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A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics

A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics

We introduce the first complete and approximately universal diagrammatic language for quantum mechanics. We make the ZX-Calculus, a diagrammatic language introduced by Coecke and Duncan, complete for the so-called Clifford+T quantum mechanics by adding two new axioms to the language. The completeness of the ZX-Calculus for Clifford+T quantum mechanics -- …