Floquet Abelian Multicycle Codes

Quantum Physics arXiv:2607.27521 (quant-ph) [Submitted on 29 Jul 2026] Title:Floquet Abelian Multicycle Codes Authors:Alexey A. Kovalev View a PDF of the paper titled Floquet Abelian Multicycle Codes, by Alexey A. Kovalev View PDF HTML (experimental) Abstract:Abelian multicycle (AMC) codes are compact quantum low-density parity-check codes whose multiblock chain-complex structure provides redundant low-weight stabilizers and supports single-shot error correction. We introduce Floquet AMC codes by deriving a quotient-lattice representation of a general level-$j$, $D$-dimensional AMC complex over a finite Abelian group algebra, lifting this lattice to spacetime, and rotating the circuit-time direction in the associated ZX network. When the check and data spiders have even valence and admit a time-oriented local port matching, the network decomposes into a periodic schedule of native two-qubit $XX$ and $ZZ$ measurements. We construct generalized-bicycle and level-$2$ AMC4 examples, determine their instantaneous stabilizer groups, and compute their embedded distances by minimizing over all inequivalent circuit cuts. For AMC4 instances locally equivalent to four-dimensional toric codes, we obtain Floquet memories with parameters $[[108,6,5]]$, $[[144,6,8]]$, and $[[324,6,10]]$. Local Pauli-web detector templates and beam-search decoding under the measurement-native EM3 noise model yield an estimated pseudothreshold of approximately $1.2\%$. These results provide compact measurement-only realizations of higher-dimensional homological redundancy without directly measuring the original weight-six stabilizers. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2607.27521 [quant-ph] (or arXiv:2607.27521v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.27521 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Alexey Kovalev [view email] [v1] Wed, 29 Jul 2026 23:20:02 UTC (543 KB) Full-text links: Access Paper: View a PDF of the paper titled Floquet Abelian Multicycle Codes, by Alexey A. KovalevView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-07 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?)