Large-scale quantum diagrammatic reasoning tools, !-boxes vs. scalable notations

TL;DR

This paper compares two large-scale diagrammatic reasoning tools in quantum computing, !-boxes and scalable notations, exploring their interactions and establishing correspondences to develop a comprehensive reasoning toolbox.

Contribution

It investigates the relationship between !-boxes and scalable notations in ZH-calculus, providing examples and establishing correspondences for large-scale quantum diagrammatic reasoning.

Findings

Correspondences between !-boxes and scalable notations are established.

Examples from literature demonstrate the interaction of the two approaches.

A path toward a unified large-scale diagrammatic reasoning toolbox is proposed.

Abstract

The application of diagrammatic reasoning techniques to large-scale quantum processes needs specific tools to describe families of diagrams of arbitrary size. For now, large-scale diagrammatic reasoning tools in ZH-calculus come in two flavours, !-boxes and scalable notations. This paper investigates the interactions between the two approaches by exhibiting correspondences through various examples from the literature, focusing on (hyper)graph states and diagrammatic transforms. In doing so, we set up a path toward a neat and tidy large-scale diagrammatic reasoning toolbox.