Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model
Logic in Computer Science
2023-06-22 v5 Category Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2012.05887,
title = {Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model},
author = {Alejandro Díaz-Caro and Octavio Malherbe},
journal= {arXiv preprint arXiv:2012.05887},
year = {2023}
}