Realizing a Universal Quantum Gate Set via Double-Braiding of SU(2)k Anyon Models
Summarize this article with:
Quantum Physics arXiv:2602.15324 (quant-ph) [Submitted on 17 Feb 2026] Title:Realizing a Universal Quantum Gate Set via Double-Braiding of SU(2)k Anyon Models Authors:Jiangwei Long, Zihui Liu, Yizhi Li, Jianxin Zhong, Lijun Meng View a PDF of the paper titled Realizing a Universal Quantum Gate Set via Double-Braiding of SU(2)k Anyon Models, by Jiangwei Long and 3 other authors View PDF Abstract:We systematically investigate the implementation of a universal gate set via double-braiding within SU(2)k anyon models. The explicit form of the double elementary braiding matrices (DEBMs) in these models are derived from the F-matrices and R-symbols obtained via the q-deformed representation theory of SU(2). Using these EBMs, standard single-qubit gates are synthesized up to a global phase by a Genetic Algorithm-enhanced Solovay-Kitaev Algorithm (GA-enhanced SKA), achieving the accuracy required for fault-tolerant quantum computation with only 2-level decomposition. For two-qubit entangling gates, Genetic Algorithm (GA) yields braidwords of 30 braiding operations that approximate the local equivalence class [CNOT]. Theoretically, we demonstrate that performing double-braiding in a three-anyon (six-anyon) encoding of single-qubit (two-qubit) is topologically equivalent to a protocol requiring the physical manipulation of only one (three) anyons to execute arbitrary braids. Our numerical results provide strong evidence that double-braiding in SU(2)k anyons models is capable of universal quantum computation. Moreover, the proposed protocol offers a potential new strategy for significantly reducing the number of non-Abelian anyons that need to be physically manipulated in future braiding-based topological quantum computations (TQC). Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2602.15324 [quant-ph] (or arXiv:2602.15324v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.15324 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jiangwei Long [view email] [v1] Tue, 17 Feb 2026 03:11:09 UTC (1,080 KB) Full-text links: Access Paper: View a PDF of the paper titled Realizing a Universal Quantum Gate Set via Double-Braiding of SU(2)k Anyon Models, by Jiangwei Long and 3 other authorsView PDF view license Current browse context: quant-ph new | recent | 2026-02 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?)