Closed form logical error rate approximations for surface codes
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Quantum Physics arXiv:2605.03054 (quant-ph) [Submitted on 4 May 2026] Title:Closed form logical error rate approximations for surface codes Authors:Shaked Regev, Daniel Dilley, Andrea Delgado, Ryan Bennink View a PDF of the paper titled Closed form logical error rate approximations for surface codes, by Shaked Regev and 3 other authors View PDF HTML (experimental) Abstract:We propose a novel method to calculate logical error rates in surface codes, assuming independent and identically distributed physical errors. We show how to use our method to analyze hypothetical quantum computers with various configurations and select designs with lower error rates. Currently, this requires expensive classical simulations of quantum decoders for various distances and physical error rates or inaccurate extrapolation from minimal experimental data. Instead, we use the symmetry of the problem to count the configurations that result in a logical error with our novel software. Given a physical error rate, we can deduce the probability of a logical error, to provably good accuracy. We include an analysis of measurement errors to allow a more complete comparison of different surface code implementations. Comments: Subjects: Quantum Physics (quant-ph); Discrete Mathematics (cs.DM); Combinatorics (math.CO) MSC classes: 05A04 ACM classes: F.2.2; G.2.2 Cite as: arXiv:2605.03054 [quant-ph] (or arXiv:2605.03054v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.03054 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Shaked Regev [view email] [v1] Mon, 4 May 2026 18:18:18 UTC (934 KB) Full-text links: Access Paper: View a PDF of the paper titled Closed form logical error rate approximations for surface codes, by Shaked Regev and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: cs cs.DM math math.CO 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?)