Error-Adaptive Quasi-local Decoding of the Toric Code

[2608.27740] Error-Adaptive Quasi-local Decoding of the Toric Code Skip to main content Search Submit Donate Log in Quantum Physics arXiv:2608.27740 (quant-ph) [Submitted on 27 Aug 2026] Title: Error-Adaptive Quasi-local Decoding of the Toric Code Authors: Hossein Dehghani , Sarang Gopalakrishnan , Michael Gullans View PDF HTML (experimental) 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. Comments: 14 pages, 8 figures. Extended version of a poster presented at QEC25: Fast Quasi-local Decoders for Topological Codes ( this https URL ) Subjects: Quantum Physics (quant-ph) ; Statistical Mechanics (cond-mat.stat-mech) Cite as: 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 Submission history From: Hossein Dehghani [ view email ] [v1] Thu, 27 Aug 2026 21:59:57 UTC (3,899 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2026-08 Change to browse by: cond-mat cond-mat.stat-mech References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

Related documents

• Error-Adaptive Quasi-local Decoding of the Toric Code#779660
• Causal-Order Identification of Memoryless Sequential Quantum Processes from Restricted Projective Data#1011093
• Quantum Topological Data Analysis Beyond Betti Numbers: Complexity Hardness $\&$ An Algorithm for Torsion Witness#1064656
• Universality Sacrifices Reliability in Classical-Quantum Channel Coding#1157212
• Phase-cycled randomized benchmarking of quantum processors: recovering hidden classical noise correlations#974024