Spin stiffness and resilience phase transition in a noisy toric-rotor code
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Quantum Physics arXiv:2602.23751 (quant-ph) [Submitted on 27 Feb 2026] Title:Spin stiffness and resilience phase transition in a noisy toric-rotor code Authors:Morteza Zarei, Mohammad Hossein Zarei View a PDF of the paper titled Spin stiffness and resilience phase transition in a noisy toric-rotor code, by Morteza Zarei and 1 other authors View PDF HTML (experimental) Abstract:We use a quantum formalism for the partition function of the classical $XY$ model to identify a resilience phase transition in a noisy toric-rotor code. Specifically, we consider the toric-rotor code under phase-shift noise described by a von Mises probability distribution and show that the fidelity between the final state after noise and the initial state is proportional to the partition function of the $XY$ model. We map the temperature of the $XY$ model to the width of the noise in the toric-rotor code, such that a Kosterlitz--Thouless phase transition at a critical temperature $T_{c}$ corresponds to a mixed-state phase transition at a critical width $\sigma_c$. To characterize this phase transition, we develop a quantum formalism for the spin stiffness in the $XY$ model and show that it is mapped to the gate fidelity in the logical subspace of the toric-rotor code. In particular, we introduce a topological order parameter that characterizes the resilience of the toric-rotor code to decoherence within the logical subspace. We show that the logical subspace does not exhibit complete resilience to noise, which is a necessary condition for correctability. However, it exhibits partial resilience to noise for widths less than $\sigma_c\approx 0.89$, where the resilience order parameter takes values near $1$ and then drops to zero at $\sigma_c$. We also use our results to shed light on the correctability of toric-rotor codes in higher dimensions $d > 2$. Our work shows that the quantum formalism for partition functions provides a mathematically rigorous framework for studying correctability in continuous-variable quantum codes. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2602.23751 [quant-ph] (or arXiv:2602.23751v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.23751 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Mohammad Hossein Zarei [view email] [v1] Fri, 27 Feb 2026 07:26:34 UTC (1,900 KB) Full-text links: Access Paper: View a PDF of the paper titled Spin stiffness and resilience phase transition in a noisy toric-rotor code, by Morteza Zarei and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 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?) 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?)