The Quantum Effect: A Recipe for QuantumPi

Jacques Carette, Chris Heunen, Robin Kaarsgaard, Amr Sabry

Research output: Other contributionResearch


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.
Original languageEnglish
Publication date3. Feb 2023
Number of pages37
Publication statusPublished - 3. Feb 2023


  • cs.PL
  • quant-ph


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