I know that for time independent Hamiltonians we can make the statement
$$U = e^{-iHt}\tag{1}$$
where $H$ is a time-independent Hamiltonian (divided by $\hbar$) and $U$ the unitary, also known as time evolution operator.
Now when studying I've met a unitary which corresponds to a two-level rotation defined as
$$U = \lvert i \rangle \langle j \rvert +\lvert j \rangle \langle i \rvert -\lvert i \rangle \langle i \rvert - \lvert j \rangle \langle j \rvert + \mathbb{I}\tag{2}$$
For clarity for a 4 state system it would look like this
$$ \begin{bmatrix} 0& 1 & 0 & 0 \\ 1& 0 & 0 & 0 \\ 0& 0 & 1 & 0 \\ 0& 0 & 0 & 1 \\ \end{bmatrix} $$
I'd like to understand how I can ever hope to use eq. (1) to obtain such a unitary eq. (2).