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Completeness of the ZX-Calculus

Emmanuel Jeandel ; Simon Perdrix ; Renaud Vilmart.

The ZX-Calculus is a graphical language for diagrammatic reasoning in quantum mechanics and quantum information theory. It comes equipped with an equational presentation. We focus here on a very important property of the language: completeness, which roughly ensures the equational theory captures&nbsp;[&hellip;]

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Rewriting and Completeness of Sum-Over-Paths in Dyadic Fragments of Quantum Computing

Renaud Vilmart.

The "Sum-Over-Paths" formalism is a way to symbolically manipulate linear maps that describe quantum systems, and is a tool that is used in formal verification of such systems. We give here a new set of rewrite rules for the formalism, and show that it is complete for "Toffoli-Hadamard", the&nbsp;[&hellip;]

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