Correcting quantum errors one gradient step at a time

Quantum Physics arXiv:2512.18061 (quant-ph) [Submitted on 19 Dec 2025] Title:Correcting quantum errors one gradient step at a time Authors:Manav Seksaria, Anil Prabhakar View a PDF of the paper titled Correcting quantum errors one gradient step at a time, by Manav Seksaria and 1 other authors View PDF HTML (experimental) Abstract:In this work, we introduce a general, gradient-based method that optimises codewords for a given noise channel and fixed recovery. We do so by differentiating fidelity and descending on the complex coefficients using finite-difference Wirtinger gradients with soft penalties to promote orthonormalisation. We validate the gradients on symmetry checks (XXX/ZZZ repetition codes) and the $[[5, 1, 3]]$ code, then demonstrate substantial gains under isotropic Pauli noise with Petz recovery: fidelity improves from 0.783 to 0.915 in 100 steps for an isotropic Pauli noise of strength 0.05. The procedure is deterministic, highly parallelisable, and highly scalable. Subjects: Quantum Physics (quant-ph); Numerical Analysis (math.NA) Cite as: arXiv:2512.18061 [quant-ph] (or arXiv:2512.18061v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.18061 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Manav Seksaria [view email] [v1] Fri, 19 Dec 2025 21:00:12 UTC (561 KB) Full-text links: Access Paper: View a PDF of the paper titled Correcting quantum errors one gradient step at a time, by Manav Seksaria and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: cs cs.NA math math.NA 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)