One-way-ness in the input-saving (Turing) machine.
Autor(a) principal: | |
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Data de Publicação: | 2014 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da EMBRAPA (Repository Open Access to Scientific Information from EMBRAPA - Alice) |
Texto Completo: | http://www.alice.cnptia.embrapa.br/alice/handle/doc/994523 |
Resumo: | Currently, a complexity-class problem is proving the existence of one-way permutations: one-to-one and onto maps that are computationally ?easy?, while their inverses are computationally ?hard?. In what follows, we make use of Bennett?s algorithm of the reversible Turing machine (quantum information heat engine) to perform a cascade of two controlled-NOT gates to physically create a permutation operation. We show that by running this input-saving (Turing) machine backwards the critical inequality of Landauer?s thermodynamic limit is reversed, which provokes the symmetry-breaking of the quantum circuit based on two successive controlled-NOT quantum gates. This finding reveals that a permutation of controlled-NOT gates becomes one-way, provided that adiabatically immersed in a heat bath, which determines the condition of existence of a thermodynamically non-invertible bijection in polynomial-time, that would otherwise be mathematically invertible. This one-way bijection can also be particularly important because it shows nonlinearities in quantum mechanics, which are detectable by watching that the mathematical reversibility of controlled-NOT gates does not work physically. |
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One-way-ness in the input-saving (Turing) machine.Complexidade computacionalPrincípio de LandauerMáquina de TuringPermutação one wayComputational complexityLandauer's principleTuring machineOne-way permutationCurrently, a complexity-class problem is proving the existence of one-way permutations: one-to-one and onto maps that are computationally ?easy?, while their inverses are computationally ?hard?. In what follows, we make use of Bennett?s algorithm of the reversible Turing machine (quantum information heat engine) to perform a cascade of two controlled-NOT gates to physically create a permutation operation. We show that by running this input-saving (Turing) machine backwards the critical inequality of Landauer?s thermodynamic limit is reversed, which provokes the symmetry-breaking of the quantum circuit based on two successive controlled-NOT quantum gates. This finding reveals that a permutation of controlled-NOT gates becomes one-way, provided that adiabatically immersed in a heat bath, which determines the condition of existence of a thermodynamically non-invertible bijection in polynomial-time, that would otherwise be mathematically invertible. This one-way bijection can also be particularly important because it shows nonlinearities in quantum mechanics, which are detectable by watching that the mathematical reversibility of controlled-NOT gates does not work physically.ALEXANDRE DE CASTRO, CNPTIA.CASTRO, A. de2014-09-09T11:11:11Z2014-09-09T11:11:11Z2014-09-0920142014-09-17T11:11:11Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlePhysica A: statistical mechanics and its applications, Amsterdam, v. 415, p. 473-478, 2014.http://www.alice.cnptia.embrapa.br/alice/handle/doc/99452310.1016/j.physa.2014.08.021enginfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da EMBRAPA (Repository Open Access to Scientific Information from EMBRAPA - Alice)instname:Empresa Brasileira de Pesquisa Agropecuária (Embrapa)instacron:EMBRAPA2017-08-16T00:59:26Zoai:www.alice.cnptia.embrapa.br:doc/994523Repositório InstitucionalPUBhttps://www.alice.cnptia.embrapa.br/oai/requestopendoar:21542017-08-16T00:59:26falseRepositório InstitucionalPUBhttps://www.alice.cnptia.embrapa.br/oai/requestcg-riaa@embrapa.bropendoar:21542017-08-16T00:59:26Repositório Institucional da EMBRAPA (Repository Open Access to Scientific Information from EMBRAPA - Alice) - Empresa Brasileira de Pesquisa Agropecuária (Embrapa)false |
dc.title.none.fl_str_mv |
One-way-ness in the input-saving (Turing) machine. |
title |
One-way-ness in the input-saving (Turing) machine. |
spellingShingle |
One-way-ness in the input-saving (Turing) machine. CASTRO, A. de Complexidade computacional Princípio de Landauer Máquina de Turing Permutação one way Computational complexity Landauer's principle Turing machine One-way permutation |
title_short |
One-way-ness in the input-saving (Turing) machine. |
title_full |
One-way-ness in the input-saving (Turing) machine. |
title_fullStr |
One-way-ness in the input-saving (Turing) machine. |
title_full_unstemmed |
One-way-ness in the input-saving (Turing) machine. |
title_sort |
One-way-ness in the input-saving (Turing) machine. |
author |
CASTRO, A. de |
author_facet |
CASTRO, A. de |
author_role |
author |
dc.contributor.none.fl_str_mv |
ALEXANDRE DE CASTRO, CNPTIA. |
dc.contributor.author.fl_str_mv |
CASTRO, A. de |
dc.subject.por.fl_str_mv |
Complexidade computacional Princípio de Landauer Máquina de Turing Permutação one way Computational complexity Landauer's principle Turing machine One-way permutation |
topic |
Complexidade computacional Princípio de Landauer Máquina de Turing Permutação one way Computational complexity Landauer's principle Turing machine One-way permutation |
description |
Currently, a complexity-class problem is proving the existence of one-way permutations: one-to-one and onto maps that are computationally ?easy?, while their inverses are computationally ?hard?. In what follows, we make use of Bennett?s algorithm of the reversible Turing machine (quantum information heat engine) to perform a cascade of two controlled-NOT gates to physically create a permutation operation. We show that by running this input-saving (Turing) machine backwards the critical inequality of Landauer?s thermodynamic limit is reversed, which provokes the symmetry-breaking of the quantum circuit based on two successive controlled-NOT quantum gates. This finding reveals that a permutation of controlled-NOT gates becomes one-way, provided that adiabatically immersed in a heat bath, which determines the condition of existence of a thermodynamically non-invertible bijection in polynomial-time, that would otherwise be mathematically invertible. This one-way bijection can also be particularly important because it shows nonlinearities in quantum mechanics, which are detectable by watching that the mathematical reversibility of controlled-NOT gates does not work physically. |
publishDate |
2014 |
dc.date.none.fl_str_mv |
2014-09-09T11:11:11Z 2014-09-09T11:11:11Z 2014-09-09 2014 2014-09-17T11:11:11Z |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
Physica A: statistical mechanics and its applications, Amsterdam, v. 415, p. 473-478, 2014. http://www.alice.cnptia.embrapa.br/alice/handle/doc/994523 10.1016/j.physa.2014.08.021 |
identifier_str_mv |
Physica A: statistical mechanics and its applications, Amsterdam, v. 415, p. 473-478, 2014. 10.1016/j.physa.2014.08.021 |
url |
http://www.alice.cnptia.embrapa.br/alice/handle/doc/994523 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da EMBRAPA (Repository Open Access to Scientific Information from EMBRAPA - Alice) instname:Empresa Brasileira de Pesquisa Agropecuária (Embrapa) instacron:EMBRAPA |
instname_str |
Empresa Brasileira de Pesquisa Agropecuária (Embrapa) |
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EMBRAPA |
institution |
EMBRAPA |
reponame_str |
Repositório Institucional da EMBRAPA (Repository Open Access to Scientific Information from EMBRAPA - Alice) |
collection |
Repositório Institucional da EMBRAPA (Repository Open Access to Scientific Information from EMBRAPA - Alice) |
repository.name.fl_str_mv |
Repositório Institucional da EMBRAPA (Repository Open Access to Scientific Information from EMBRAPA - Alice) - Empresa Brasileira de Pesquisa Agropecuária (Embrapa) |
repository.mail.fl_str_mv |
cg-riaa@embrapa.br |
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1794503393704673280 |