The geometry of quantum codes

Quantum particles are continuously interacting with the environment hence quantum information is always susceptible to errors. Consequently when encoding information into quantum bits a special treatment is required such that there is a recovery map between the information sent and the information r...

Descripción completa

Detalles Bibliográficos
Autor: Puig Pericas, Pablo
Tipo de recurso: tesis de maestría
Fecha de publicación:2021
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/349594
Acceso en línea:https://hdl.handle.net/2117/349594
Access Level:acceso abierto
Palabra clave:Error-correcting codes (Information theory)
Error Correcting Quantum Codes
Qubits
Stabilizer Codes
Non Additive Quantum Codes
Pauli Group
Projective Space
Codis de correcció d'errors (Teoria de la informació)
Classificació AMS::94 Information And Communication, Circuits::94B Theory of error-correcting codes and error-detecting codes
Àrees temàtiques de la UPC::Matemàtiques i estadística
id ES_097ba206ffc595c3fffc2204741a4df1
oai_identifier_str oai:upcommons.upc.edu:2117/349594
network_acronym_str ES
network_name_str España
repository_id_str
spelling The geometry of quantum codesPuig Pericas, PabloError-correcting codes (Information theory)Error Correcting Quantum CodesQubitsStabilizer CodesNon Additive Quantum CodesPauli GroupProjective SpaceCodis de correcció d'errors (Teoria de la informació)Classificació AMS::94 Information And Communication, Circuits::94B Theory of error-correcting codes and error-detecting codesÀrees temàtiques de la UPC::Matemàtiques i estadísticaQuantum particles are continuously interacting with the environment hence quantum information is always susceptible to errors. Consequently when encoding information into quantum bits a special treatment is required such that there is a recovery map between the information sent and the information received capable to correct certain class of errors. We allow the quantum bits to take two orthogonal values (qubits) and we encode k logical qubits on n physical qubits. We first present the already well known class of quantum codes called stabiliser codes and its geometry from which one can deduce the code parameters. Finally we shall study the much less known class of quantum codes called non additive codes, result of direct sums of stabilizer codes, and for which we provide a geometric framework which appears to be new.Universitat Politècnica de CatalunyaBall, Simeon Michael20212021-07-0120212021-07-19master thesishttp://purl.org/coar/resource_type/c_bdccNAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/masterThesisapplication/pdfhttps://hdl.handle.net/2117/349594reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3495942026-05-27T15:37:01Z
dc.title.none.fl_str_mv The geometry of quantum codes
title The geometry of quantum codes
spellingShingle The geometry of quantum codes
Puig Pericas, Pablo
Error-correcting codes (Information theory)
Error Correcting Quantum Codes
Qubits
Stabilizer Codes
Non Additive Quantum Codes
Pauli Group
Projective Space
Codis de correcció d'errors (Teoria de la informació)
Classificació AMS::94 Information And Communication, Circuits::94B Theory of error-correcting codes and error-detecting codes
Àrees temàtiques de la UPC::Matemàtiques i estadística
title_short The geometry of quantum codes
title_full The geometry of quantum codes
title_fullStr The geometry of quantum codes
title_full_unstemmed The geometry of quantum codes
title_sort The geometry of quantum codes
dc.creator.none.fl_str_mv Puig Pericas, Pablo
author Puig Pericas, Pablo
author_facet Puig Pericas, Pablo
author_role author
dc.contributor.none.fl_str_mv Ball, Simeon Michael
dc.subject.none.fl_str_mv Error-correcting codes (Information theory)
Error Correcting Quantum Codes
Qubits
Stabilizer Codes
Non Additive Quantum Codes
Pauli Group
Projective Space
Codis de correcció d'errors (Teoria de la informació)
Classificació AMS::94 Information And Communication, Circuits::94B Theory of error-correcting codes and error-detecting codes
Àrees temàtiques de la UPC::Matemàtiques i estadística
topic Error-correcting codes (Information theory)
Error Correcting Quantum Codes
Qubits
Stabilizer Codes
Non Additive Quantum Codes
Pauli Group
Projective Space
Codis de correcció d'errors (Teoria de la informació)
Classificació AMS::94 Information And Communication, Circuits::94B Theory of error-correcting codes and error-detecting codes
Àrees temàtiques de la UPC::Matemàtiques i estadística
description Quantum particles are continuously interacting with the environment hence quantum information is always susceptible to errors. Consequently when encoding information into quantum bits a special treatment is required such that there is a recovery map between the information sent and the information received capable to correct certain class of errors. We allow the quantum bits to take two orthogonal values (qubits) and we encode k logical qubits on n physical qubits. We first present the already well known class of quantum codes called stabiliser codes and its geometry from which one can deduce the code parameters. Finally we shall study the much less known class of quantum codes called non additive codes, result of direct sums of stabilizer codes, and for which we provide a geometric framework which appears to be new.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-07-01
2021
2021-07-19
dc.type.none.fl_str_mv master thesis
http://purl.org/coar/resource_type/c_bdcc
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/349594
url https://hdl.handle.net/2117/349594
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universitat Politècnica de Catalunya
publisher.none.fl_str_mv Universitat Politècnica de Catalunya
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869403108386275328
score 15,198674

Similares en LA Referencia