Completeness of the ZH-calculus

Understand

There are various gate sets used for describing quantum computation.

• A particularly popular one consists of Clifford gates and arbitrary single-qubit phase gates.
• Computations in this gate set can be elegantly described by the ZX-calculus, a graphical language for a class of string diagrams describing linear maps between qubits.
• The ZX-calculus has proven useful in a variety of areas of quantum information, but is less suitable for reasoning about operations outside its natural gate set such as multi-linear Boolean operations like the Toffoli gate.