Estimating average fidelity error based on local random quantum circuits

This paper proposes a general method to estimate the practical average fidelity error using an ϵ -approximate unitary 2t -design. We then build a specific model of local random circuits to construct the ϵ -approximate unitary t -design under a tighter bound on the diamond norm of the corresponding error. For a twirled t -tensor product noisy channel constructed by local random circuits, we extend the estimation of average fidelity using approximate unitary 2t -designs to an -fold noise scenario. Compared to previous randomized benchmarking, the average fidelity estimated by the method of local random circuits requires less experiments but longer circuit lengths for large n quantum system.