Local unitary representations of the braid group and their applications to quantum computing
We provide an elementary introduction to topological quantum computation based on the Jones representation of the braid group. We first cover the Burau representation and Alexander polynomial. Then we discuss the Jones representation and Jones polynomial and their application to anyonic quantum comp...
- Autores:
-
Delaney, Colleen
Rowell, Eric C.
Wang, Zhenghan
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2016
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/66448
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/66448
http://bdigital.unal.edu.co/67476/
- Palabra clave:
- 51 Matemáticas / Mathematics
topological quantum computation
braid group representations
localizations
quantum algebra
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | We provide an elementary introduction to topological quantum computation based on the Jones representation of the braid group. We first cover the Burau representation and Alexander polynomial. Then we discuss the Jones representation and Jones polynomial and their application to anyonic quantum computation. Finally we outline the approximation of the Jones polynomial by a quantum computer and explicit localizations of braid group representations. |
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