Universal Topological Gates from Braiding and Fusing Anyons on Quantum Hardware

• URL: http://arxiv.org/abs/2601.20956v1
• Date: Wed, 28 Jan 2026 19:00:09 GMT
• Title: Universal Topological Gates from Braiding and Fusing Anyons on Quantum Hardware
• Authors: Chiu Fan Bowen Lo, Anasuya Lyons, Dan Gresh, Michael Mills, Peter E. Siegfried, Maxwell D. Urmey, Nathanan Tantivasadakarn, Henrik Dreyer, Ashvin Vishwanath, Ruben Verresen, Mohsin Iqbal,
• Abstract summary: Topological quantum computation encodes quantum information in the internal fusion space of non-Abelian quasiparticles.<n>We show that such minimally non-Abelian TOs can be made universal by treating anyon fusion as a computational primitive.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Topological quantum computation encodes quantum information in the internal fusion space of non-Abelian anyonic quasiparticles, whose braiding implements logical gates. This goes beyond Abelian topological order (TO) such as the toric code, as its anyons lack internal structure. However, the simplest non-Abelian generalizations of the toric code do not support universality via braiding alone. Here we demonstrate that such minimally non-Abelian TOs can be made universal by treating anyon fusion as a computational primitive. We prepare a 54-qubit TO wavefunction associated with the smallest non-Abelian group, $S_3$, on Quantinuum's H2 quantum processor. This phase of matter exhibits cyclic anyon fusion rules, known to underpin universality, which we evidence by trapping a single non-Abelian anyon on the torus. We encode logical qutrits in the nonlocal fusion space of non-Abelian fluxes and, by combining an entangling braiding operation with anyon charge measurements, realize a universal topological gate set and read-out, which we further demonstrate by topologically preparing a magic state. This work establishes $S_3$ TO as simple enough to be prepared efficiently, yet rich enough to enable universal topological quantum computation.

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