一句话：从 rig groupoid 内部语言 Π 的两个副本出发，用范畴构造与计算效应构造计算普遍的量子语言 Quantum Π。
论文从 rig groupoid 的内部语言 Π 的两个副本出发，构造计算普遍的量子编程语言 Quantum Π。作者先在 Unitary 的推广范畴中为每个态射引入旋转角，以解释每个 Π 副本；再用自由范畴构造（可表达为计算效应）将两个副本融合，得到无测量的纯项语言。该语言仅在特定旋转角取值下呈现量子行为，这一性质由对所得范畴施加少量方程来保证。随后，作者通过叠加另一层计算效应引入测量。其贡献在于以范畴语义和计算效应为原则，给出从内部语言到量子语言的可组合构造。
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 effect. The amalgamated language only exhibits quantum behaviour for specific values of the rotation angles, a property which is enforced by imposing a small number of equations on the resulting category. The second step in the construction introduces measurements by layering an additional computational effect.
DOI 原文 · arXiv · PDF（开放获取） · DBLP
@article{CaretteHKS24a,
title = {How to Bake a Quantum Π},
author = {Jacques Carette and Chris Heunen and Robin Kaarsgaard and Amr Sabry},
journal = {Proceedings of the ACM on Programming Languages},
volume = {8},
number = {ICFP},
year = {2024},
doi = {10.1145/3674625}
}