A Near-Minimal Axiomatisation of ZX-Calculus for Pure Qubit Quantum Mechanics

Renaud Vilmart (1)

1 MOCQUA - Designing the Future of Computational Models

Recent developments in the ZX-Calculus have resulted in complete axiomatisations first for an approximately universal restriction of the language, and then for the whole language. The main drawbacks were that the axioms that were added to achieve completeness were numerous, tedious to manipulate and lacked a physical interpretation. We present in this paper two complete axiomatisations for the general ZX-Calculus, that we believe are optimal, in that all their equations are necessary and moreover have a nice physical interpretation.

Domaines: Logique en informatique [cs.LO]; Physique Quantique [quant-ph]

Renaud Vilmart. A Near-Minimal Axiomatisation of ZX-Calculus for Pure Qubit Quantum Mechanics. LICS 2019 - 34th Annual ACM/IEEE Symposium on Logic in Computer Science, Jun 2019, Vancouver, Canada. ⟨10.1109/LICS.2019.8785765⟩. ⟨hal-01963426⟩