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  • Open Access

Simulating Quantum Circuits with Arbitrary Local Noise Using Pauli Propagation

Armando Angrisani1,2,*, Antonio A. Mele3,4,†, Manuel S. Rudolph1,2, M. Cerezo5, and Zoë Holmes1,2

  • *Contact author: armando.angrisani@epfl.ch
  • †Contact author: a.mele@fu-berlin.de
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PRX Quantum 7, 020313 – Published 22 April, 2026

DOI: https://doi.org/10.1103/fb28-wlv2

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 6×6 lattice of qubits under the effects of amplitude damping and dephasing noise, as well as real-time dynamics on an 11×11 lattice of qubits affected by amplitude damping.

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Popular Summary

Quantum computers are inherently noisy: interactions with the environment gradually corrupt the information stored in qubits. Understanding when this noise destroys a quantum advantage is therefore a central challenge for the field. In this work, we show that for a broad class of typical quantum circuits, arbitrary local noise makes the task of predicting measurement outcomes much easier on a classical computer than previously known.

Our method extends a recently developed simulation framework called Pauli propagation to circuits affected not only by depolarizing noise but also by more realistic noise processes including dephasing and amplitude damping. We prove that, for random enough circuits, noise effectively suppresses the complicated many-qubit contributions that make quantum systems hard to simulate, allowing accurate estimation of observable expectation values in polynomial time. In this sense, generic noise makes deep circuits behave as if only a logarithmic number of layers really matter.

Beyond the theory, we also demonstrate the method numerically by simulating quantum circuits with up to 121 qubits. These results help clarify the computational power of noisy quantum devices and provide practical tools for studying realistic quantum systems on classical hardware.

Article Text

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Outline

Information

PRX Quantum 7, 020313– Published 22 April, 2026
  • Received 14 May 2025
  • Revised 23 December 2025
  • Accepted 17 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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