T Gate

The T gate is a single-qubit operation given by: $\ T = \begin{pmatrix} 1 & 0 \\ 0 & \exp \left ( \frac{i \pi}{4} \right ) \end{pmatrix}$

The T gate is related to the S gate by the relationship $\ S=T^{2}$.

The conjugate transpose of the T gate is defined by: $\ T^{\dagger} = \begin{pmatrix} 1 & 0 \\ 0 & \exp \left ( \frac{-i \pi}{4} \right ) \end{pmatrix}$

Examples: