Geometry of Interaction for ZX-Diagrams

TL;DR

This paper introduces a token-machine-based asynchronous model for ZX-Calculus, providing a new operational perspective on quantum diagram semantics and connecting it to standard interpretations.

Contribution

It presents a novel asynchronous token-machine model for ZX-Calculus, extending to mixed processes and linking to standard semantics.

Findings

Provides a local, operational view of ZX-diagram semantics

Connects new model to standard interpretation of ZX-diagrams

Enhances understanding of quantum computation represented by ZX-diagrams

Abstract

ZX-Calculus is a versatile graphical language for quantum computation equipped with an equational theory. Getting inspiration from Geometry of Interaction, in this paper we propose a token-machine-based asynchronous model of both pure ZX-Calculus and its extension to mixed processes. We also show how to connect this new semantics to the usual standard interpretation of ZX-diagrams. This model allows us to have a new look at what ZX-diagrams compute, and give a more local, operational view of the semantics of ZX-diagrams.