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      Fast Automated Reasoning over String Diagrams using Multiway Causal Structure

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          Abstract

          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 full 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.

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          Author and article information

          Journal
          09 May 2021
          Article
          2105.04057
          639ed3be-99fa-46ab-bac8-56a56e0a20bd

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          Submitted to Applied Category Theory 2021. 14 pages, 9 figures
          cs.LO cs.DM

          Theoretical computer science,Discrete mathematics & Graph theory
          Theoretical computer science, Discrete mathematics & Graph theory

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