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arXiv · 2012.05887

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

Alejandro Díaz-Caro·Octavio Malherbe
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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.

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Alejandro Díaz-Caro, Octavio Malherbe. 2020-12-10. Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model. https://doi.org/10.46298/lmcs-18(3%3A32)2022

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