Reconstructing non-Abelian braiding and fusion without anyon transport

2026/08/04 by Lucy Byles, Matthew D. Horner, Benjamin T. H. Varcoe +1
Physics and Astronomy · #quant-ph #cond-mat.str-el #hep-th

paper · pdf

13+10 pages, 4+4 figures

arxiv created 2026/08/04 · arxiv updated 2026/08/06

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(S₃) 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 F_R=0.9988 and 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.

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