The Arrow Calculus as a Quantum Programming Language

TL;DR

This paper introduces an arrow calculus framework extended with monadic constructions to express quantum computations, including measurements, enabling familiar classical programming patterns and equational reasoning.

Contribution

It presents a novel arrow calculus-based approach for quantum programming that incorporates measurements and supports equational reasoning.

Findings

Framework effectively models quantum computations with measurements.

Provides a set of laws for reasoning about quantum programs.

Facilitates classical programming patterns in quantum computing.

Abstract

We express quantum computations (with measurements) using the arrow calculus extended with monadic constructions. This framework expresses quantum programming using well-understood and familiar classical patterns for programming in the presence of computational effects. In addition, the five laws of the arrow calculus provide a convenient framework for equational reasoning about quantum computations that include measurements.