End-to-End Formalization of Quantum Error Correction
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Quantum Physics arXiv:2605.16523 (quant-ph) [Submitted on 15 May 2026] Title:End-to-End Formalization of Quantum Error Correction Authors:Mattias Ehatamm, Yi Lee, Xiaodi Wu, Runzhou Tao View a PDF of the paper titled End-to-End Formalization of Quantum Error Correction, by Mattias Ehatamm and 3 other authors View PDF Abstract:Quantum error-correcting codes (QECCs) sit between noisy quantum hardware and reliable computation, so the code parameters used in practice must be trustworthy. The single number that summarizes a code's strength is its distance, yet certifying a distance lower bound is NP-hard in general, placing it beyond the reach of pen-and-paper proofs as well as direct proof-assistant scripting. As a result, distance values in the literature come either from non-scaling hand proofs, or from unverified solvers that leave a trust gap exactly where the code is supposed to provide a guarantee. We present Lean-QEC, the first Lean 4 formalization of stabilizer-code theory that delivers end-to-end, machine-checked distance certificates at industrial code sizes. Lean-QEC formalizes the linear algebra of qubit states, the Pauli group, stabilizer codes, the binary symplectic representation, classical coding theory, and the CSS and Bivariate Bicycle families. To break the combinatorial barrier, Lean-QEC translates the distance condition into a Boolean satisfiability formula through a verified reduction. The pipeline scales through a BitVec-flattened encoding that replaces Lean's Matrix representation, and an error-location encoding that reduces the variable count from $n$ to $k\lceil \log_2 n\rceil$. With these, we obtain automatically-generated Lean-checked distance proofs for a large range of industrially viable qLDPC codes within the Bivariate Bicycle and Generalized Bicycle families, including [[90, 8, 10]] and [[70, 6, 9]] BB codes, with the formulation scaling up to 144 qubits when performed outside the Lean kernel. The resulting library is reusable and is designed to plug into broader Lean-based efforts toward end-to-end verification of fault-tolerant quantum computation. Subjects: Quantum Physics (quant-ph); Logic in Computer Science (cs.LO) Cite as: arXiv:2605.16523 [quant-ph] (or arXiv:2605.16523v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.16523 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Mattias Ehatamm [view email] [v1] Fri, 15 May 2026 18:17:55 UTC (111 KB) Full-text links: Access Paper: View a PDF of the paper titled End-to-End Formalization of Quantum Error Correction, by Mattias Ehatamm and 3 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: cs cs.LO 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?)