Completeness of the ZX-Calculus

Understand

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 all of quantum mechanics.
• We first improve on the known-to-be-complete presentation for the so-called Clifford fragment of the language - a restriction that is not universal - by adding some axioms.