Braid group representations from braiding gapped boundaries of Dijkgraaf-Witten theories
In Topological Quantum Computation, quantum gates are implemented by representations of the braid group, B_n, on spaces of morphisms in a modular category C. For a given group G and a 3-cocycle \omega, images of that representation on C = Z(Vec^\omega_G) are finite, but is not known in general what...
- Autores:
-
Escobar Velásquez, Nicolás
- Tipo de recurso:
- Fecha de publicación:
- 2017
- Institución:
- Universidad de los Andes
- Repositorio:
- Séneca: repositorio Uniandes
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniandes.edu.co:1992/34167
- Acceso en línea:
- http://hdl.handle.net/1992/34167
- Palabra clave:
- Física matemática - Investigaciones
Funciones de Lagrange - Investigaciones
Grupos topológicos - Investigaciones
Teoría cuántica - Procesamiento de datos - Investigaciones
Matemáticas
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-sa/4.0/
| Summary: | In Topological Quantum Computation, quantum gates are implemented by representations of the braid group, B_n, on spaces of morphisms in a modular category C. For a given group G and a 3-cocycle \omega, images of that representation on C = Z(Vec^\omega_G) are finite, but is not known in general what specific gates can be obtained. A family of algebras in Z(G, \omega) called Lagrangian Algebras are of particular physical interest. They are denoted L[H, \gamma], where H is a subgroup and \gamma is a 2-cocycle on H. We show that the spaces Hom_{Z(G,\omega)}(1, L[H, \gamma]^n) have a canonical structure of monomial spaces and that with respect to this structure, the representation of B_n is monomial. We calculate the nonzero entries of these matrices and use this information to show how they can be used to implement a CNOT gate. |
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