Performance Comparison for Quantum Approximate Optimization Algorithm (QAOA) across Noiseless Simulation, Experimentally Benchmarked Noisy Simulation, and Experimental Hardware Platforms

We implement Quantum Approximate Optimization Algorithm (QAOA) on NP-Hard problem MaxCut (for 3-chain and 4-node chain graphs, and 4-node and 6node Mobius Ladder graphs) on a quantum simulator without noise, a simulator with experimentally bench-marked noise (fake back-end), and 5-qubit and 7-qubit processors. We use the following modes of operation: QAOA parameters updated through forward pass on the quantum circuit, modelled by the noiseless simulator as well as fake back-end, and the quantum circuit for final run with updated parameters implemented on the noiseless simulator, fake back-end, and real quantum processors. While QAOA yields higher approximation ratio compared to random guess for almost all graph instances, we also conclude that given the noise in existing quantum hardware, a quantum circuit with more than two stages is not suitable for experimental implementation of QAOA currently.