Diagrammatic Reasoning beyond Clifford+T Quantum Mechanics

Understand

The ZX-Calculus is a graphical language for quantum mechanics.

• An axiomatisation has recently been proven to be complete for an approximatively universal fragment of quantum mechanics, the so-called Clifford+T fragment.
• We focus here on the expressive power of this axiomatisation beyond Clifford+T Quantum mechanics.
• We consider the full pure qubit quantum mechanics, and mainly prove two results: (i) First, the axiomatisation for Clifford+T quantum mechanics is also complete for all equations involving some kind of linear diagrams.