Simulating general noise nearly as cheaply as Pauli noise

TL;DR

This paper introduces a stratified importance sampling method that enables efficient classical simulation of general, non-Pauli noise in Clifford quantum circuits, significantly broadening the scope of noise models that can be studied.

Contribution

The authors develop a new simulation technique that allows nearly as cheap simulation of general noise as Pauli noise within the stabilizer formalism, including coherent errors.

Findings

General noise can be simulated efficiently using stratified importance sampling.

Non-unitary noise simulation is nearly as fast as Pauli noise simulation.

Coherent noise simulations are feasible within reasonable computational times.

Abstract

Stabilizer simulation of Clifford quantum circuits - error-correction circuits, Clifford subroutines, etc. - on classical computers has played a central role in our understanding of circuit performance. The stabilizer description, however, restricts the accessible noise one can incorporate into the simulation to Pauli-type noise. More general noise, including coherent errors, may have more severe impact on circuit performance than Pauli noise; yet, such general noise have been difficult to access, much less investigate fully, in numerical simulations. Here, through the use of stratified importance sampling, we show how general noise can be simulated within the stabilizer formalism in reasonable time, with non-unitary noise being nearly as cheap as Pauli noise. Unitary (or coherent) noise can require an order of magnitude more time for the simulation, but nevertheless completes in very reasonable times, a drastic improvement over past approaches that typically fail to converge altogether. Our work thus enables detailed beyond-Pauli understanding of circuit performance in the presence of real device noise, which is rarely Pauli in nature. Among other examples, we present direct simulation results for the performance of the popular rotated planar surface codes under circuit-level general noise, previously available only in limited situations and/or through mappings to efficiently simulatable physical models.