Completeness and the ZX-calculus

Understand

Graphical languages offer intuitive and rigorous formalisms for quantum physics.

• They can be used to simplify expressions, derive equalities, and do computations.
• Yet in order to replace conventional formalisms, rigour alone is not sufficient: the new formalisms also need to have equivalent deductive power.
• This requirement is captured by the property of completeness, which means that any equality that can be derived using some standard formalism can also be derived graphically.