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...
| Autores: | , |
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| 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 |
| 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. |
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