The Quantum Effect: A Recipe for QuantumPi
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.
Cite
@article{arxiv.2302.01885,
title = {The Quantum Effect: A Recipe for QuantumPi},
author = {Jacques Carette and Chris Heunen and Robin Kaarsgaard and Amr Sabry},
journal= {arXiv preprint arXiv:2302.01885},
year = {2025}
}
Comments
This version: fix some strange characters and missing 'inv' in two of the Frobenius laws