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Representing and Implementing Matrices Using Algebraic ZX-calculus

arXiv 2110.06898 ↗First posted 13 Oct 2021quant-ph cs.AIcited by 0

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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.

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.

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3 of 27 references.

References · 3

  1. 2019Graph-theoretic Simplification of Quantum Circuits with the ZX-calculuscited by 20
  2. 2019Phase Gadget Synthesis for Shallow Circuitscited by 9
  3. 2021Kindergarden quantum mechanics graduates (...or how I learned to stop gluing LEGO together and love the ZX-calculus)cited by 4

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