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 Rmatch, with mismatch εmatch=1−Rmatch. Across geometry families, εmatch shows strong buffer-controlled suppression and is well organized by a two-geometry scaling form. For scaled families, especially a=b=d/8, Rmatch exhibits a clear crossing and finite-size collapse near p ∼ 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 a0=b0=d/8, the resulting logical-failure curves show an apparent finite-size crossing at p≃0.09--$0.10$, below the conventional MWPM threshold scale. We focus on dephasing noise with perfect syndrome measurements to cleanly isolate the underlying behavior.
Related
- Topological Quantum Error-Correcting Thresholds of a Symmetry-Enriched Toric Code
- Geometry Dependence of Error Thresholds in Two-Dimensional Toric Codes
- Quantum Error Correction in Nearly Critical Toric Codes
- Discovering correlated error mechanisms: data-driven augmentation of detector error models improving decoding
- Reducing Decoding Latency in Quantum Error Correction by Early Starting Clustering
BibTeX
@misc{dehghani2026erroradaptive,
title = {{Error-Adaptive Quasi-local Decoding of the Toric Code}},
author = {Hossein Dehghani and Sarang Gopalakrishnan and Michael Gullans},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27740},
eprint = {2608.27740},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27740},
}
RIS
TY - UNPB
TI - Error-Adaptive Quasi-local Decoding of the Toric Code
AU - Hossein Dehghani
AU - Sarang Gopalakrishnan
AU - Michael Gullans
PY - 2026
DA - 2026/08/27
PB - arXiv
DO - 10.48550/arxiv.2608.27740
UR - https://arxiv.org/abs/2608.27740
AB - 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_match, with mismatch ε_match=1−R_match. Across geometry families, ε_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_match exhibits a clear crossing and finite-size collapse near p ∼ 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≃0.09--$0.10$, below the conventional MWPM threshold scale. We focus on dephasing noise with perfect syndrome measurements to cleanly isolate the underlying behavior.
ER -