Completeness of the ZX-calculus

Understand

The ZX-calculus is an intuitive but also mathematically strict graphical language for quantum computing, which is especially powerful for the framework of quantum circuits.

• Completeness of the ZX-calculus means any equality of matrices with size powers of $n$ can be derived purely diagrammatically.
• In this thesis, we give the first complete axiomatisation the ZX-calculus for the overall pure qubit quantum mechanics, via a translation from the completeness result of another graphical language for quantum computing -- the ZW-calculus.
• This paves the way for automated pictorial quantum computing, with the aid of some software like Quantomatic.