Simulating quantum circuits with arbitrary local noise using Pauli Propagation

TL;DR

This paper introduces a polynomial-time classical algorithm for efficiently estimating expectation values of quantum circuits affected by local noise, applicable to average-case circuits and validated through numerical simulations.

Contribution

It demonstrates that average-case noisy quantum circuits can be efficiently simulated using Pauli-path methods under broad conditions, extending prior limitations.

Findings

Efficient classical simulation of typical noisy quantum circuits achieved.

Pauli propagation algorithms with truncation yield small simulation errors.

Most noisy circuits can be approximated by logarithmic depth circuits for expectation estimation.

Abstract

We present a polynomial-time classical algorithm for estimating expectation values of arbitrary observables on typical quantum circuits under any incoherent local noise, including non-unital or dephasing. Although previous research demonstrated that some carefully designed quantum circuits affected by non-unital noise cannot be efficiently simulated, we show that this does not apply to average-case circuits, as these can be efficiently simulated using Pauli-path methods. Specifically, we prove that, with high probability over the circuit gates choice, Pauli propagation algorithms with tailored truncation strategies achieve an inversely polynomially small simulation error. This result holds for arbitrary circuit topologies and for any local noise, under the assumption that the distribution of each circuit layer is invariant under single-qubit random gates. Under the same minimal assumptions, we also prove that most noisy circuits can be truncated to an effective logarithmic depth for the task of {estimating} expectation values of observables, thus generalizing prior results to a significantly broader class of circuit ensembles. We further numerically validate our algorithm with simulations on a $6\times6$ lattice of qubits under the effects of amplitude damping and dephasing noise, as well as real-time dynamics on an $11\times11$ lattice of qubits affected by amplitude damping.