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

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...

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Detalles Bibliográficos
Autores: Díaz Caro, Alejandro, Malherbe, Octavio
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/204623
Acceso en línea:http://hdl.handle.net/11336/204623
Access Level:acceso abierto
Palabra clave:CATEGORICAL SEMANTICS
LAMBDA CALCULUS
QUANTUM COMPUTING
https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
Descripción
Sumario: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.