Alejandro Díaz-Caro ; Octavio Malherbe - Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model

lmcs:7408 - Logical Methods in Computer Science, September 12, 2022, Volume 18, Issue 3 - https://doi.org/10.46298/lmcs-18(3:32)2022
Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical ModelArticle

Authors: Alejandro Díaz-Caro ; Octavio Malherbe

    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.


    Volume: Volume 18, Issue 3
    Published on: September 12, 2022
    Accepted on: May 5, 2022
    Submitted on: April 27, 2021
    Keywords: Computer Science - Logic in Computer Science,Mathematics - Category Theory,18C50, 03B40

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