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  • Open Access

Efficient Self-Consistent Learning of Gate Set Pauli Noise

Senrui Chen1,2,*, Zhihan Zhang3, Liang Jiang1, and Steven T. Flammia4,5

  • 1Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
  • 2Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California, USA
  • 3Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
  • 4Department of Computer Science, Virginia Tech, Alexandria, Virginia, USA
  • 5Phasecraft Inc., Washington, DC, USA

  • *Contact author: csenrui@gmail.com
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PRX Quantum 7, 010305 – Published 9 January, 2026

DOI: https://doi.org/10.1103/1pnv-t9px

Abstract

Understanding quantum noise is an essential step towards building practical quantum information processing systems. Pauli noise is a useful model that has been widely applied in quantum benchmarking, error mitigation, and error correction. Despite intensive study into Pauli noise learning, most existing works focus on learning Pauli channels associated with some specific gates rather than treating the gate set as a whole. A learning algorithm that is self-consistent, complete, and efficient at the same time has yet to be established. In this work, we study the task of gate set Pauli noise learning, where a set of quantum gates, state preparation, and measurements all suffer from unknown Pauli noise channels with a customized noise ansatz. Using tools from algebraic graph theory, we analytically characterize the self-consistently learnable degrees of freedom for Pauli noise models with arbitrary linear ansatz, and design experiments to efficiently learn all the learnable information. Specifically, we show that all learnable information about the gate noise can be learned to relative precision, under mild assumptions on the noise ansatz. We then demonstrate the flexibility of our theory by applying it to concrete physically motivated ansatze (such as spatially local or quasi-local noise) and experimentally relevant gate sets (such as parallel CZ gates). These results not only enhance the theoretical understanding of quantum noise learning, but also provide a feasible recipe for characterizing existing and near-future quantum computing devices.

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Physics Subject Headings (PhySH)

Popular Summary

Quantum computers hold immense promise, but their power is limited by a persistent challenge: noise. To unlock practical quantum advantages, we must first understand and characterize this noise. That knowledge is essential for improving both quantum hardware and software, particularly in error mitigation and correction. However, learning about quantum noise is not easy—it involves estimating a huge number of parameters and dealing with imperfections in the very tools we use to measure it. These difficulties can also hinder the effectiveness of noise-aware techniques that rely on accurate noise models.

In this work, we introduce a new approach called gate set Pauli noise learning, designed to meet the dual demands of efficiency and self-consistency. By blending ideas from gate set tomography with recent advances in efficient Pauli noise characterization, we offer a framework that is both theoretically sound and experimentally practical. Our method rigorously identifies which aspects of noise can be meaningfully learned and provides concrete proposals on real quantum devices, supported by open-source simulation code.

Looking ahead, we believe this framework is ready for immediate use in today’s quantum experiments. It lays the groundwork for more effective error-mitigation strategies and could pave the way toward more comprehensive noise models—including those relevant to logical qubits and fault-tolerant quantum computing.

Article Text

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PRX Quantum 7, 010305– Published 9 January, 2026
  • Received 30 April 2025
  • Revised 23 August 2025
  • Accepted 5 November 2025
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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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