Minimality of the Pure Qubit ZX Calculus

Abstract:The ZX calculus is a graphical language for reasoning about quantum processes. In this paper, we develop a minimal pure-qubit ZX calculus based on the work of Vilmart [arXiv:1812.09114], Backens, Perdrix, and Wang [arXiv:1709.08903], and Stoltz [arXiv:2606.12383]. This resolves a problem that has remained open for nearly a decade, since completeness was first proved. Specifically, we show that $(I_r)$ is derivable and establish the necessity of $(B)$ and $(I_g)$, yielding two complete and minimal rulesets.

arXiv:2608.14872 [quant-ph]

(or arXiv:2608.14872v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.14872 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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