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arXiv · 2302.01885

The Quantum Effect: A Recipe for QuantumPi

Jacques Carette·Chris Heunen·Robin Kaarsgaard·Amr Sabry
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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.

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Jacques Carette, Chris Heunen, Robin Kaarsgaard, Amr Sabry. 2023-02-03. The Quantum Effect: A Recipe for QuantumPi. https://doi.org/10.1145/3674625

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