Embedding Stabilizer Codes and Leakage Correction in Multilevel Quantum Systems

Quantum Physics arXiv:2608.12450 (quant-ph) [Submitted on 12 Aug 2026] Title:Embedding Stabilizer Codes and Leakage Correction in Multilevel Quantum Systems Authors:Ali Abu-Nada, Lian-Ao Wu View a PDF of the paper titled Embedding Stabilizer Codes and Leakage Correction in Multilevel Quantum Systems, by Ali Abu-Nada and Lian-Ao Wu View PDF HTML (experimental) Abstract:Leakage beyond the computational subspace is a major source of error in multilevel quantum hardware. We show that any \( [[n,k,d]] \) stabilizer code can be embedded isometrically into a single \(D\)-dimensional system while preserving its complete error-correcting structure. We further derive a necessary and sufficient condition for exact leakage correction, proving that leakage is correctable precisely when it does not distinguish between logical states. These results establish a unified framework for quantum error correction in multilevel quantum systems. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2608.12450 [quant-ph] (or arXiv:2608.12450v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.12450 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Ali Abu-Nada [view email] [v1] Wed, 12 Aug 2026 17:53:05 UTC (35 KB) Full-text links: Access Paper: View a PDF of the paper titled Embedding Stabilizer Codes and Leakage Correction in Multilevel Quantum Systems, by Ali Abu-Nada and Lian-Ao WuView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 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?) 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?)