Error-Adaptive Quasi-local Decoding of the Toric Code

Abstract:Topological quantum memories need decoders that are both reliable and scalable, but these goals compete: globally informed decoders are accurate near threshold yet expensive, while strictly local rules are fast but can miss long-range structure. Motivated by recent recoverability and mixed-state viewpoints, we make this tradeoff operational for the dephased toric code through a decoder-level local recoverability diagnostic. We compare global MWPM corrections to quasi-local corrections inside a target region and define a matching ratio $R_{\mathrm{match}}$, with mismatch $\epsilon_{\mathrm{match}}=1-R_{\mathrm{match}}$. Across geometry families, $\epsilon_{\mathrm{match}}$ shows strong buffer-controlled suppression and is well organized by a two-geometry scaling form. For scaled families, especially $a=b=d/8$, $R_{\mathrm{match}}$ exhibits a clear crossing and finite-size collapse near $p\!\sim\!0.09$, consistent with a growing recoverability scale near the decoding transition. We use this scaling to formulate an adaptive buffer-selection rule and to identify a distance-scaled initialization for a composite quasi-local RG decoder on the full torus. In the tuned family $a_0=b_0=d/8$, the resulting logical-failure curves show an apparent finite-size crossing at $p\simeq0.09$--$0.10$, below the conventional MWPM threshold scale. We focus on dephasing noise with perfect syndrome measurements to cleanly isolate the underlying behavior.

14 pages, 8 figures. Extended version of a poster presented at QEC25: Fast Quasi-local Decoders for Topological Codes (this https URL)

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2608.27740 [quant-ph]

(or arXiv:2608.27740v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.27740 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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