Efficient benchmarking and classical simulation of quantum processes in the Weyl basis

Daniel Stilck França, Sergii Strelchuk, Michał Studziński

Published 2020-08-27Version 1

One of the crucial steps in building a scalable quantum computer is to identify the noise sources which lead to errors in the process of quantum evolution. Different implementations come with multiple hardware-dependent sources of noise and decoherence making the problem of their detection manyfoldly more complex. We develop a randomized benchmarking algorithm which uses Weyl unitaries to efficiently identify and learn a mixture of error models which occur during the computation. We provide an efficiently computable estimate of the overhead required to compute expectation values on outputs of the noisy circuit. The overhead decreases with the noise rate and this enables us to compute analytic noise thresholds that imply efficient classical simulability. We apply our methods to ansatz circuits that appear in the Variational Quantum Eigensolver and establish an upper bound on classical simulation complexity as a function of noise, identifying regimes when they become classically efficiently simulatable.