T gate
= T gate
{c}
{title2=$T=\operatorname{diag}(1,e^{i\pi/4})$}
The <phase gate> with angle $\pi/4$. It rotates the <Bloch vector> by $\pi/4$ around $z$, and $T^2=S$. It is not a <Clifford gate>: it takes the positive $X$ eigenstate to a state with vector $(1/\sqrt2,1/\sqrt2,0)$, outside the <stabilizer octahedron>.