{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/representing-matrices-using-algebraic-zx","title":"Representing and Implementing Matrices Using Algebraic ZX-calculus","arxiv_id":"2110.06898","date":"2021-10-13","proceeding":null,"authors":["Quanlong Wang","Richie Yeung"],"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.","url_abs":"https://arxiv.org/abs/2110.06898v4","url_pdf":"https://arxiv.org/pdf/2110.06898v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"representing-matrices-using-algebraic-zx","repo_url":"https://github.com/y-richie-y/qpl-represent-matrix","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"representing-matrices-using-algebraic-zx","repo_url":"https://github.com/y-richie-y/qpl2022-represent-matrix","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}