Entropic Rigidity in Quantum Memories: How Geometry and Algebra Control the Onset of Degeneracy Corrections

Quantum Physics arXiv:2608.18420 (quant-ph) [Submitted on 19 Aug 2026] Title:Entropic Rigidity in Quantum Memories: How Geometry and Algebra Control the Onset of Degeneracy Corrections Authors:Yixin Zhao, Fei Yan View a PDF of the paper titled Entropic Rigidity in Quantum Memories: How Geometry and Algebra Control the Onset of Degeneracy Corrections, by Yixin Zhao and 1 other authors View PDF HTML (experimental) Abstract:Maximum-probability (MP) decoding selects the most probable microscopic error, whereas degenerate maximum-likelihood (MLD) decoding includes the configurational entropy of an entire logical sector. Using code-capacity Pauli noise to isolate rigidity intrinsic to the code, we determine the first physical error weight $m$ at which their logical winner sets become disjoint, even under optimal MP tie resolution. Code distance imposes the universal bound $m\geq h=\lceil d/2\rceil$. We define the entropic rigidity depth $r$ through $m=h+r$ and certify a three-level hierarchy: $r=0$ for planar surface codes and two concatenated families, $r=1$ for odd-distance square toric codes and the Gross $[[144,12,12]]$ quantum low-density-parity-check code, and $r=2$ for a separable family with hypergraph product and bivariate bicycle descriptions. The onset fixes the leading operational failure gap, proportional to the $m$th power of the physical noise strength. Geometry and algebra therefore provide quantifiable controls of configurational entropy and an exact benchmark for low-noise decoder selection. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2608.18420 [quant-ph] (or arXiv:2608.18420v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.18420 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Yixin Zhao [view email] [v1] Wed, 19 Aug 2026 01:17:59 UTC (443 KB) Full-text links: Access Paper: View a PDF of the paper titled Entropic Rigidity in Quantum Memories: How Geometry and Algebra Control the Onset of Degeneracy Corrections, by Yixin Zhao and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 Change to browse by: cond-mat cond-mat.stat-mech 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?)