The Phase gate (or S gate) is a single-qubit operation defined by:
The S gate is also known as the phase gate or the Z90 gate, because it represents a 90-degree rotation around the z-axis.
The S gate is related to the T gate by the relationship .
The conjugate transpose of the S gate, the gate is defined by:
S q # execute phase gate on qubit 0 Sdag q[1:2,5] # execute conjugate transpose of the S gate on qubits 1,2 and 5