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  • Open Access

Adaptive Estimation of Drifting Noise in Quantum Error Correction

Devansh Bhardwaj* and Evangelia Takou

Yingjia Lin

Kenneth R. Brown†

  • Duke Quantum Center, Duke University, Durham, North Carolina 27701, USA and Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA

  • Duke Quantum Center, Duke University, Durham, North Carolina 27701, USA; Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA; Department of Physics, Duke University, Durham, North Carolina 27708, USA and Department of Chemistry, Duke University, Durham, North Carolina 27708, USA

  • *Contact author: devansh.bhardwaj@duke.edu
  • †Contact author: kenneth.r.brown@duke.edu
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PRX Quantum 7, 033024 – Published 6 August, 2026

DOI: https://doi.org/10.1103/z1hc-nqw5

Abstract

Advancing quantum information processors and building fault-tolerant architectures rely on the ability to accurately characterize the noise sources and suppress their impact on quantum devices. In practice, noise often drifts over time, whereas conventional noise characterization and decoding methods typically assume stationarity or provide only a time-average behavior of the noise. This treatment can result in suboptimal decoding performance. In this work, we present a rigorous analytical framework to capture time-dependent Pauli noise, which is designed to use only syndrome data obtained from quantum error correction experiments. We validate this framework through numerical simulations. We propose a sliding-window estimation method which allows us to recover the frequency components of the noise, by using optimal window sizes that we derive analytically. We prove the noise-filtering behavior of sliding windows, linking window size to spectral cutoff frequencies, and provide an iterative algorithm that captures multiple drift frequencies. We further introduce an overlapping window algorithm that enables us to capture rapid multi-frequency noise drifts in a single-pass fashion. Simulations for both phenomenological and circuit-level noise models validate our framework, demonstrating robust tracking of multi-frequency drift. The logical error rate obtained from our estimated models consistently aligns with the ground-truth logical error rate, and we find suppression of logical errors compared to static error models. Our window-based estimation methods and adaptive decoding offer new insights into noise spectroscopy and decoder optimization under drift using only syndrome data.

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Physics Subject Headings (PhySH)

Popular Summary

Quantum computing hardware platforms suffer from environmental instabilities which often lead to time-varying noise. Quantum computers might require to run for sufficiently long times to execute complicated algorithms, which necessitates the protection of computations against errors, using quantum error correction (QEC). Noise drift occurring during computations can significantly degrade the logical performance of quantum computers. While noise drifts can be in part suppressed by calibration routines, those cannot be run in parallel with computation. Hence, adapting the decoders to drifting noise is highly desirable. Syndrome data obtained from QEC experiments carry rich information about the noise profile and can be exploited without perturbing the experiments. Detector error models (DEMs) provide sufficient information to decode and correct errors in QEC experiments. Correlations in the syndrome data have been previously used to obtain time-average DEMs. However, capturing drifting noise using syndromes is not yet studied and remains a challenge. The authors present sliding window estimation methods which accurately reconstruct the time-varying error rates of DEMs. For single-frequency spectrums the authors find the optimal window size that balances trade-offs between statistical uncertainty and time-lags. The methods presented can track multi-frequency spectrums as well as rapidly drifting noise. Through simulations of repetition and surface-code memories under drifting noise, the authors demonstrate the effectiveness of their methods. The estimated DEMs improve the decoding performance compared to DEMs built based on the static noise assumption. The proposed methods pave the way to efficient characterization of QEC devices which can improve the decoding performance of QEC experiments.

Article Text

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Outline

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PRX Quantum 7, 033024– Published 6 August, 2026
  • Received 12 January 2026
  • Revised 9 June 2026
  • Accepted 23 June 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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