Work

Minimality of the Pure Qubit ZX Calculus

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.14872

Authors: Stoltz, Harry K., Vilmart, Renaud

Institutions: Courant Institute of Mathematical Sciences, New York University, Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Laboratoire Lorrain de Recherche en Informatique et ses Applications, Université de Lorraine

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7203660243

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