How to Bake a Quantum Π

We construct a computationally universal quantum programming language Quantum Π from two copies of Π, the internal language of rig groupoids. The first step constructs a pure (measurement-free) term language by interpreting each copy of Π in a generalisation of the category Unitary in which every morphism is “rotated” by a particular angle, and the two copies are amalgamated using a free categorical construction expressed as a computational …