A Lie-algebraic Criterion for the Universality of Exponentiated Quantum Gates
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Quantum Physics arXiv:2604.25971 (quant-ph) [Submitted on 28 Apr 2026] Title:A Lie-algebraic Criterion for the Universality of Exponentiated Quantum Gates Authors:Yinuo Xue, Qian Chen, Jing-Song Huang View a PDF of the paper titled A Lie-algebraic Criterion for the Universality of Exponentiated Quantum Gates, by Yinuo Xue and 2 other authors View PDF HTML (experimental) Abstract:We present a criterion that serves as the basis for a polynomial-time algorithm to decide whether a finite set of qudit gates exponentiated by some Hamiltonians is universal. Our approach formulates universality in Lie algebraic terms and applies Borel--de Siebenthal theory with a diagonal generator having incommensurate spectrum. In this framework, nonuniversality is detected by invariant subspaces, equivalently by a graph-connectivity obstruction, while universality is repaired by adding generators that couple disconnected components. We further prove that two generators are sufficient for universal control. Our work reveals a profound link between qudit universality and irreducibility of Lie algebra representations. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.25971 [quant-ph] (or arXiv:2604.25971v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.25971 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Yinuo Xue [view email] [v1] Tue, 28 Apr 2026 07:36:28 UTC (20 KB) Full-text links: Access Paper: View a PDF of the paper titled A Lie-algebraic Criterion for the Universality of Exponentiated Quantum Gates, by Yinuo Xue and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?)