Protocols for Creating Anyons and Defects via Gauging
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909911716200448 |
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| author | Lyons, Anasuya Lo, Chiu Fan Bowen Tantivasadakarn, Nathanan Vishwanath, Ashvin Verresen, Ruben |
| author_facet | Lyons, Anasuya Lo, Chiu Fan Bowen Tantivasadakarn, Nathanan Vishwanath, Ashvin Verresen, Ruben |
| contents | Creating and manipulating anyons and symmetry defects in topological phases, especially those with a non-Abelian character, constitutes a primitive for topological quantum computation. We provide a physical protocol for implementing the ribbon operators of non-Abelian anyons and symmetry defects. We utilize dualities, in particular the Kramers-Wannier or gauging map, which have previously been used to construct topologically ordered ground states by relating them to simpler states. In this work, ribbon operators are implemented by applying a gauging procedure to a lower-dimensional region of such states. This protocol uses sequential unitary circuits or, in certain cases, constant-depth adaptive circuits. We showcase this for anyons and defects in the $\mathbb{Z}_3$ toric code and $S_3$ quantum double. The general applicability of our method is demonstrated by deriving unitary expressions for ribbon operators of various (twisted) quantum doubles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04181 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Protocols for Creating Anyons and Defects via Gauging Lyons, Anasuya Lo, Chiu Fan Bowen Tantivasadakarn, Nathanan Vishwanath, Ashvin Verresen, Ruben Quantum Physics Strongly Correlated Electrons Creating and manipulating anyons and symmetry defects in topological phases, especially those with a non-Abelian character, constitutes a primitive for topological quantum computation. We provide a physical protocol for implementing the ribbon operators of non-Abelian anyons and symmetry defects. We utilize dualities, in particular the Kramers-Wannier or gauging map, which have previously been used to construct topologically ordered ground states by relating them to simpler states. In this work, ribbon operators are implemented by applying a gauging procedure to a lower-dimensional region of such states. This protocol uses sequential unitary circuits or, in certain cases, constant-depth adaptive circuits. We showcase this for anyons and defects in the $\mathbb{Z}_3$ toric code and $S_3$ quantum double. The general applicability of our method is demonstrated by deriving unitary expressions for ribbon operators of various (twisted) quantum doubles. |
| title | Protocols for Creating Anyons and Defects via Gauging |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2411.04181 |