Spectral arc length of a phase gate
= Spectral arc length of a phase gate
For $U_\gamma=\operatorname{diag}(1,e^{i\gamma})$ with $0\leq\gamma<2\pi$,
$$
\theta(U_\gamma)=\min\{\gamma,2\pi-\gamma\}.
$$
= Spectral arc length of a phase gate
For $U_\gamma=\operatorname{diag}(1,e^{i\gamma})$ with $0\leq\gamma<2\pi$,
$$
\theta(U_\gamma)=\min\{\gamma,2\pi-\gamma\}.
$$