迭代次数（iteration, ITR。这里我们设定学习速率为 0.3，迭代次数为 50 次。读者不妨自行调整来直观感受下超参数调整对训练效果的影响。" - ], - "metadata": {} + ] }, { "cell_type": "code", "execution_count": 11, - "source": [ - "ITR = 100 # 设置训练的总迭代次数\n", - "LR = 0.3 # 设置学习速率" - ], - "outputs": [], "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:12:59.351881Z", "start_time": "2021-04-30T09:12:59.343240Z" } - } + }, + "outputs": [], + "source": [ + "ITR = 100 # 设置训练的总迭代次数\n", + "LR = 0.3 # 设置学习速率" + ] }, { "cell_type": "markdown", + "metadata": {}, "source": [ "## 进行训练\n", "- 当训练模型的各项参数都设置完成后，我们将数据转化为 PaddlePaddle 动态图中的张量，进而进行量子神经网络的训练。\n", "- 过程中我们用的是 Adam Optimizer，也可以调用 PaddlePaddle 中提供的其他优化器。\n", "- 我们可以将训练过程中的每一轮 loss 打印出来。" - ], - "metadata": {} + ] }, { "cell_type": "code", "execution_count": 13, + "metadata": { + "ExecuteTime": { + "end_time": "2021-04-30T09:13:07.503094Z", + "start_time": "2021-04-30T09:13:04.968574Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "iter: 10 loss: -4.5668\n", + "iter: 20 loss: -5.3998\n", + "iter: 30 loss: -5.6210\n", + "iter: 40 loss: -5.8872\n", + "iter: 50 loss: -5.9246\n", + "iter: 60 loss: -5.9471\n", + "iter: 70 loss: -5.9739\n", + "iter: 80 loss: -5.9833\n", + "iter: 90 loss: -5.9846\n", + "iter: 100 loss: -5.9848\n", + "\n", + "训练后的电路：\n", + "--U----x----Rz(-1.18)----*-----------------x----U--\n", + " | | | \n", + "--U----*----Ry(-0.03)----x----Ry(2.362)----*----U--\n", + " \n" + ] + } + ], "source": [ "paddle.seed(SEED)\n", " \n", @@ -261,40 +291,11 @@ " if itr == ITR:\n", " print(\"\\n训练后的电路：\")\n", " print(cir)" - ], - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "iter: 10 loss: -4.5668\n", - "iter: 20 loss: -5.3998\n", - "iter: 30 loss: -5.6210\n", - "iter: 40 loss: -5.8872\n", - "iter: 50 loss: -5.9246\n", - "iter: 60 loss: -5.9471\n", - "iter: 70 loss: -5.9739\n", - "iter: 80 loss: -5.9833\n", - "iter: 90 loss: -5.9846\n", - "iter: 100 loss: -5.9848\n", - "\n", - "训练后的电路：\n", - "--U----x----Rz(-1.18)----*-----------------x----U--\n", - " | | | \n", - "--U----*----Ry(-0.03)----x----Ry(2.362)----*----U--\n", - " \n" - ] - } - ], - "metadata": { - "ExecuteTime": { - "end_time": "2021-04-30T09:13:07.503094Z", - "start_time": "2021-04-30T09:13:04.968574Z" - } - } + ] }, { "cell_type": "markdown", + "metadata": {}, "source": [ "## 测试效果\n", "\n", @@ -302,12 +303,28 @@ "- 理论值由 NumPy 中的工具来求解哈密顿量的各个本征值；\n", "- 我们将训练 QNN 得到的各个能级的能量和理想情况下的理论值进行比对。\n", "- 可以看到，SSVQE 训练输出的值与理想值高度接近。" - ], - "metadata": {} + ] }, { "cell_type": "code", "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The estimated ground state energy is: [-2.18762366]\n", + "The theoretical ground state energy is: -2.18790201165885\n", + "The estimated 1st excited state energy is: [-0.13721024]\n", + "The theoretical 1st excited state energy is: -0.13704127143749587\n", + "The estimated 2nd excited state energy is: [0.85251457]\n", + "The theoretical 2nd excited state energy is: 0.8523274042087416\n", + "The estimated 3rd excited state energy is: [1.47231932]\n", + "The theoretical 3rd excited state energy is: 1.4726158788876045\n" + ] + } + ], "source": [ "def output_ordinalvalue(num):\n", " r\"\"\"\n", @@ -339,27 +356,11 @@ " print('The theoretical {} excited state energy is: {}'.format(\n", " output_ordinalvalue(i), numpy.linalg.eigh(H)[0][i])\n", " )" - ], - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "The estimated ground state energy is: [-2.18762366]\n", - "The theoretical ground state energy is: -2.18790201165885\n", - "The estimated 1st excited state energy is: [-0.13721024]\n", - "The theoretical 1st excited state energy is: -0.13704127143749587\n", - "The estimated 2nd excited state energy is: [0.85251457]\n", - "The theoretical 2nd excited state energy is: 0.8523274042087416\n", - "The estimated 3rd excited state energy is: [1.47231932]\n", - "The theoretical 3rd excited state energy is: 1.4726158788876045\n" - ] - } - ], - "metadata": {} + ] }, { "cell_type": "markdown", + "metadata": {}, "source": [ "_______\n", "\n", @@ -374,14 +375,17 @@ "[4] Nakanishi, K. M., Mitarai, K. & Fujii, K. Subspace-search variational quantum eigensolver for excited states. [Phys. Rev. Res. 1, 033062 (2019).](https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.1.033062)\n", "\n", "[5] Vatan, F. & Williams, C. Optimal quantum circuits for general two-qubit gates. [Phys. Rev. A 69, 032315 (2004).](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.69.032315)" - ], - "metadata": {} + ] } ], "metadata": { + "interpreter": { + "hash": "1ba3360425d54dc61cc146cb8ddc529b6d51be6719655a3ca16cefddffc9595a" + }, "kernelspec": { - "name": "python3", - "display_name": "Python 3.8.10 64-bit ('paddle_quantum_test': conda)" + "display_name": "Python 3", + "language": "python", + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -393,7 +397,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.10" + "version": "3.7.10" }, "toc": { "base_numbering": 1, @@ -407,11 +411,8 @@ "toc_position": {}, "toc_section_display": true, "toc_window_display": false - }, - "interpreter": { - "hash": "1ba3360425d54dc61cc146cb8ddc529b6d51be6719655a3ca16cefddffc9595a" } }, "nbformat": 4, "nbformat_minor": 4 -} \ No newline at end of file +} diff --git a/tutorial/quantum_simulation/VQE_CN.ipynb b/tutorial/quantum_simulation/VQE_CN.ipynb index 30b856c..96cf6c5 100644 --- a/tutorial/quantum_simulation/VQE_CN.ipynb +++ b/tutorial/quantum_simulation/VQE_CN.ipynb @@ -117,7 +117,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:13:45.528201Z", @@ -152,7 +152,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:13:45.545018Z", @@ -164,24 +164,24 @@ "name": "stdout", "output_type": "stream", "text": [ - "FCI energy for H2_sto-3g_singlet (2 electrons) is -1.137283834485513.\n", + "FCI energy for H2_sto-3g_singlet (2 electrons) is -1.1372838344855134.\n", "\n", "The generated h2 Hamiltonian is \n", - " -0.09706626861762556 I\n", + " -0.0970662686176252 I\n", "-0.04530261550868938 X0, X1, Y2, Y3\n", "0.04530261550868938 X0, Y1, Y2, X3\n", "0.04530261550868938 Y0, X1, X2, Y3\n", "-0.04530261550868938 Y0, Y1, X2, X3\n", - "0.1714128263940239 Z0\n", - "0.16868898168693286 Z0, Z1\n", - "0.12062523481381837 Z0, Z2\n", - "0.16592785032250773 Z0, Z3\n", - "0.17141282639402394 Z1\n", - "0.16592785032250773 Z1, Z2\n", - "0.12062523481381837 Z1, Z3\n", - "-0.2234315367466399 Z2\n", - "0.17441287610651626 Z2, Z3\n", - "-0.2234315367466399 Z3\n" + "0.1714128263940238 Z0\n", + "0.16868898168693292 Z0, Z1\n", + "0.12062523481381847 Z0, Z2\n", + "0.1659278503225078 Z0, Z3\n", + "0.17141282639402383 Z1\n", + "0.1659278503225078 Z1, Z2\n", + "0.12062523481381847 Z1, Z3\n", + "-0.22343153674664024 Z2\n", + "0.17441287610651632 Z2, Z3\n", + "-0.2234315367466403 Z3\n" ] } ], @@ -203,7 +203,7 @@ "molecular_hamiltonian = qchem.spin_hamiltonian(molecule=molecule,\n", " filename=None, \n", " multiplicity=1, \n", - " mapping_method = 'jordan_wigner',)\n", + " mapping_method='jordan_wigner',)\n", "# 打印结果\n", "print(\"\\nThe generated h2 Hamiltonian is \\n\", molecular_hamiltonian)" ] @@ -236,7 +236,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -281,7 +281,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ @@ -318,7 +318,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:14:03.744957Z", @@ -344,30 +344,30 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "iter: 20 loss: -1.0621\n", - "iter: 20 Ground state energy: -1.0621 Ha\n", - "iter: 40 loss: -1.1305\n", - "iter: 40 Ground state energy: -1.1305 Ha\n", - "iter: 60 loss: -1.1358\n", - "iter: 60 Ground state energy: -1.1358 Ha\n", - "iter: 80 loss: -1.1370\n", - "iter: 80 Ground state energy: -1.1370 Ha\n", + "iter: 20 loss: -1.0861\n", + "iter: 20 Ground state energy: -1.0861 Ha\n", + "iter: 40 loss: -1.1304\n", + "iter: 40 Ground state energy: -1.1304 Ha\n", + "iter: 60 loss: -1.1363\n", + "iter: 60 Ground state energy: -1.1363 Ha\n", + "iter: 80 loss: -1.1372\n", + "iter: 80 Ground state energy: -1.1372 Ha\n", "\n", "训练后的电路：\n", - "--Ry(4.702)----*--------------x----Ry(4.759)----*--------------x----Ry(0.001)--\n", + "--Ry(1.572)----*--------------x----Ry(1.568)----*--------------x----Ry(0.012)--\n", " | | | | \n", - "--Ry(-1.56)----x----*---------|----Ry(4.698)----x----*---------|----Ry(1.607)--\n", + "--Ry(4.724)----x----*---------|----Ry(4.722)----x----*---------|----Ry(1.619)--\n", " | | | | \n", - "--Ry(3.170)---------x----*----|----Ry(1.789)---------x----*----|----Ry(4.817)--\n", + "--Ry(-0.03)---------x----*----|----Ry(4.954)---------x----*----|----Ry(-0.41)--\n", " | | | | \n", - "--Ry(6.365)--------------x----*----Ry(1.562)--------------x----*----Ry(3.178)--\n", + "--Ry(4.288)--------------x----*----Ry(1.564)--------------x----*----Ry(3.137)--\n", " \n" ] } @@ -418,12 +418,12 @@ "metadata": {}, "source": [ "### 测试效果\n", - "我们现在已经完成了量子神经网络的训练，通过 VQE 得到的基态能量的估计值大致为 $E_0 \\approx -1.137$ Ha，这与通过全价构型相互作用（FCI）$E_0 = -1.13728$ Ha 计算得出的值是在化学精度 $\\varepsilon = 1.6 \\times 10^{-3}$ Ha 内相符合的。" + "我们现在已经完成了量子神经网络的训练，通过 VQE 得到的基态能量的估计值大致为 $E_0 \\approx -1.137$ Ha，这与通过 `Psi4` 在 sto-3g 基底下使用 FCI (full configuration-interaction) 方法计算得到的基态能量值 $E_0 = -1.13728$ Ha 是在化学精度 $\\varepsilon = 1.6 \\times 10^{-3}$ Ha 内相符合的。" ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:14:21.341323Z", @@ -433,14 +433,12 @@ "outputs": [ { "data": { - "image/png": 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\n", "text/plain": [ - "
    " + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -469,7 +467,7 @@ " r'\\right|H\\left| {\\psi \\left( {\\theta } \\right)} \\right\\rangle $',\n", " 'Ground-state energy',\n", " ], loc='best')\n", - "\n", + "plt.text(-15.5, -1.145, f'{min_eig_H:.5f}', fontsize=10, color='b')\n", "#plt.savefig(\"vqe.png\", bbox_inches='tight', dpi=300)\n", "plt.show()" ] @@ -484,7 +482,7 @@ "\n", "![vqe-fig-dist](figures/vqe-fig-distance.png)\n", "\n", - "从上图可以看出，最小值确实发生在 $d = 74$ pm (1 pm = $1\\times 10^{-12}$m) 附近，这是与[实验测得数据](https://cccbdb.nist.gov/exp2x.asp?casno=1333740&charge=0)相符合的 $d_{exp} (H_2) = 74.14$ pm." + "从上图可以看出，最小值确实发生在 $d = 74$ pm (1 pm = $1\\times 10^{-12}$ m) 附近，这是与[实验测得数据](https://cccbdb.nist.gov/exp2x.asp?casno=1333740&charge=0)相符合的 $d_{exp} (H_2) = 74.14$ pm." ] }, { @@ -530,7 +528,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.10" + "version": "3.8.0" }, "toc": { "base_numbering": 1, diff --git a/tutorial/quantum_simulation/VQE_EN.ipynb b/tutorial/quantum_simulation/VQE_EN.ipynb index ab3344f..3f6aa4a 100644 --- a/tutorial/quantum_simulation/VQE_EN.ipynb +++ b/tutorial/quantum_simulation/VQE_EN.ipynb @@ -109,7 +109,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:14:44.970178Z", @@ -144,7 +144,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:14:44.982005Z", @@ -156,24 +156,24 @@ "name": "stdout", "output_type": "stream", "text": [ - "FCI energy for H2_sto-3g_singlet (2 electrons) is -1.137283834485513.\n", + "FCI energy for H2_sto-3g_singlet (2 electrons) is -1.1372838344855134.\n", "\n", "The generated h2 Hamiltonian is \n", - " -0.09706626861762556 I\n", + " -0.0970662686176252 I\n", "-0.04530261550868938 X0, X1, Y2, Y3\n", "0.04530261550868938 X0, Y1, Y2, X3\n", "0.04530261550868938 Y0, X1, X2, Y3\n", "-0.04530261550868938 Y0, Y1, X2, X3\n", - "0.1714128263940239 Z0\n", - "0.16868898168693286 Z0, Z1\n", - "0.12062523481381837 Z0, Z2\n", - "0.16592785032250773 Z0, Z3\n", - "0.17141282639402394 Z1\n", - "0.16592785032250773 Z1, Z2\n", - "0.12062523481381837 Z1, Z3\n", - "-0.2234315367466399 Z2\n", - "0.17441287610651626 Z2, Z3\n", - "-0.2234315367466399 Z3\n" + "0.1714128263940238 Z0\n", + "0.16868898168693292 Z0, Z1\n", + "0.12062523481381847 Z0, Z2\n", + "0.1659278503225078 Z0, Z3\n", + "0.17141282639402383 Z1\n", + "0.1659278503225078 Z1, Z2\n", + "0.12062523481381847 Z1, Z3\n", + "-0.22343153674664024 Z2\n", + "0.17441287610651632 Z2, Z3\n", + "-0.2234315367466403 Z3\n" ] } ], @@ -195,7 +195,7 @@ "molecular_hamiltonian = qchem.spin_hamiltonian(molecule=molecule,\n", " filename=None, \n", " multiplicity=1, \n", - " mapping_method = 'jordan_wigner',)\n", + " mapping_method='jordan_wigner',)\n", "# Print results\n", "print(\"\\nThe generated h2 Hamiltonian is \\n\", molecular_hamiltonian)" ] @@ -226,7 +226,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:14:50.083041Z", @@ -277,7 +277,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:14:50.183996Z", @@ -319,7 +319,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:14:50.222465Z", @@ -345,7 +345,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:15:52.165788Z", @@ -357,23 +357,23 @@ "name": "stdout", "output_type": "stream", "text": [ - "iter: 20 loss: -1.0510\n", - "iter: 20 Ground state energy: -1.0510 Ha\n", - "iter: 40 loss: -1.1298\n", - "iter: 40 Ground state energy: -1.1298 Ha\n", - "iter: 60 loss: -1.1361\n", - "iter: 60 Ground state energy: -1.1361 Ha\n", - "iter: 80 loss: -1.1371\n", - "iter: 80 Ground state energy: -1.1371 Ha\n", + "iter: 20 loss: -1.0487\n", + "iter: 20 Ground state energy: -1.0487 Ha\n", + "iter: 40 loss: -1.1070\n", + "iter: 40 Ground state energy: -1.1070 Ha\n", + "iter: 60 loss: -1.1152\n", + "iter: 60 Ground state energy: -1.1152 Ha\n", + "iter: 80 loss: -1.1165\n", + "iter: 80 Ground state energy: -1.1165 Ha\n", "\n", "Circuit after training:\n", - "--Ry(4.710)----*--------------x----Ry(1.569)----*--------------x----Ry(-0.01)--\n", + "--Ry(4.725)----*--------------x----Ry(-0.01)----*--------------x----Ry(-1.56)--\n", " | | | | \n", - "--Ry(1.507)----x----*---------|----Ry(1.566)----x----*---------|----Ry(4.392)--\n", + "--Ry(4.718)----x----*---------|----Ry(3.132)----x----*---------|----Ry(4.703)--\n", " | | | | \n", - "--Ry(5.984)---------x----*----|----Ry(4.476)---------x----*----|----Ry(1.692)--\n", + "--Ry(4.720)---------x----*----|----Ry(3.124)---------x----*----|----Ry(4.721)--\n", " | | | | \n", - "--Ry(0.132)--------------x----*----Ry(7.773)--------------x----*----Ry(3.194)--\n", + "--Ry(1.574)--------------x----*----Ry(6.291)--------------x----*----Ry(1.552)--\n", " \n" ] } @@ -424,13 +424,12 @@ "metadata": {}, "source": [ "### Benchmarking\n", - "We have now completed the training of the quantum neural network, and the estimated value of the ground state energy obtained is $E_0 \\approx -1.137 $ Hartree, we compare it with the theoretical value $E_0 = -1.1371$ to benchmark our model. The estimation obtained with VQE agree with a full configuration-interaction (FCI) calculation within chemical accuracy $\\varepsilon = 1.6 \\times 10^{-3}$ Hartree.\n", - "\n" + "We have now completed the training of the quantum neural network, and the estimated value of the ground state energy obtained is $E_0 \\approx -1.137 $ Hartree. The estimation obtained with VQE is consistent with the value of the ground state energy $E_0 = -1.13728$ Hartree calculated by `Psi4` at sto-3g basis using the full configuration-interaction (FCI) method within the chemical accuracy $\\varepsilon = 1.6 \\times 10^{-3}$ Hartree.\n" ] }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 14, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:15:18.096944Z", @@ -440,14 +439,12 @@ "outputs": [ { "data": { - "image/png": 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\n", 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"text/plain": [ - "
    " + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -476,7 +473,7 @@ " r'\\right|H\\left| {\\psi \\left( {\\theta } \\right)} \\right\\rangle $',\n", " 'Ground-state energy',\n", " ], loc='best')\n", - "\n", + "plt.text(-15.5, -1.145, f'{min_eig_H:.5f}', fontsize=10, color='b')\n", "#plt.savefig(\"vqe.png\", bbox_inches='tight', dpi=300)\n", "plt.show()" ] @@ -535,7 +532,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.10" + "version": "3.8.0" }, "toc": { "base_numbering": 1, -- GitLab

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