Kinetics of sliding-window quantum error correction

• URL: http://arxiv.org/abs/2608.10081v1
• Date: Mon, 10 Aug 2026 18:00:26 GMT
• Title: Kinetics of sliding-window quantum error correction
• Abstract summary: We study the kinetics of sliding window decoding (SWD), an implementation of real-time decoding.<n>SWD acts on temporally local windows of noisy syndrome information and commits to corrections irreversibly at a nonzero rate.<n>We propose an effective description of SWD in terms of a kinetic process, where $mathbbZ$-charged point particles undergo parity-conserving reaction and diffusion.
• Score: 39.34750401159749
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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