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arXiv:2302.01885 (cs)
[Submitted on 3 Feb 2023 (v1), last revised 8 May 2023 (this version, v3)]

Title:The Quantum Effect: A Recipe for QuantumPi

Authors: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.
Comments: This version: fix some strange characters and missing 'inv' in two of the Frobenius laws
Subjects: Programming Languages (cs.PL); Quantum Physics (quant-ph)
Cite as: arXiv:2302.01885 [cs.PL]
  (or arXiv:2302.01885v3 [cs.PL] for this version)
  https://doi.org/10.48550/arXiv.2302.01885

Submission history

From: Jacques Carette [view email]
[v1] Fri, 3 Feb 2023 17:38:22 UTC (77 KB)
[v2] Fri, 7 Apr 2023 09:46:59 UTC (70 KB)
[v3] Mon, 8 May 2023 16:55:30 UTC (72 KB)
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