# Representing and Implementing Matrices Using Algebraic ZX-calculus

arXiv: https://arxiv.org/abs/2110.06898 · HTML: https://mlsanity.com/paper/2110.06898/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 27 references that are in the map.
- First posted on arXiv 13 Oct 2021.

## Builds on (most cited first, 3 of 3)

- [Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus](https://mlsanity.com/paper/1902.03178/) (2019)
- [Phase Gadget Synthesis for Shallow Circuits](https://mlsanity.com/paper/1906.01734/) (2019)
- [Kindergarden quantum mechanics graduates (...or how I learned to stop gluing LEGO together and love the ZX-calculus)](https://mlsanity.com/paper/2102.10984/) (2021)

## Abstract (arXiv)

In linear algebra applications, elementary matrices hold a significant role. This paper presents a diagrammatic representation of all 2m× 2n-sized elementary matrices in algebraic ZX-calculus, showcasing their properties on inverses and transpose through diagrammatic rewriting. Additionally, the paper uses this representation to depict the Jozsa-style matchgate in algebraic ZX-calculus. To further enhance practical use, we have implemented this representation in textttdiscopy. Overall, this work sets the groundwork for more applications of ZX-calculus such as synthesising controlled matrices [arXiv:2212.04462] in quantum computing.