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

TL;DR

This paper introduces a Weyl basis-based randomized benchmarking algorithm to efficiently identify noise in quantum processes, providing bounds on classical simulability depending on noise levels.

Contribution

It develops a novel benchmarking method using Weyl unitaries for noise identification and analyzes classical simulation complexity under noise.

Findings

Efficient noise identification in quantum circuits using Weyl unitaries.

Analytic bounds on classical simulability depending on noise rate.

Application to Variational Quantum Eigensolver circuits.

Abstract

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 relying only on locality of the interactions and no further assumptions on the circuit structure. The overhead decreases with the noise rate and this enables us to compute analytic noise bounds 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.