Representing and Implementing Matrices Using Algebraic ZX-calculus
This work provides a foundational tool for quantum computing researchers, though it is incremental in extending ZX-calculus to matrix representation.
The paper tackled representing elementary matrices and Jozsa-style matchgates using algebraic ZX-calculus, resulting in a diagrammatic framework implemented in discopy for quantum computing applications.
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.