I want to express the square root of NOT as a time-dependent unitary matrix such that each $n$ units of time, the square root of NOT is produced.
More precisely, I want to find a $U(t_0,t_1)$ such that $U(t_0,t_1) = \sqrt{\text{NOT}}$, if $t_1-t_0=n$ for some $n$.
One possible solution is to express $\sqrt{\text{NOT}}$ as a product of rotation matrices, and then, parametrize the angles in a clever way to depend on the time. But I do not know how to express $\sqrt{\text{NOT}}$ as a product of rotation matrices.
Any help?