Noise Analysis of Quantum Approximate Optimization Algorithm on Weighted MAX-CUT

In this paper, we describe the simulation of Ising minimization on a classical machine by executing variational quantum algorithms on our density-matrix simulator. We outline the Ising formulation of the Graph Partitioning problem and the Hamiltonian Cycle problem, and solve the Max-Cut variant of graph partitioning for a weighted square graph $Sq_{2}$ using the Quantum Approximate Optimization Algorithm. We finally study the effect of errors present in Noisy Intermediate-Scale Quantum processors on the obtained solutions. This paper illustrates the approach to approximately solving hard combinatorial optimization problems using a hybrid quantum-classical scheme and describes the issues in hardware implementation of such schemes. The simulations of NISQ noise models will be useful in understanding the performance and capabilities of such approaches.