12. Gates: Phase Gates

Phase Gates (S, T)

Sometimes we need finer control than a full Z-flip (180 degrees).

• S Gate: 90-degree rotation around Z axis ($\sqrt{Z}$).
• T Gate: 45-degree rotation around Z axis ($\sqrt[4]{Z}$).

The T gate is crucial because H, S, and CNOT are not enough to build any quantum circuit. Adding the T gate makes the set "Universal".