Universal Gates from Braiding and Fusing Anyons on Quantum Hardware
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| Main Authors: | , , , , , , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866916056453349376 |
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| author | Lo, Chiu Fan Bowen Lyons, Anasuya Gresh, Dan Mills, Michael Siegfried, Peter E. Urmey, Maxwell D. Tantivasadakarn, Nathanan Dreyer, Henrik Vishwanath, Ashvin Verresen, Ruben Iqbal, Mohsin |
| author_facet | Lo, Chiu Fan Bowen Lyons, Anasuya Gresh, Dan Mills, Michael Siegfried, Peter E. Urmey, Maxwell D. Tantivasadakarn, Nathanan Dreyer, Henrik Vishwanath, Ashvin Verresen, Ruben Iqbal, Mohsin |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_20956 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Universal Gates from Braiding and Fusing Anyons on Quantum Hardware Lo, Chiu Fan Bowen Lyons, Anasuya Gresh, Dan Mills, Michael Siegfried, Peter E. Urmey, Maxwell D. Tantivasadakarn, Nathanan Dreyer, Henrik Vishwanath, Ashvin Verresen, Ruben Iqbal, Mohsin Quantum Physics Strongly Correlated Electrons 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. |
| title | Universal Gates from Braiding and Fusing Anyons on Quantum Hardware |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2601.20956 |