Categorifying the ZX-calculus

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.

In Proceedings QPL 2017, arXiv:1802.09737

References in corpus (3)

• A Compositional Framework for Reaction Networks
• Open Markov processes: A compositional perspective on non-equilibrium steady states in biology
• Open Graphs and Computational Reasoning

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