A gauge-invariant theory of small Markovian errors in quantum gate sets

Quantum Physics arXiv:2608.14891 (quant-ph) [Submitted on 14 Aug 2026] Title:A gauge-invariant theory of small Markovian errors in quantum gate sets Authors:Juan Gonzalez De Mendoza, Corey Ostrove, Timothy Proctor, Kevin Young, Erik Nielsen, Robin Blume-Kohout View a PDF of the paper titled A gauge-invariant theory of small Markovian errors in quantum gate sets, by Juan Gonzalez De Mendoza and 5 other authors View PDF HTML (experimental) Abstract:Noisy logic operations on a quantum computational register -- e.g., one or more qubits -- can be described by transfer matrices (a.k.a. CPTP maps or superoperators) that act linearly on the density matrix representing the register's quantum state. Collectively, these operations form a gate set. Gate sets have a gauge freedom; many gate sets that appear different actually predict the same experimental outcomes. A property of a gate set can be observable (and thus physically relevant) only if it is gauge-invariant. Unfortunately, no good gauge-invariant parameterizations of gate sets are known. We introduce the next best thing, a perturbative gauge-invariant parameterization of small Markovian errors in gate sets. We construct vector spaces of properties that are first-order gauge-invariant (FOGI). We show how to construct and understand FOGI properties, how to use them as coordinates to parameterize gate sets without gauge freedom, and how to extract approximately gauge-invariant error metrics. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2608.14891 [quant-ph] (or arXiv:2608.14891v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.14891 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Juan Gonzalez De Mendoza [view email] [v1] Fri, 14 Aug 2026 21:00:06 UTC (1,002 KB) Full-text links: Access Paper: View a PDF of the paper titled A gauge-invariant theory of small Markovian errors in quantum gate sets, by Juan Gonzalez De Mendoza and 5 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 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?)