Fast Automated Reasoning over String Diagrams using Multiway Causal Structure

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.

arXiv commentSubmitted to Applied Category Theory 2021. 14 pages, 9 figures

References in corpus (7)

• Causal categories: relativistically interacting processes
• A Universal Construction for (Co)Relations
• Pictures of Processes: Automated Graph Rewriting for Monoidal Categories and Applications to Quantum Computing
• Some Relativistic and Gravitational Properties of the Wolfram Model
• Finite matrices are complete for (dagger-)hypergraph categories
• ZX-Calculus and Extended Wolfram Model Systems II: Fast Diagrammatic Reasoning with an Application to Quantum Circuit Simplification
• Hypergraph Discretization of the Cauchy Problem in General Relativity via Wolfram Model Evolution