Kinetics of sliding-window quantum error correction

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.

Adithya Sriram, Charles Stahl, Aleksander Kubica, Yaodong Li · 2026