Efficiently estimating failure rates of fault-tolerant logical non-Clifford blocks

Quantum Physics arXiv:2609.19485 (quant-ph) [Submitted on 16 Sep 2026] Title:Efficiently estimating failure rates of fault-tolerant logical non-Clifford blocks Authors:Julio C. Magdalena de la Fuente, Thomas R. Scruby View a PDF of the paper titled Efficiently estimating failure rates of fault-tolerant logical non-Clifford blocks, by Julio C. Magdalena de la Fuente and 1 other authors View PDF HTML (experimental) Abstract:Useful quantum computation requires the fault-tolerant implementations of a universal gate set which are generically not efficiently simulable. We devise an algebraic framework that allows for efficient sampling from the measurement distribution of fault-tolerant circuits that implement diagonal logic gates in the third level of the Clifford hierarchy. Upon successful sampling we also provide sufficient conditions for decoding success. The resulting estimate for the logical failure rate is an overestimate, which becomes more accurate for blocks that are fault tolerant against arbitrary local errors. The non-Clifford simulation overhead is independent of the number of logical qubits, making the method particularly attractive for large-scale simulations. The framework is based on viewing the non-Clifford gates in the circuit as a cohomology invariant of an underlying spacetime fault complex. The method can also be interfaced with Clifford simulators to simulate larger fault-tolerant circuits and algorithmic subroutines. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.19485 [quant-ph] (or arXiv:2609.19485v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.19485 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Julio Carlos Magdalena De La Fuente [view email] [v1] Wed, 16 Sep 2026 22:57:23 UTC (39 KB) Full-text links: Access Paper: View a PDF of the paper titled Efficiently estimating failure rates of fault-tolerant logical non-Clifford blocks, by Julio C. Magdalena de la Fuente and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 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?)