Representing and Implementing Matrices Using Algebraic ZX-calculus
Abstract
In linear algebra applications, elementary matrices hold a significant role. This paper presents a diagrammatic representation of all $2^m\times 2^n$-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 \texttt{discopy}. Overall, this work sets the groundwork for more applications of ZX-calculus such as synthesising controlled matrices [arXiv:2212.04462] in quantum computing.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2021
- DOI:
- arXiv:
- arXiv:2110.06898
- Bibcode:
- 2021arXiv211006898W
- Keywords:
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- Quantum Physics;
- Computer Science - Artificial Intelligence
- E-Print:
- 25 pages, totally changed the application section with matchgate representation