Reconstructing non-Abelian braiding and fusion without anyon transport

Quantum Physics arXiv:2608.04103 (quant-ph) [Submitted on 4 Aug 2026] Title:Reconstructing non-Abelian braiding and fusion without anyon transport Authors:Lucy Byles, Matthew D. Horner, Benjamin T. H. Varcoe, Jiannis K. Pachos View a PDF of the paper titled Reconstructing non-Abelian braiding and fusion without anyon transport, by Lucy Byles and 2 other authors View PDF HTML (experimental) Abstract:Non-Abelian anyons offer a route to fault-tolerant and universal quantum computing, but experimental access to their defining braiding and fusion data remains limited by the resource overhead of implementing extended anyonic processes on quantum hardware. Here we introduce and experimentally realise a measurement-only protocol based on temporally ordered ribbon operations that reconstructs the non-Abelian braiding and fusion primitives of the quantum double model $D(S_3)$ without physical anyon transport. We implement a reduced two-qutrit version of the protocol on Quantinuum's H2 trapped-ion processors, realising ancilla-assisted ribbon operations and anyonic charge projections in a qubit encoding. We reconstruct the squared braiding phases and fusion amplitudes using an adapted Hadamard test and post-selected measurements, respectively. The associated braiding and fusion transformations reproduce their ideal actions with average normalised output-state fidelities of $\overline{\mathcal{F}}_{R}=0.9988$ and $\overline{\mathcal{F}}_{F}=0.9987$. Combining these primitives produces a non-Clifford braid and a non-stabilizer resource state, supporting measurement-only anyonic encodings as building blocks for larger topologically encoded quantum processors. Comments: Subjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th) Cite as: arXiv:2608.04103 [quant-ph] (or arXiv:2608.04103v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.04103 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jiannis Pachos [view email] [v1] Tue, 4 Aug 2026 18:01:02 UTC (632 KB) Full-text links: Access Paper: View a PDF of the paper titled Reconstructing non-Abelian braiding and fusion without anyon transport, by Lucy Byles and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 Change to browse by: cond-mat cond-mat.str-el hep-th 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?)