English

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.

Keywords

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

R2 v1 2026-06-22T19:25:13.603Z