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Categorifying the ZX-calculus
Published 24 Apr 2017 in math.CT, cs.LO, math-ph, math.MP, and quant-ph | (1704.07034v2)
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.
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