Multivariate Multicycle Codes for Complete Single-Shot Decoding

Quantum Physics arXiv:2601.18879 (quant-ph) [Submitted on 26 Jan 2026] Title:Multivariate Multicycle Codes for Complete Single-Shot Decoding Authors:Feroz Ahmed Mian, Owen Gwilliam, Stefan Krastanov View a PDF of the paper titled Multivariate Multicycle Codes for Complete Single-Shot Decoding, by Feroz Ahmed Mian and 2 other authors View PDF HTML (experimental) Abstract:We introduce multivariate multicycle (MM) codes, a new family of quantum error correcting codes that unifies and generalizes bivariate bicycle codes, multivariate bicycle codes, abelian two-block group algebra codes, generalized bicycle codes, trivariate tricycle codes, and n-dimensional toric codes. MM codes are Calderbank-Shor-Steane (CSS) codes defined from length-t chain complexes with $t \ge 4$. The chief advantage of these codes is that they possess metachecks and high confinement that permit complete single-shot decoding, while also having additional algebraic structure that might enable logical non-Clifford gates. We offer a framework that facilitates the construction of long-length chain complexes through the use of Koszul complex. In particular, obtaining explicit boundary maps (parity check and metacheck matrices) is particularly straightforward in our approach. This simple but very general parameterization of codes permitted us to efficiently perform a numerical search, where we identify several MM code candidates that demonstrate these capabilities at high rates and high code distances. Examples of new codes with parameters $[[n,k,d]]$ include $[[96, 12, 8]]$, $[[96, 44, 4]]$ $[[144, 40, 4]]$, $[[216, 12, 12]]$, $[[360, 30, 6]]$, $[[384, 80, 4]]$, $[[486, 24, 12]]$, $[[486, 66, 9]]$ and $[[648, 60, 9]]$. Notably, our codes achieve confinement profiles that surpass all known single-shot decodable quantum CSS codes of practical blocksize. Subjects: Quantum Physics (quant-ph); Information Theory (cs.IT) Cite as: arXiv:2601.18879 [quant-ph] (or arXiv:2601.18879v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.18879 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Stefan Krastanov [view email] [v1] Mon, 26 Jan 2026 19:00:03 UTC (2,808 KB) Full-text links: Access Paper: View a PDF of the paper titled Multivariate Multicycle Codes for Complete Single-Shot Decoding, by Feroz Ahmed Mian and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: cs cs.IT math math.IT 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?)