Statistical Mechanics and Symmetries of Non-Abelian Anyon Proliferation: From Deformation to Decoherence
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Quantum Physics arXiv:2606.12527 (quant-ph) [Submitted on 10 Jun 2026] Title:Statistical Mechanics and Symmetries of Non-Abelian Anyon Proliferation: From Deformation to Decoherence Authors:Avi Vadali, Robijn Vanhove, Ruben Verresen, Jason Alicea, Pablo Sala View a PDF of the paper titled Statistical Mechanics and Symmetries of Non-Abelian Anyon Proliferation: From Deformation to Decoherence, by Avi Vadali and 4 other authors View PDF HTML (experimental) Abstract:Topological quantum computation relies on braiding non-Abelian anyons, but requires the underlying topological order to survive imperfect state preparation and environmental noise. We show that the instability of topological order to wavefunction deformations and to decoherence, with the latter probed by syndrome distributions, are generically captured by stat-mech models whose symmetries naturally expose the corrupting anyonic excitations. As an example, we combine this framework with Monte-Carlo simulations to resolve the stability of $D_4$ topological order under deformations and quantum channels that proliferate multiple non-Abelian anyon species that individually are unable to condense. We show that beyond a finite threshold, proliferation of two non-Abelian anyon species parasitically condenses a shared Abelian-anyon fusion outcome, destroying the topological order. Our symmetry-based approach sharply differentiates the resulting trivial phase from that obtained by condensing all Abelian charges; in other words, the trivial phase "remembers" which anyons condensed. This framework provides a first step into identifying the relevant symmetry for optimal decoders, conditioned on syndrome measurements, of non-Abelian topological order. Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2606.12527 [quant-ph] (or arXiv:2606.12527v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.12527 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Avinash Vadali [view email] [v1] Wed, 10 Jun 2026 18:00:03 UTC (5,492 KB) Full-text links: Access Paper: View a PDF of the paper titled Statistical Mechanics and Symmetries of Non-Abelian Anyon Proliferation: From Deformation to Decoherence, by Avi Vadali and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: cond-mat cond-mat.stat-mech cond-mat.str-el 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?)