Efficient quantum circuits for high-dimensional representations of SU(n) and Ramanujan quantum expanders
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Quantum Physics arXiv:2602.15180 (quant-ph) [Submitted on 16 Feb 2026] Title:Efficient quantum circuits for high-dimensional representations of SU(n) and Ramanujan quantum expanders Authors:Vishnu Iyer, Siddhartha Jain, Stephen Jordan, Rolando Somma View a PDF of the paper titled Efficient quantum circuits for high-dimensional representations of SU(n) and Ramanujan quantum expanders, by Vishnu Iyer and 3 other authors View PDF HTML (experimental) Abstract:We present efficient quantum circuits that implement high-dimensional unitary irreducible representations (irreps) of $SU(n)$, where $n \ge 2$ is constant. For dimension $N$ and error $\epsilon$, the number of quantum gates in our circuits is polynomial in $\log(N)$ and $\log(1/\epsilon)$. Our construction relies on the Jordan-Schwinger representation, which allows us to realize irreps of $SU(n)$ in the Hilbert space of $n$ quantum harmonic oscillators. Together with a recent efficient quantum Hermite transform, which allows us to map the computational basis states to the eigenstates of the quantum harmonic oscillator, this allows us to implement these irreps efficiently. Our quantum circuits can be used to construct explicit Ramanujan quantum expanders, a longstanding open problem. They can also be used to fast-forward the evolution of certain quantum systems. Comments: Subjects: Quantum Physics (quant-ph); Computational Complexity (cs.CC) Cite as: arXiv:2602.15180 [quant-ph] (or arXiv:2602.15180v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.15180 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Vishnu Iyer [view email] [v1] Mon, 16 Feb 2026 20:38:26 UTC (974 KB) Full-text links: Access Paper: View a PDF of the paper titled Efficient quantum circuits for high-dimensional representations of SU(n) and Ramanujan quantum expanders, by Vishnu Iyer and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: cs cs.CC 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?)