Semiclassical grounds of the Calderbank-Shor-Steane quantum error correction codes

A valid Calderbank-Shor-Steane (CSS) error correction code requires two classical linear codes for the preparation of the initial state (codewords). This code allow to correct for certain errors caused by an unwanted interaction which produces a degraded quantum state. However, this initial seven qu...

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Autor: Manuel Avila Aoki
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2009
País:México
Institución:Universidad Autónoma del Estado de México
Repositorio:Redalyc-UAEMEX
OAI Identifier:oai:redalyc.org:638067316001
Acceso en línea:https://www.redalyc.org/articulo.oa?id=638067316001
Access Level:acceso abierto
Palabra clave:Computación
encoding
syndrome
Quantum information
quantum computation
quantum error correction codes
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spelling Semiclassical grounds of the Calderbank-Shor-Steane quantum error correction codesManuel Avila AokiComputaciónencodingsyndromeQuantum informationquantum computationquantum error correction codesA valid Calderbank-Shor-Steane (CSS) error correction code requires two classical linear codes for the preparation of the initial state (codewords). This code allow to correct for certain errors caused by an unwanted interaction which produces a degraded quantum state. However, this initial seven qubits encoding can be obtained from a maximally entangled Bell state | |/√ through an operation Hint whose explicit expression is derived in the present work. The price the CSS syndrome has to pay due to its classical grounds is that the operator Hint is not unitary. In other words, Hint is not a valid quantum gate i. e. this does not represent a logical operation. Consequently, the final state is not completely robust for the standard cryptography of Quantum Computation. Besides to be a non unitary operator, Hint, is not reversible introducing with this dissipative effects that destroy the coherence in the quantum computer. Additionally, this operator is not invariant under rotations of the protector qubits inducing then preferred directions of the propagation of the logical information. These are indeed the reasons that prompt us for extending the semi classical CSS quantum error correction codes formalism to a pure quantum Hamming codes.Universidad Nacional de La Plata2009info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdf1666-6046https://www.redalyc.org/articulo.oa?id=638067316001Journal of Computer Science and Technology (Argentina) Num.02 Vol.9reponame:Redalyc-UAEMEXinstname:Universidad Autónoma del Estado de Méxicoinstacron:UAEMEXenhttp://www.redalyc.org/revista.oa?id=6380Journal of Computer Science and Technologyinfo:eu-repo/semantics/openAccessoai:redalyc.org:6380673160012025-09-09T00:37:23Z
dc.title.none.fl_str_mv Semiclassical grounds of the Calderbank-Shor-Steane quantum error correction codes
title Semiclassical grounds of the Calderbank-Shor-Steane quantum error correction codes
spellingShingle Semiclassical grounds of the Calderbank-Shor-Steane quantum error correction codes
Manuel Avila Aoki
Computación
encoding
syndrome
Quantum information
quantum computation
quantum error correction codes
title_short Semiclassical grounds of the Calderbank-Shor-Steane quantum error correction codes
title_full Semiclassical grounds of the Calderbank-Shor-Steane quantum error correction codes
title_fullStr Semiclassical grounds of the Calderbank-Shor-Steane quantum error correction codes
title_full_unstemmed Semiclassical grounds of the Calderbank-Shor-Steane quantum error correction codes
title_sort Semiclassical grounds of the Calderbank-Shor-Steane quantum error correction codes
dc.creator.none.fl_str_mv Manuel Avila Aoki
author Manuel Avila Aoki
author_facet Manuel Avila Aoki
author_role author
dc.subject.none.fl_str_mv Computación
encoding
syndrome
Quantum information
quantum computation
quantum error correction codes
topic Computación
encoding
syndrome
Quantum information
quantum computation
quantum error correction codes
description A valid Calderbank-Shor-Steane (CSS) error correction code requires two classical linear codes for the preparation of the initial state (codewords). This code allow to correct for certain errors caused by an unwanted interaction which produces a degraded quantum state. However, this initial seven qubits encoding can be obtained from a maximally entangled Bell state | |/√ through an operation Hint whose explicit expression is derived in the present work. The price the CSS syndrome has to pay due to its classical grounds is that the operator Hint is not unitary. In other words, Hint is not a valid quantum gate i. e. this does not represent a logical operation. Consequently, the final state is not completely robust for the standard cryptography of Quantum Computation. Besides to be a non unitary operator, Hint, is not reversible introducing with this dissipative effects that destroy the coherence in the quantum computer. Additionally, this operator is not invariant under rotations of the protector qubits inducing then preferred directions of the propagation of the logical information. These are indeed the reasons that prompt us for extending the semi classical CSS quantum error correction codes formalism to a pure quantum Hamming codes.
publishDate 2009
dc.date.none.fl_str_mv 2009
dc.type.none.fl_str_mv info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.none.fl_str_mv 1666-6046
https://www.redalyc.org/articulo.oa?id=638067316001
identifier_str_mv 1666-6046
url https://www.redalyc.org/articulo.oa?id=638067316001
dc.language.none.fl_str_mv en
language_invalid_str_mv en
dc.relation.none.fl_str_mv http://www.redalyc.org/revista.oa?id=6380
dc.rights.none.fl_str_mv Journal of Computer Science and Technology
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Journal of Computer Science and Technology
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidad Nacional de La Plata
publisher.none.fl_str_mv Universidad Nacional de La Plata
dc.source.none.fl_str_mv Journal of Computer Science and Technology (Argentina) Num.02 Vol.9
reponame:Redalyc-UAEMEX
instname:Universidad Autónoma del Estado de México
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instname_str Universidad Autónoma del Estado de México
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