Projected logical ensembles in surface codes via the random-matrix theory of quantum dots
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Quantum Physics arXiv:2606.17140 (quant-ph) [Submitted on 15 Jun 2026] Title:Projected logical ensembles in surface codes via the random-matrix theory of quantum dots Authors:Mircea Bejan, Jan Behrends, Max McGinley, Benjamin Béri View a PDF of the paper titled Projected logical ensembles in surface codes via the random-matrix theory of quantum dots, by Mircea Bejan and 3 other authors View PDF HTML (experimental) Abstract:Measurements underpin active quantum error correction (QEC) and have been recognized as a source of novel measurement-induced many-body phenomena. Here, we study the statistical properties of post-measurement logical states arising in QEC on topological codes subject to deterministic transversal unitary gates. Upon syndrome extraction followed by maximum-likelihood decoding, a Born-weighted ensemble arises which we dub the "projected logical ensemble" (PLE). Focusing on surface codes subject to uniform single-qubit Pauli-$X$ rotations, we characterize the measurement-induced randomness of the PLE. To this end, we show that for a code with a single logical qubit, the PLE is isomorphic to an ensemble of scattering matrices describing mesoscopic quantum dots obtained from a 2D Majorana network model with suitable boundary conditions. We uncover regimes where these quantum dots are chaotic such that their scattering matrices are well-described by random matrix theory. In these regimes, the PLE approaches a universal ensemble that is maximally random up to symmetry and decoder-induced constraints. The symmetry constraints, set by stabilizer and logical operator weights, realize Altland-Zirnbauer classes D or DIII, which we both illustrate. Our results establish a fundamental connection between emergent universality concepts in mesoscopic physics, quantum many-body systems, and QEC. Comments: Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2606.17140 [quant-ph] (or arXiv:2606.17140v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.17140 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Mircea Bejan [view email] [v1] Mon, 15 Jun 2026 18:00:01 UTC (2,716 KB) Full-text links: Access Paper: View a PDF of the paper titled Projected logical ensembles in surface codes via the random-matrix theory of quantum dots, by Mircea Bejan and 3 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.dis-nn cond-mat.mes-hall 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?)