A theory of quantum error correction for permutation-invariant codes
Summarize this article with:
Quantum Physics arXiv:2602.13638 (quant-ph) [Submitted on 14 Feb 2026] Title:A theory of quantum error correction for permutation-invariant codes Authors:Yingkai Ouyang, Gavin K. Brennen View a PDF of the paper titled A theory of quantum error correction for permutation-invariant codes, by Yingkai Ouyang and Gavin K. Brennen View PDF HTML (experimental) Abstract:We present for the first time a general theory of error correction for permutation invariant (PI) codes. Using representation theory of the symmetric group we construct efficient algorithms that can correct any correctible error on any PI code. These algorithms involve measurements of total angular momentum, quantum Schur transforms or logical state teleportations, and geometric phase gates. For erasure errors, or more generally deletion errors, on certain PI codes, we give a simpler quantum error correction algorithm. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2602.13638 [quant-ph] (or arXiv:2602.13638v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.13638 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Yingkai Ouyang [view email] [v1] Sat, 14 Feb 2026 07:05:03 UTC (4,435 KB) Full-text links: Access Paper: View a PDF of the paper titled A theory of quantum error correction for permutation-invariant codes, by Yingkai Ouyang and Gavin K. BrennenView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)