Universal Quantum Computation with the $S_3$ Quantum Double: A Pedagogical Exposition
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arXiv
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| Format: | Preprint |
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2025
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| author | Lo, Chiu Fan Bowen Lyons, Anasuya Verresen, Ruben Vishwanath, Ashvin Tantivasadakarn, Nathanan |
| author_facet | Lo, Chiu Fan Bowen Lyons, Anasuya Verresen, Ruben Vishwanath, Ashvin Tantivasadakarn, Nathanan |
| contents | Non-Abelian topological order (TO) enables topologically protected quantum computation with its anyonic quasiparticles. Recently, TO with $S_3$ gauge symmetry was identified as a sweet spot -- simple enough to emerge from finite-depth adaptive circuits yet powerful enough to support a universal topological gate-set. In these notes, we review how anyon braiding and measurement in $S_3$ TO are primitives for topological quantum computation and we explicitly demonstrate universality. These topological operations are made concrete in the $S_3$ quantum double lattice model, aided by the introduction of a generalized ribbon operator. This provides a roadmap for near-term quantum platforms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14974 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal Quantum Computation with the $S_3$ Quantum Double: A Pedagogical Exposition Lo, Chiu Fan Bowen Lyons, Anasuya Verresen, Ruben Vishwanath, Ashvin Tantivasadakarn, Nathanan Quantum Physics Strongly Correlated Electrons Non-Abelian topological order (TO) enables topologically protected quantum computation with its anyonic quasiparticles. Recently, TO with $S_3$ gauge symmetry was identified as a sweet spot -- simple enough to emerge from finite-depth adaptive circuits yet powerful enough to support a universal topological gate-set. In these notes, we review how anyon braiding and measurement in $S_3$ TO are primitives for topological quantum computation and we explicitly demonstrate universality. These topological operations are made concrete in the $S_3$ quantum double lattice model, aided by the introduction of a generalized ribbon operator. This provides a roadmap for near-term quantum platforms. |
| title | Universal Quantum Computation with the $S_3$ Quantum Double: A Pedagogical Exposition |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2502.14974 |