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  • Open Access

Efficient Characterization of Coherent and Correlated Low-Degree Noise in Layers of Gates

Marianna Crupi1,2,*, J. Ignacio Cirac1,2, and Flavio Baccari3

  • *Contact author: marianna.crupi@mpq.mpg.de
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PRX Quantum 6, 040374 – Published 30 December, 2025

DOI: https://doi.org/10.1103/8ng1-4c1k

Abstract

We present a quantum process-tomography protocol based on a low-degree ansatz for the quantum channel, i.e., when it can be expressed as a fixed-degree polynomial in terms of Pauli operators. We demonstrate how to perform tomography of such channels with a logarithmic amount of effort relative to the size of the system, by employing random state preparation and measurements in the Pauli basis. We extend the applicability of the protocol to channels consisting of a layer of quantum gates with a polylogarithmic number of non-Clifford gates, followed by a low-degree noise channel. Rather than inverting the layer of quantum gates on the hardware—which would introduce additional errors—we instead carry out the inversion in classical postprocessing, while adding to the sample complexity a factor at most polynomial in system size. Numerical simulations support our theoretical findings and demonstrate the feasibility of our method.

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Popular Summary

Characterizing how noise affects quantum devices is essential for making quantum computers reliable, but standard methods become impractical as systems grow. We show that many realistic noise processes can be learned far more efficiently by exploiting their underlying structure. Our tomography method scales only logarithmically with system size and requires only simple single-qubit operations already available on today’s hardware. This enables the reconstruction of quantum processes on large systems, without relying on resource-intensive procedures.

Many realistic noise processes admit a low-degree representation, i.e., their action is dominated by only the lower-order terms in their Pauli expansion. Using a framework based on random single-qubit measurements, we show how to efficiently reconstruct this kind of noise. By modifying the classical postprocessing used in standard shadow tomography, we obtain two key advantages: (1) we obtain an efficient reconstruction method tailored to low-degree noise, something that standard shadow-tomography techniques cannot provide, and (2) we isolate the noise affecting a layer of gates without having to physically invert the gates on hardware, which would introduce extra errors. These improvements allow us to learn the noise affecting large quantum systems much more efficiently than previously possible.

This approach opens the door to scalable and experimentally friendly noise characterization for large quantum systems. Since it requires only simple single-qubit operations and avoids noisy multiqubit gates, it is aligned with the capabilities of today’s devices. By efficiently isolating and reconstructing error processes, it provides a practical tool for benchmarking and improving quantum hardware as systems size grows.

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Outline

Information

PRX Quantum 6, 040374– Published 30 December, 2025
  • Received 16 July 2025
  • Revised 23 October 2025
  • Accepted 24 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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