Symmetry-Based Quantum Codes Beyond the Pauli Group

Quantum Physics arXiv:2512.07908 (quant-ph) [Submitted on 8 Dec 2025] Title:Symmetry-Based Quantum Codes Beyond the Pauli Group Authors:Zachary P. Bradshaw, Margarite L. LaBorde, Dillon Montero View a PDF of the paper titled Symmetry-Based Quantum Codes Beyond the Pauli Group, by Zachary P. Bradshaw and 2 other authors View PDF Abstract:Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that allows the code designer to take this structure into account. For any representation of a finite group, we produce a quantum code with a code space invariant under the group action, providing passive error mitigation against errors belonging to the image of the representation. Furthermore, errors outside this scope are detected and diagnosed by performing a projective measurement onto the isotypic components corresponding to irreducible representations of the chosen group, effectively generalizing syndrome extraction to symmetry-resolved quantum measurements. We show that all stabilizer codes are a special case of this construction, including qudit stabilizer codes, and show that there is a natural one logical qubit code associated to the dihedral group. Thus we provide a unifying framework for existing codes while simultaneously facilitating symmetry-aware codes tailored to specific systems. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) MSC classes: 81P73 (Primary) 20C99 (Secondary) Cite as: arXiv:2512.07908 [quant-ph] (or arXiv:2512.07908v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.07908 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Zachary Bradshaw [view email] [v1] Mon, 8 Dec 2025 01:34:11 UTC (208 KB) Full-text links: Access Paper: View a PDF of the paper titled Symmetry-Based Quantum Codes Beyond the Pauli Group, by Zachary P. Bradshaw and 2 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: math math-ph math.MP 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?)