Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model

Autores
Díaz Caro, Alejandro; Malherbe, Octavio
Año de publicación
2022
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In a recent paper, a realizability technique has been used to give a semantics of a quantum lambda calculus. Such a technique gives rise to an infinite number of valid typing rules, without giving preference to any subset of those. In this paper, we introduce a valid subset of typing rules, defining an expressive enough quantum calculus. Then, we propose a categorical semantics for it. Such a semantics consists of an adjunction between the category of distributive-action spaces of value distributions (that is, linear combinations of values in the lambda calculus), and the category of sets of value distributions.
Fil: Díaz Caro, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina
Fil: Malherbe, Octavio. Universidad de la República; Uruguay
Materia
CATEGORICAL SEMANTICS
LAMBDA CALCULUS
QUANTUM COMPUTING
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/204623
Acceder
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spelling Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical ModelDíaz Caro, AlejandroMalherbe, OctavioCATEGORICAL SEMANTICSLAMBDA CALCULUSQUANTUM COMPUTINGhttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1In a recent paper, a realizability technique has been used to give a semantics of a quantum lambda calculus. Such a technique gives rise to an infinite number of valid typing rules, without giving preference to any subset of those. In this paper, we introduce a valid subset of typing rules, defining an expressive enough quantum calculus. Then, we propose a categorical semantics for it. Such a semantics consists of an adjunction between the category of distributive-action spaces of value distributions (that is, linear combinations of values in the lambda calculus), and the category of sets of value distributions.Fil: Díaz Caro, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; ArgentinaFil: Malherbe, Octavio. Universidad de la República; UruguayTechnische Universität Braunschweig2022-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/204623Díaz Caro, Alejandro; Malherbe, Octavio; Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model; Technische Universität Braunschweig; Logical Methods in Computer Science; 18; 3; 9-2022; 32:1-361860-5974CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://lmcs.episciences.org/10027info:eu-repo/semantics/altIdentifier/doi/10.46298/LMCS-18(3:32)2022info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:00:40Zoai:ri.conicet.gov.ar:11336/204623instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:00:41.015CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model
title Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model
spellingShingle Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model
Díaz Caro, Alejandro
CATEGORICAL SEMANTICS
LAMBDA CALCULUS
QUANTUM COMPUTING
title_short Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model
title_full Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model
title_fullStr Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model
title_full_unstemmed Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model
title_sort Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model
dc.creator.none.fl_str_mv Díaz Caro, Alejandro
Malherbe, Octavio
author Díaz Caro, Alejandro
author_facet Díaz Caro, Alejandro
Malherbe, Octavio
author_role author
author2 Malherbe, Octavio
author2_role author
dc.subject.none.fl_str_mv CATEGORICAL SEMANTICS
LAMBDA CALCULUS
QUANTUM COMPUTING
topic CATEGORICAL SEMANTICS
LAMBDA CALCULUS
QUANTUM COMPUTING
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In a recent paper, a realizability technique has been used to give a semantics of a quantum lambda calculus. Such a technique gives rise to an infinite number of valid typing rules, without giving preference to any subset of those. In this paper, we introduce a valid subset of typing rules, defining an expressive enough quantum calculus. Then, we propose a categorical semantics for it. Such a semantics consists of an adjunction between the category of distributive-action spaces of value distributions (that is, linear combinations of values in the lambda calculus), and the category of sets of value distributions.
Fil: Díaz Caro, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina
Fil: Malherbe, Octavio. Universidad de la República; Uruguay
description In a recent paper, a realizability technique has been used to give a semantics of a quantum lambda calculus. Such a technique gives rise to an infinite number of valid typing rules, without giving preference to any subset of those. In this paper, we introduce a valid subset of typing rules, defining an expressive enough quantum calculus. Then, we propose a categorical semantics for it. Such a semantics consists of an adjunction between the category of distributive-action spaces of value distributions (that is, linear combinations of values in the lambda calculus), and the category of sets of value distributions.
publishDate 2022
dc.date.none.fl_str_mv 2022-09
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/204623
Díaz Caro, Alejandro; Malherbe, Octavio; Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model; Technische Universität Braunschweig; Logical Methods in Computer Science; 18; 3; 9-2022; 32:1-36
1860-5974
CONICET Digital
CONICET
url http://hdl.handle.net/11336/204623
identifier_str_mv Díaz Caro, Alejandro; Malherbe, Octavio; Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model; Technische Universität Braunschweig; Logical Methods in Computer Science; 18; 3; 9-2022; 32:1-36
1860-5974
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://lmcs.episciences.org/10027
info:eu-repo/semantics/altIdentifier/doi/10.46298/LMCS-18(3:32)2022
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Technische Universität Braunschweig
publisher.none.fl_str_mv Technische Universität Braunschweig
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.885934

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