Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2608.10081

Kinetics of sliding-window quantum error correction

Adithya Sriram, Charles Stahl, Aleksander Kubica, Yaodong Li

quant-phcond-mat.dis-nncond-mat.stat-mechSubmitted Aug 10, 2026• Announced Aug 12, 2026• 0 citations
arXivHTMLPDF

Abstract

Practical implementations of quantum error correction (QEC) require rapid measurement and continuous processing of the syndrome information in order to prevent a backlog of unprocessed data. While ``static'' QEC is theoretically well understood via mappings to equilibrium statistical mechanics models, such an understanding of ``real-time'' QEC is currently lacking. Here, we study the kinetics of sliding window decoding (SWD), an implementation of real-time decoding that acts on temporally local windows of noisy syndrome information and commits to corrections irreversibly at a nonzero rate. We propose an effective description of SWD in terms of a stochastic kinetic process, where $\mathbb{Z}_2$-charged point particles undergo parity-conserving reaction and diffusion. This model describes dynamics at length and time scales large compared to the window size $W$, whereas physics at scales smaller than $W$ leads to nontrivial $W$-dependent scaling of the effective parameters. We identify the rate of decoding $1/W$ as a relevant perturbation to the decodable phase. We also show broad applicability of our results by changing many microscopic details of SWD without affecting the effective description.

Comments
8 pages, 3 pages of supplemental information

Related papers

Increasing memory lifetime of quantum low-density parity check codes with sliding-window noisy syndrome decoding

Shilin Huang, Shruti Puri

Quantum error correction (QEC) with single-shot decoding enables the reduction of errors after every single round of noisy stabilizer measurement, easing the time-overhead requirements for fault tolerance. Notably, several classes of quantum low-density parity check (qLDPC) codes are known which facilitate single-shot decoding, potentially giving them an additional overhead advantage. However, the perceived advantage of single-shot decoding is limited because it can significantly degrade the effective code distance. This degradation may be compensated for by using a much larger code size to achieve the desired target logical error rate, at the cost of increasing the amount of syndrome information to be processed, as well as increasing complexity of logical operations. Alternatively, in this paper we study sliding-window decoding, which corrects errors from previous syndrome measurement rounds while leaving the most recent errors for future correction. We observe that sliding-window decoding significantly improves the logical memory lifetime and hence the effective distance compared to single-shot decoding on hypergraph-product codes and lifted-product codes. Remarkably, we find that this improvement may not cost a larger decoding complexity. Thus, the sliding-window strategy can be more desirable for fast and accurate decoding for fault-tolerant quantum computing with qLDPC codes.

Physical Review A•Jul 22, 2024•7 citations

Improved Noisy Syndrome Decoding of Quantum LDPC Codes with Sliding Window

Shilin Huang, Shruti Puri

Quantum error correction (QEC) with single-shot decoding enables reduction of errors after every single round of noisy stabilizer measurement, easing the time-overhead requirements for fault tolerance. Notably, several classes of quantum low-density-parity-check (qLDPC) codes are known which facilitate single-shot decoding, potentially giving them an additional overhead advantage. However, the perceived advantage of single-shot decoding is limited because it can significantly degrade the effective code distance. This degradation may be compensated for by using a much larger code size to achieve the desired target logical error rate, at the cost of increasing the amount of syndrome information to be processed, as well as, increasing complexity of logical operations. Alternatively, in this work we study sliding-window decoding, which corrects errors from previous syndrome measurement rounds while leaving the most recent errors for future correction. We observe that sliding-window decoding significantly improves the logical memory lifetime and hence the effective distance compared to single-shot decoding on hypergraph-product codes and lifted-product codes. Remarkably, we find that this improvement may not cost a larger decoding complexity. Thus, the sliding-window strategy can be more desirable for fast and accurate decoding for fault-tolerant quantum computing with qLDPC codes.

arXiv:2311.03307•Nov 6, 2023•0 citations

Adaptive Estimation of Drifting Noise in Quantum Error Correction

Devansh Bhardwaj, Evangelia Takou, Yingjia Lin +1 more

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, by exploiting the syndrome statistics of quantum error correction experiments. 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 align 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.

quant-pharXiv:2511.09491•Nov 13, 2025•0 citations

Backlog Metastability in Windowed Quantum Error Correction Decoding

Jean-Jacques Dubray

Real-time quantum error correction requires a classical decoder to consume syndrome measurements at the rate the quantum hardware produces them, roughly one round per microsecond on superconducting devices. The standard stability requirement is a utilization condition: the mean decode time per round must be less than the round period, ρ < 1. We show that this condition is inadequate for windowed decoders whose per-window cost grows superlinearly in the number of detection events, which is the empirical shape of matching-based decoders under burst-like syndrome content. For this class, stability is not a threshold but a basin. The deterministic backlog dynamics have a stable operating point and an unstable boundary B∗. Noise erodes that boundary downward, and sufficiently superlinear decoders escape spontaneously. In discrete-event simulations paired under common random numbers, a decoder with cost exponent γ = 1.5 and mean utilization ρ0 = 0.6 (forty percent nominal headroom) fails without provocation, with a mean time to failure of 1,344 ± 289 rounds, about 1.3ms of wall clock at a 1µs cycle. We measure the cost exponent of a production decoder (PyMatching 2, sparse blossom) and find it anisotropic: near-linear (γ ≈ 1.1–1.2) when a window grows in length at fixed syndrome density, but approximately quadratic (γ ≈ 2) when the same window grows denser. Bursts travel along the dangerous axis, where the basin is 2–4 rounds deep for ρ0 between 0.5 and 0.8. Spatially clustered event content, the syndrome footprint of leakage and cosmic-ray bursts, is worse still: at matched event count, clustered windows cost 7.6× length-grown ones and 4.8× uniformly densified ones, so the quadratic density exponent is a conservative proxy for burst content. Greedy catch-up (“decode everything queued”) is precisely the divergent policy. A bounded decoding window restores stability, and the measured stability edge lands on a closed-form line. The simulation model is cross-validated against Stim at the level of individual fault mechanisms.

•Aug 20, 2026•0 citations

The Syndrome Buffer Sizing Problem in Quantum Error Correction

Sumeet Shirgure, Siyuan Niu

A fault-tolerant quantum computer must continuously decode a stream of syndrome data, yet the computational work required by each decoding window is random. Although average throughput determines whether the syndrome backlog is stable (doesn’t grow without bound), it does not determine the buffer capacity needed to meet a target overflow probability. Here, we model syndrome buffering as a queue and show how its required depth depends on the tail of the decoding-work distribution. For heavy-tailed work, established queueing results imply that sliding-window decoding can require buffer depths that grow superpolynomially in the logarithm of the inverse overflow probability. Parallel-window decoding suppresses the overflow tail through concurrent service, with the suppression exponent determined by the number of spare decoders; under out-of-order release, the number of spare decoders required for a fixed buffer and target overflow probability grows logarithmically with the inverse target probability. We find evidence of heavy-tailed decoding work in Relay-BP on the gross-code and minimum-weight perfect matching on the surface code. These results identify syndrome-buffer capacity and memory-release policy as important design considerations for real-time quantum error correction.

•Oct 15, 2026•0 citations

Adaptive Estimation of Drifting Noise in Quantum Error Correction

Anonymous, Evangelia Takou, Yingjia Lin +1 more

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.

PRX Quantum•Jun 23, 2026•0 citations
Practical implementations of quantum error correction (QEC) require rapid measurement and continuous processing of the syndrome information in order to prevent a backlog of unprocessed data. While static'' QEC is theoretically well understood via mappings to equilibrium statistical mechanics models, such an understanding of real-time'' QEC is currently lacking. Here, we study the kinetics of sliding window decoding (SWD), an implementation of real-time decoding that acts on temporally local windows of noisy syndrome information and commits to corrections irreversibly at a nonzero rate. We propose an effective description of SWD in terms of a stochastic kinetic process, where Z2\mathbb{Z}_2Z2​-charged point particles undergo parity-conserving reaction and diffusion. This model describes dynamics at length and time scales large compared to the window size WWW, whereas physics at scales smaller than WWW leads to nontrivial WWW-dependent scaling of the effective parameters. We identify the rate of decoding 1/W1/W1/W as a relevant perturbation to the decodable phase. We also show broad applicability of our results by changing many microscopic details of SWD without affecting the effective description.
Quantum error correction (QEC) with single-shot decoding enables the reduction of errors after every single round of noisy stabilizer measurement, easing the time-overhead requirements for fault tolerance. Notably, several classes of quantum low-density parity check (qLDPC) codes are known which facilitate single-shot decoding, potentially giving them an additional overhead advantage. However, the perceived advantage of single-shot decoding is limited because it can significantly degrade the effective code distance. This degradation may be compensated for by using a much larger code size to achieve the desired target logical error rate, at the cost of increasing the amount of syndrome information to be processed, as well as increasing complexity of logical operations. Alternatively, in this paper we study sliding-window decoding, which corrects errors from previous syndrome measurement rounds while leaving the most recent errors for future correction. We observe that sliding-window decoding significantly improves the logical memory lifetime and hence the effective distance compared to single-shot decoding on hypergraph-product codes and lifted-product codes. Remarkably, we find that this improvement may not cost a larger decoding complexity. Thus, the sliding-window strategy can be more desirable for fast and accurate decoding for fault-tolerant quantum computing with qLDPC codes.
Quantum error correction (QEC) with single-shot decoding enables reduction of errors after every single round of noisy stabilizer measurement, easing the time-overhead requirements for fault tolerance. Notably, several classes of quantum low-density-parity-check (qLDPC) codes are known which facilitate single-shot decoding, potentially giving them an additional overhead advantage. However, the perceived advantage of single-shot decoding is limited because it can significantly degrade the effective code distance. This degradation may be compensated for by using a much larger code size to achieve the desired target logical error rate, at the cost of increasing the amount of syndrome information to be processed, as well as, increasing complexity of logical operations. Alternatively, in this work we study sliding-window decoding, which corrects errors from previous syndrome measurement rounds while leaving the most recent errors for future correction. We observe that sliding-window decoding significantly improves the logical memory lifetime and hence the effective distance compared to single-shot decoding on hypergraph-product codes and lifted-product codes. Remarkably, we find that this improvement may not cost a larger decoding complexity. Thus, the sliding-window strategy can be more desirable for fast and accurate decoding for fault-tolerant quantum computing with qLDPC codes.
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, by exploiting the syndrome statistics of quantum error correction experiments. 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 align 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.
Real-time quantum error correction requires a classical decoder to consume syndrome measurements at the rate the quantum hardware produces them, roughly one round per microsecond on superconducting devices. The standard stability requirement is a utilization condition: the mean decode time per round must be less than the round period, ρ < 1. We show that this condition is inadequate for windowed decoders whose per-window cost grows superlinearly in the number of detection events, which is the empirical shape of matching-based decoders under burst-like syndrome content. For this class, stability is not a threshold but a basin. The deterministic backlog dynamics have a stable operating point and an unstable boundary B∗. Noise erodes that boundary downward, and sufficiently superlinear decoders escape spontaneously. In discrete-event simulations paired under common random numbers, a decoder with cost exponent γ = 1.5 and mean utilization ρ0 = 0.6 (forty percent nominal headroom) fails without provocation, with a mean time to failure of 1,344 ± 289 rounds, about 1.3ms of wall clock at a 1µs cycle. We measure the cost exponent of a production decoder (PyMatching 2, sparse blossom) and find it anisotropic: near-linear (γ ≈ 1.1–1.2) when a window grows in length at fixed syndrome density, but approximately quadratic (γ ≈ 2) when the same window grows denser. Bursts travel along the dangerous axis, where the basin is 2–4 rounds deep for ρ0 between 0.5 and 0.8. Spatially clustered event content, the syndrome footprint of leakage and cosmic-ray bursts, is worse still: at matched event count, clustered windows cost 7.6× length-grown ones and 4.8× uniformly densified ones, so the quadratic density exponent is a conservative proxy for burst content. Greedy catch-up (“decode everything queued”) is precisely the divergent policy. A bounded decoding window restores stability, and the measured stability edge lands on a closed-form line. The simulation model is cross-validated against Stim at the level of individual fault mechanisms.
A fault-tolerant quantum computer must continuously decode a stream of syndrome data, yet the computational work required by each decoding window is random. Although average throughput determines whether the syndrome backlog is stable (doesn’t grow without bound), it does not determine the buffer capacity needed to meet a target overflow probability. Here, we model syndrome buffering as a queue and show how its required depth depends on the tail of the decoding-work distribution. For heavy-tailed work, established queueing results imply that sliding-window decoding can require buffer depths that grow superpolynomially in the logarithm of the inverse overflow probability. Parallel-window decoding suppresses the overflow tail through concurrent service, with the suppression exponent determined by the number of spare decoders; under out-of-order release, the number of spare decoders required for a fixed buffer and target overflow probability grows logarithmically with the inverse target probability. We find evidence of heavy-tailed decoding work in Relay-BP on the gross-code and minimum-weight perfect matching on the surface code. These results identify syndrome-buffer capacity and memory-release policy as important design considerations for real-time quantum error correction.
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.