{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/minimum-weight-perfect-matching-of-fault","title":"Minimum weight perfect matching of fault-tolerant topological quantum error correction in average $O(1)$ parallel time","arxiv_id":"1307.1740","date":"2013-07-06","proceeding":null,"authors":["Austin G. Fowler"],"abstract":"Consider a 2-D square array of qubits of extent $L\\times L$. We provide a proof that the minimum weight perfect matching problem associated with running a particular class of topological quantum error correction codes on this array can be exactly solved with a 2-D square array of classical computing devices, each of which is nominally associated with a fixed number $N$ of qubits, in constant average time per round of error detection independent of $L$ provided physical error rates are below fixed nonzero values, and other physically reasonable assumptions. This proof is applicable to the fully fault-tolerant case only, not the case of perfect stabilizer measurements.","url_abs":"https://arxiv.org/abs/1307.1740v3","url_pdf":"https://arxiv.org/pdf/1307.1740v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"minimum-weight-perfect-matching-of-fault","repo_url":"https://github.com/dtqec/anatevka","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1307.1740","atlas_url":"https://app.syntology.ai/?focus=1307.1740","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}