Fixed z rotations with phase shift gates S, 
, T, and 
The S, 
, T, and 
gates all perform rotations around the z axis of the qubit. This means that when you measure the qubit, there is no change in the probability of measuring the outcome as 1 or 0. What does change is the phase of the qubit.
The S-gate and T-gate are not their own inverses
As the S and T gates perform set rotations around the z axis, they are not reversible. Adding two of these gates in a row does not negate them. Instead, Qiskit includes the S†and T†gates which serve as the reverse S and T gates. For a quick reminder, see the A quick introduction to quantum gates recipe in Chapter 2, Quantum Computing and Qubits with Python.
Mathematically, the S and T gates can be expressed as the following unitary matrixes:
The sample script is available at: https://github.com/PacktPublishing/Quantum-Computing-in-Practice-with-Qiskit-and-IBM-Quantum-Experience/blob/master/Chapter06/ch6_r1_quantum_qate_ui...
