Benchmarking noise with Quantum alternating operator ansatz (QAOA) circuits with a symmetry

QAOA as a quantum heuristic algorithm has attracted a lot of interest with its simple iterative structure. We propose adapting a symmetry-preserving QAOA circuit for benchmarking noise. Consider the system consisting of a number of subsets of qubits, we design the QAOA such that it preserves certain quantity of the subsets (e.g., a constant Hamming weight). When errors are present, the evolution will quickly escape from the preserved subspace. We study how this escaping rate scales with the iteration of the circuit and system size. Our analysis shows for a wide range of local noise channels the escaping rate can be exactly obtained with only the knowledge of the error model, thanks to the non-increasing reverse causal cone with QAOA level with respect to noise. We show that the analysis is stable against inhomogeneity in the subsystem, hence our scheme is feasible for benchmarking local noises in realistic situations.