Diagnosing and Restoring the Degraded Fault Distance of Magic State Cultivation

Quantum Physics arXiv:2609.17706 (quant-ph) [Submitted on 15 Sep 2026] Title:Diagnosing and Restoring the Degraded Fault Distance of Magic State Cultivation Authors:Tim Chan, Armands Strikis, Zhu Sun, Zhenyu Cai View a PDF of the paper titled Diagnosing and Restoring the Degraded Fault Distance of Magic State Cultivation, by Tim Chan and 3 other authors View PDF Abstract:T-state cultivation is a resource-efficient protocol producing logical T states but recent benchmarks show that its logical error rate is considerably higher than intended i.e. than S-state cultivation, which is the analogous protocol for producing logical S states. In this paper, we explain this T-S discrepancy by analytically showing, under circuit-level depolarising noise, that distance-3 (-5) T-state cultivation has fault distance 2 (3) due to Pauli hook errors that propagate to coherent Clifford errors after its final double-check circuit; such errors remain Pauli in S-state cultivation, which consequently retains fault distance 3 (5). As part of our analysis we derive a general formula, and an $\mathcal O(n^3)$-time algorithm for fixed logical-qubit count, for the acceptance probability of a logical mixed state afflicted with a Clifford error, where $n$ is the physical qubit count. We then design flags that detect the malignant hook errors in cultivation, improving the pre-escape logical error rate from $\mathcal O(p^3)$ to $\mathcal O(p^5)$. At noise level $p =10^{-3}$, this is a 4.9$\times$ improvement, costing a 1.36$\times$ increase in attempts per accepted shot. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.17706 [quant-ph] (or arXiv:2609.17706v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.17706 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Tim Chan [view email] [v1] Tue, 15 Sep 2026 18:18:21 UTC (1,054 KB) Full-text links: Access Paper: View a PDF of the paper titled Diagnosing and Restoring the Degraded Fault Distance of Magic State Cultivation, by Tim Chan and 3 other authorsView PDFTeX 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?)