Representing and Implementing Matrices Using Algebraic ZX-calculus
2021-10-13Code Available0· sign in to hype
Quanlong Wang, Richie Yeung
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- github.com/y-richie-y/qpl2022-represent-matrixOfficialIn papernone★ 2
- github.com/y-richie-y/qpl-represent-matrixOfficialIn papernone★ 2
Abstract
In linear algebra applications, elementary matrices hold a significant role. This paper presents a diagrammatic representation of all 2^m 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 discopy. Overall, this work sets the groundwork for more applications of ZX-calculus such as synthesising controlled matrices [arXiv:2212.04462] in quantum computing.