Fast Automated Reasoning over String Diagrams using Multiway Causal Structure [article]

Jonathan Gorard, Manojna Namuduri, Xerxes D. Arsiwalla
2021 arXiv   pre-print
We introduce an intuitive algorithmic methodology for enacting automated rewriting of string diagrams within a general double-pushout (DPO) framework, in which the sequence of rewrites is chosen in accordance with the causal structure of the underlying diagrammatic calculus. The combination of the rewriting structure and the causal structure may be elegantly formulated as a weak 2-category equipped with both total and partial monoidal bifunctors, thus providing a categorical semantics for the
more » ... ll multiway evolution causal graph of a generic Wolfram model hypergraph rewriting system. As an illustrative example, we show how a special case of this algorithm enables highly efficient automated simplification of quantum circuits, as represented in the ZX-calculus.
arXiv:2105.04057v1 fatcat:zjfepnkfubbu5pk3fmng6tibge