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
| id |
UNACIONAL2_8beb17940fb6b97fe95cc2c14ba2f62e |
|---|---|
| oai_identifier_str |
oai:repositorio.unal.edu.co:unal/66448 |
| network_acronym_str |
UNACIONAL2 |
| network_name_str |
Universidad Nacional de Colombia |
| repository_id_str |
|
| spelling |
Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Delaney, Colleen14525316-18b6-4c9d-b136-d68d493102dc300Rowell, Eric C.e6cb91f8-ece5-4891-947f-90b9bd2d93e4300Wang, Zhenghan28defabc-c2f0-46b1-ba7c-9e7cdefeb63b3002019-07-03T02:08:50Z2019-07-03T02:08:50Z2016-07-01ISSN: 2357-4100https://repositorio.unal.edu.co/handle/unal/66448http://bdigital.unal.edu.co/67476/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.application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas - Sociedad Colombiana de Matemáticashttps://revistas.unal.edu.co/index.php/recolma/article/view/62211Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasDelaney, Colleen and Rowell, Eric C. and Wang, Zhenghan (2016) Local unitary representations of the braid group and their applications to quantum computing. Revista Colombiana de Matemáticas, 50 (2). pp. 211-276. ISSN 2357-410051 Matemáticas / Mathematicstopological quantum computationbraid group representationslocalizationsquantum algebraLocal unitary representations of the braid group and their applications to quantum computingArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL62211-316280-1-SM.pdfapplication/pdf682964https://repositorio.unal.edu.co/bitstream/unal/66448/1/62211-316280-1-SM.pdf039efd879965a318694b02dbb0a024b0MD51THUMBNAIL62211-316280-1-SM.pdf.jpg62211-316280-1-SM.pdf.jpgGenerated Thumbnailimage/jpeg4955https://repositorio.unal.edu.co/bitstream/unal/66448/2/62211-316280-1-SM.pdf.jpg96daa1a4ee607f76d544c258bee79012MD52unal/66448oai:repositorio.unal.edu.co:unal/664482023-05-25 23:02:44.95Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co |
| dc.title.spa.fl_str_mv |
Local unitary representations of the braid group and their applications to quantum computing |
| title |
Local unitary representations of the braid group and their applications to quantum computing |
| spellingShingle |
Local unitary representations of the braid group and their applications to quantum computing 51 Matemáticas / Mathematics topological quantum computation braid group representations localizations quantum algebra |
| title_short |
Local unitary representations of the braid group and their applications to quantum computing |
| title_full |
Local unitary representations of the braid group and their applications to quantum computing |
| title_fullStr |
Local unitary representations of the braid group and their applications to quantum computing |
| title_full_unstemmed |
Local unitary representations of the braid group and their applications to quantum computing |
| title_sort |
Local unitary representations of the braid group and their applications to quantum computing |
| dc.creator.fl_str_mv |
Delaney, Colleen Rowell, Eric C. Wang, Zhenghan |
| dc.contributor.author.spa.fl_str_mv |
Delaney, Colleen Rowell, Eric C. Wang, Zhenghan |
| dc.subject.ddc.spa.fl_str_mv |
51 Matemáticas / Mathematics |
| topic |
51 Matemáticas / Mathematics topological quantum computation braid group representations localizations quantum algebra |
| dc.subject.proposal.spa.fl_str_mv |
topological quantum computation braid group representations localizations quantum algebra |
| description |
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. |
| publishDate |
2016 |
| dc.date.issued.spa.fl_str_mv |
2016-07-01 |
| dc.date.accessioned.spa.fl_str_mv |
2019-07-03T02:08:50Z |
| dc.date.available.spa.fl_str_mv |
2019-07-03T02:08:50Z |
| dc.type.spa.fl_str_mv |
Artículo de revista |
| dc.type.coar.fl_str_mv |
http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/article |
| dc.type.version.spa.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
| dc.type.coar.spa.fl_str_mv |
http://purl.org/coar/resource_type/c_6501 |
| dc.type.coarversion.spa.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
| dc.type.content.spa.fl_str_mv |
Text |
| dc.type.redcol.spa.fl_str_mv |
http://purl.org/redcol/resource_type/ART |
| format |
http://purl.org/coar/resource_type/c_6501 |
| status_str |
publishedVersion |
| dc.identifier.issn.spa.fl_str_mv |
ISSN: 2357-4100 |
| dc.identifier.uri.none.fl_str_mv |
https://repositorio.unal.edu.co/handle/unal/66448 |
| dc.identifier.eprints.spa.fl_str_mv |
http://bdigital.unal.edu.co/67476/ |
| identifier_str_mv |
ISSN: 2357-4100 |
| url |
https://repositorio.unal.edu.co/handle/unal/66448 http://bdigital.unal.edu.co/67476/ |
| dc.language.iso.spa.fl_str_mv |
spa |
| language |
spa |
| dc.relation.spa.fl_str_mv |
https://revistas.unal.edu.co/index.php/recolma/article/view/62211 |
| dc.relation.ispartof.spa.fl_str_mv |
Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas Revista Colombiana de Matemáticas |
| dc.relation.references.spa.fl_str_mv |
Delaney, Colleen and Rowell, Eric C. and Wang, Zhenghan (2016) Local unitary representations of the braid group and their applications to quantum computing. Revista Colombiana de Matemáticas, 50 (2). pp. 211-276. ISSN 2357-4100 |
| dc.rights.spa.fl_str_mv |
Derechos reservados - Universidad Nacional de Colombia |
| dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
| dc.rights.license.spa.fl_str_mv |
Atribución-NoComercial 4.0 Internacional |
| dc.rights.uri.spa.fl_str_mv |
http://creativecommons.org/licenses/by-nc/4.0/ |
| dc.rights.accessrights.spa.fl_str_mv |
info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
Atribución-NoComercial 4.0 Internacional Derechos reservados - Universidad Nacional de Colombia http://creativecommons.org/licenses/by-nc/4.0/ http://purl.org/coar/access_right/c_abf2 |
| eu_rights_str_mv |
openAccess |
| dc.format.mimetype.spa.fl_str_mv |
application/pdf |
| dc.publisher.spa.fl_str_mv |
Universidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas - Sociedad Colombiana de Matemáticas |
| institution |
Universidad Nacional de Colombia |
| bitstream.url.fl_str_mv |
https://repositorio.unal.edu.co/bitstream/unal/66448/1/62211-316280-1-SM.pdf https://repositorio.unal.edu.co/bitstream/unal/66448/2/62211-316280-1-SM.pdf.jpg |
| bitstream.checksum.fl_str_mv |
039efd879965a318694b02dbb0a024b0 96daa1a4ee607f76d544c258bee79012 |
| bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 |
| repository.name.fl_str_mv |
Repositorio Institucional Universidad Nacional de Colombia |
| repository.mail.fl_str_mv |
repositorio_nal@unal.edu.co |
| _version_ |
1814090003815333888 |