AI 中文总结
针对拓扑量子存储器解码器可靠性与可扩展性的权衡问题，提出基于局部可恢复性诊断的准局部解码方法，通过匹配比标度分析构建自适应规则，实现了低于传统MWPM阈值的解码性能。
AI 中文摘要
拓扑量子存储器需要兼具可靠性与可扩展性的解码器，但这两个目标存在权衡：全局信息解码器在阈值附近精度高但计算成本大，而严格局部规则速度快却会遗漏长程结构。受近期可恢复性与混合态观点的启发，我们通过解码器层面的局部可恢复性诊断，将这种权衡应用于退相toric码。我们将目标区域内的全局MWPM（最小权完美匹配）校正与准局部校正进行对比，定义了匹配比$R_{\text{match}}$，失配度为$ε_{\text{match}}=1-R_{\text{match}}$。在不同几何结构族中，$ε_{\text{match}}$表现出显著的缓冲控制抑制效应，且符合双几何标度形式。对于标度族，尤其是$a=b=d/8$的情况，$R_{\text{match}}$在$p\thicksim0.09$附近呈现清晰的交叉点与有限尺寸塌缩，这与解码转变附近可恢复性尺度增长的现象一致。我们利用该标度提出了自适应缓冲选择规则，并为全环面上的复合准局部RG（重整化群）解码器确定了距离标度的初始化方式。在调优的$a_0=b_0=d/8$族中，得到的逻辑失效曲线在$p\backsimeq0.09$–$0.10$处呈现明显的有限尺寸交叉点，低于传统MWPM的阈值尺度。我们聚焦于具有完美症状测量的退相噪声，以清晰分离出底层行为。
英文摘要
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 $ε_{\mathrm{match}}=1-R_{\mathrm{match}}$. Across geometry families, $ε_{\mathrm{match}}$ 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.
Comments14 pages, 8 figures. Extended version of a poster presented at QEC25: Fast Quasi-local Decoders for Topological Codes (https://qec25.yalepages.org/assets/images/QEC25-Posters.pdf)
