The Quantum Effect: A Recipe for QuantumPi

TL;DR

This paper presents a categorical construction that models quantum computing as a combination of classical reversible computation, using internal languages and effects, providing a new framework for quantum programming and reasoning.

Contribution

It introduces a novel categorical recipe for constructing a universal quantum programming language from classical structures, incorporating effects and complementarity.

Findings

Constructs a quantum programming language from classical models

Enables reasoning about quantum programs through classical logic

Shows how measurements can be integrated as effects

Abstract

Free categorical constructions characterise quantum computing as the combination of two copies of a reversible classical model, glued by the complementarity equations of classical structures. This recipe effectively constructs a computationally universal quantum programming language from two copies of Pi, the internal language of rig groupoids. The construction consists of Hughes' arrows. Thus answer positively the question whether a computational effect exists that turns reversible classical computation into quantum computation: the quantum effect. Measurements can be added by layering a further effect on top. Our construction also enables some reasoning about quantum programs (with or without measurement) through a combination of classical reasoning and reasoning about complementarity.