# Tag Info

Existence (as mentioned on Wikipedia, for example), is easy, although not necessarily unique. Any unitary can be written as $$U=\sum_ie^{i\theta_i}P_i$$ where $P_i$ are projectors such that $\sum_iP_i=1$, and $\theta_i$ is in the range 0 to $2\pi$. Then we have that $$\sqrt{U}=\sum_ie^{i\theta_i/2}P_i.$$ Giving a circuit construction of the gate is an ...