T-gate

Last updated Jun 24, 2022

• Type atom
• Status good

T-gate is the square root of the S-gate. ¹ $$\displaylines{
T\ket0 = \ket 0, \newline
T\ket1 = e^{i\frac\pi4}\ket 1.
}$$ It is a rotation of $45^\circ$ about the $z$-axis, so $T^2 = S$ and $T^4 = Z$. It’s Matrix representation is: $$T = \begin{pmatrix}1 & 0 \\ 0 & e^{i\pi/4} \end{pmatrix}.$$