Categorifying the ZX-calculus

Daniel Cicala
(University of California, Riverside)

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.

In Bob Coecke and Aleks Kissinger: Proceedings 14th International Conference on Quantum Physics and Logic (QPL 2017), Nijmegen, The Netherlands, 3-7 July 2017, Electronic Proceedings in Theoretical Computer Science 266, pp. 294–314.
Published: 27th February 2018.

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