Estimating average fidelity error based on local random quantum circuits

¹ State Key Laboratory of Integrated Services Networks, Xidian University - Xi'an, Shannxi, China
² College of Electronics, Communications and Physics, Shandong University of Science and Technology Qingdao, China

Received: 6 September 2018
Accepted: 11 February 2019

Abstract

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.