ZX-Calculus Seminar Paper

This repository contains my seminar paper and presentation materials for the Applications of Quantum Computing in IT Security seminar conducted at the Technical University of Munich (TUM). The paper and slides provide an introductory exploration of the ZX-Calculus, a powerful graphical formalism for quantum computing quantum circuit simplifcation.

Table of Contents

1. Introduction
2. Category Theory
3. Introduction to ZX-Calculus
4. Simplifcation Rules
5. Example: ZX-Diagrams Optimization
6. Universality & Completeness
7. Further Work
8. Conclusion

Abstract

ZX-Calculus is a graphical language that extends classical quantum circuits by replacing the logic gates with more fundamental building blocks. Those building blocks are called spiders and are represented by colored nodes in a graph. Together with edges connecting those nodes, they form a ZX diagram. A set of rewrite rules allows to perform transformations and simplifications on those ZX diagrams. ZX-Calculus promises a more intuitive way of reasoning about quantum circuits, as there are fewer rewrite rules to remember than in the classical logic gate model. In this paper I will introduce the ZX-Calculus, its rewrite rules, and some of its applications. I will give a particular focus on optimizing quantum circuits, as this is one of the main applications of the ZX-Calculus.

Index Terms: quantum computing, ZX-Calculus, quantum circuits, circuit optimization

Paper

The seminar paper is available in LaTeX format in this repository. You can access the rendered version in PDF format by clicking the following link:

Read the Seminar Paper (PDF)

Slides

The presentation slides are available in PDF format and can be accessed via the following link:

View the Seminar Slides (PDF)