A polynomial-time classical algorithm for noisy quantum circuits

TL;DR

This paper introduces a polynomial-time classical algorithm that efficiently simulates noisy quantum circuits by leveraging the exponential damping of non-local correlations due to noise, impacting quantum advantage prospects.

Contribution

It presents the first polynomial-time classical simulation method for noisy quantum circuits that computes expectation values and samples output distributions under certain conditions.

Findings

Classical simulation is feasible for noisy circuits with local correlations.

Noise exponentially suppresses non-local correlations, simplifying simulation.

Implications for the limits of quantum error mitigation strategies.

Abstract

We provide a polynomial-time classical algorithm for noisy quantum circuits. The algorithm computes the expectation value of any observable for any circuit, with a small average error over input states drawn from an ensemble (e.g. the computational basis). Our approach is based upon the intuition that noise exponentially damps non-local correlations relative to local correlations. This enables one to classically simulate a noisy quantum circuit by only keeping track of the dynamics of local quantum information. Our algorithm also enables sampling from the output distribution of a circuit in quasi-polynomial time, so long as the distribution anti-concentrates. A number of practical implications are discussed, including a fundamental limit on the efficacy of noise mitigation strategies: for constant noise rates, any quantum circuit for which error mitigation is efficient on most input states, is also classically simulable on most input states.