We introduce the first complete and approximatively 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 four new axioms to the language. The completeness
of the ZX-Calculus for Clifford+T quantum mechanics was one of the main open
questions in categorical quantum mechanics. We prove the completeness of the
Clifford+T fragment of the ZX-Calculus using the recently studied ZW-Calculus,
a calculus dealing with integer matrices. We also prove that the Clifford+T
fragment of the ZX-Calculus represents exactly all the matrices over some
finite dimensional extension of the ring of dyadic rationals
