"Given a graph $G$ composed of $N$ nodes and $M$ edges, the problem is to find a cut protocol which divides the node set into two complementary subsets $S$ and $S^\\prime$ such that the number of edges between these sets is as large as possible. For example, consider the ring case with four nodes as shown in the figure.\n",
"Thus, given a cut protocol, if the node $i$ belongs to the set $S$, then it is assigned to $z_i =1$, while $z_j= -1$ for $j \\in S^\\prime$. Then, for any edge connecting nodes $i$ and $j$, if both nodes are in the same set $S$ or $S^\\prime$, then there is $z_iz_j=1$; otherwise, $z_iz_j=-1$. Hence, the cut problem can be formulated as the optimization problem \n",
"Further, each module in the QAOA circuit can be decomposed into a series of operations acting on single qubits and two qubits. In particular, the first has the decomposition of $U_c(\\gamma)=\\prod_{(i, j)}e^{-i \\gamma Z_iZ_j }$ while there is $U_x(\\beta)=\\prod_{i}e^{-i \\beta X_i}$ for the second. This is illustrated in the following figure.\n",
