# Kinetics of sliding-window quantum error correction Source: [Kinetics of sliding-window quantum error correction]() Collection index: [llms.txt]() Data updated: 2026-08-13T05:00:05.217Z Authors: Adithya Sriram, Charles Stahl, Aleksander Kubica, Yaodong Li Published: 2026-08-10T18:00:26.000Z ## 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()