Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Institutions: Stanford University, Yale University
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: Emergent Phenomena in Quantum Systems Theory Center, G1938338418, QLCI-CI: NSF Quantum Leap Challenge Institute for Robust Quantum Simulation, G3398237449, G3719423973, G4486752075, G4689434848, G5356677024, G5723341926, Kavli Institute for Theoretical Physics, HOLOGRAPHIC QUANTUM SIMULATION WITH ATOMS AND PHOTONS: FROM ENTANGLEMENT TO NON-EUCLIDEAN GEOMETRY., G7452299184, G8876996369
OpenAlex ID: W7202260646
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