$d$-pod realization of nonadiabatic holonomic quantum computation

Quantum Physics arXiv:2609.16216 (quant-ph) [Submitted on 14 Sep 2026] Title:$d$-pod realization of nonadiabatic holonomic quantum computation Authors:Oskar Axelsson, Claes Fälth, Elias Henriksson Lindberg, Erik Sjöqvist View a PDF of the paper titled $d$-pod realization of nonadiabatic holonomic quantum computation, by Oskar Axelsson and 3 other authors View PDF HTML (experimental) Abstract:Holonomic quantum computation (HQC) realizes quantum gates through non-Abelian geometric phases, providing an experimentally accessible approach to quantum control. While the nonadiabatic HQC framework has been extensively developed for three-level $\Lambda$ systems encoding qubits, its systematic extension to higher-dimensional qudits remains largely unexplored. In this work, we generalize nonadiabatic HQC to a $d$-pod configuration, where a single excited state is coupled to $d$ ground states, the latter forming the computational subspace. This scheme enables universal holonomic single- and two-qudit gates using only optical or microwave pulses on trapped atoms or ions, offering an efficient route to implement a discrete universal gate set with minimal pulse coordination. As an explicit example, we analyze in detail the qutrit ($d=3$) case, demonstrating compact realizations of single- and two-qutrit holonomic gates, each gate requiring at most two loops in the Grassmannian generated by at most three pulses. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.16216 [quant-ph] (or arXiv:2609.16216v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.16216 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Erik Sjoqvist [view email] [v1] Mon, 14 Sep 2026 18:49:10 UTC (106 KB) Full-text links: Access Paper: View a PDF of the paper titled $d$-pod realization of nonadiabatic holonomic quantum computation, by Oskar Axelsson and 3 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?)