Categorifying the ZX-calculus
Category Theory
2018-03-05 v2 Logic in Computer Science
Mathematical Physics
math.MP
Quantum Physics
Abstract
We build a symmetric monoidal and compact closed bicategory by combining spans and cospans inside a topos. This can be used as a framework in which to study open networks and diagrammatic languages. We illustrate this framework with Coecke and Duncan's zx-calculus by constructing a bicategory with the natural numbers for 0-cells, the zx-calculus diagrams for 1-cells, and rewrite rules for 2-cells.
Cite
@article{arxiv.1704.07034,
title = {Categorifying the ZX-calculus},
author = {Daniel Cicala},
journal= {arXiv preprint arXiv:1704.07034},
year = {2018}
}
Comments
In Proceedings QPL 2017, arXiv:1802.09737