Qutrit Clifford+T gates by two-body angular momentum couplings, rotations and one-axis-twistings
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Quantum Physics arXiv:2604.23007 (quant-ph) [Submitted on 24 Apr 2026] Title:Qutrit Clifford+T gates by two-body angular momentum couplings, rotations and one-axis-twistings Authors:F. E. S. Steinhoff View a PDF of the paper titled Qutrit Clifford+T gates by two-body angular momentum couplings, rotations and one-axis-twistings, by F. E. S. Steinhoff View PDF HTML (experimental) Abstract:We develop an angular momentum representation and implementation of the Clifford+T set of unitaries for qutrits. We show that local gates from this set can be realized by the sole use of suitable rotations and one-axis-twisting operations, which are at most quadratic in the angular momentum operators and thus can be experimentally realized in many quantum systems. Controlled rotations are shown to only require linear angular momentum couplings and, as a consequence, the full qutrit Clifford+T set is shown to be expressed solely in terms of two-body angular momentum couplings, rotations and one-axis-twisting operations. By employing the Jordan-Schwinger map, we show an analogous implementation in terms of bosonic modes, improving on the number of modes with regard to a previous scheme. Moreover, we employ the cross-Kerr interaction in order to obtain any qutrit Clifford+T gate for bosonic modes. We illustrate our findings with simple schemes for preparing entangled states of interest. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Atomic Physics (physics.atom-ph); Optics (physics.optics) Cite as: arXiv:2604.23007 [quant-ph] (or arXiv:2604.23007v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.23007 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Frank Steinhoff [view email] [v1] Fri, 24 Apr 2026 20:54:19 UTC (51 KB) Full-text links: Access Paper: View a PDF of the paper titled Qutrit Clifford+T gates by two-body angular momentum couplings, rotations and one-axis-twistings, by F. E. S. SteinhoffView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: cond-mat cond-mat.stat-mech physics physics.atom-ph physics.optics 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?)