  The ZX-calculus is a graphical calculus for reasoning about pure state qubit
quantum mechanics. It is complete for pure qubit stabilizer quantum mechanics,
meaning any equality involving only stabilizer operations that can be derived
using matrices can also be derived pictorially. Stabilizer operations include
the unitary Clifford group, as well as preparation of qubits in the state |0>,
and measurements in the computational basis. For general pure state qubit
quantum mechanics, the ZX-calculus is incomplete: there exist equalities
involving non-stabilizer unitary operations on single qubits which cannot be
derived from the current rule set for the ZX-calculus. Here, we show that the
ZX-calculus for single qubits remains complete upon adding the operator T to
the single-qubit stabilizer operations. This is particularly interesting as the
resulting single-qubit Clifford+T group is approximately universal, i.e. any
unitary single-qubit operator can be approximated to arbitrary accuracy using
only Clifford operators and T.
