Quantum Programming with Inductive Datatypes

HAL (Le Centre pour la Communication Scientifique Directe)

Abstract

Inductive datatypes in programming languages allow users to define useful data structures such as natural numbers, lists, trees, and others. In this paper we show how inductive datatypes may be added to the quantum programming language QPL. We construct a sound categorical model for the language and by doing so we provide the first detailed semantic treatment of user-defined inductive datatypes in quantum programming. We also show our denotational interpretation is invariant with respect to big-step reduction, thereby establishing another novel result for quantum programming. Compared to classical programming, this property is considerably more difficult to prove and we demonstrate its usefulness by showing how it immediately implies computational adequacy at all types. To further cement our results, our semantics is entirely based on a physically natural model of von Neumann algebras, which are mathematical structures used by physicists to study quantum mechanics.

Authors 4

1. Romain Péchoux
   Affiliation as printed

   Designing the Future of Computational Models

2. Simon Perdrix
   Affiliation as printed

   Designing the Future of Computational Models

3. Mathys Rennela Aachen

   Leiden University

   Affiliation as printed

   Universiteit Leiden [Leiden]

4. Vladimir Zamdzhiev
   Affiliation as printed

   Designing the Future of Computational Models