{"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/concatenation-schemes-for-topological-fault","title":"Concatenation Schemes for Topological Fault-tolerant Quantum Error Correction","arxiv_id":"2209.09390","date":"2022-09-20","proceeding":null,"authors":["Zhaoyi Li","Isaac Kim","Patrick Hayden"],"abstract":"We investigate a family of fault-tolerant quantum error correction schemes based on the concatenation of small error detection or error correction codes with the three-dimensional cluster state. We propose fault-tolerant state preparation and decoding schemes that effectively convert every circuit-level error into an erasure error, leveraging the cluster state's high threshold against such errors. We find a set of codes for which such a conversion is possible, and study their performance against the standard circuit-level depolarizing model. Our best performing scheme, which is based on a concatenation with a classical code, improves the threshold by $16.5\\%$ and decreases the spacetime overhead by $32\\%$ compared to the scheme without concatenation, with each scheme subject to a physical error rate of $10^{-3}$ and achieving a logical error rate of $10^{-6}$.","url_abs":"https://arxiv.org/abs/2209.09390v2","url_pdf":"https://arxiv.org/pdf/2209.09390v2.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":"concatenation-schemes-for-topological-fault","repo_url":"https://github.com/ZhaoyiLi-HekJukZaaiZyuJan/QEC-decoders","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"tf","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}