I have matrix $B=\begin{bmatrix}0&&0&&0&&0\\0&&1&&0&&0\\0&&0&&2&&0\\0&&0&&0&&3\end{bmatrix}$.
By doing $A=e^{\pi i B/2}$, I get $A=\begin{bmatrix}0&&0&&0&&0\\0&&i&&0&&0\\0&&0&&-1&&0\\0&&0&&0&&-i\end{bmatrix}$. Now I have to implement this gate to two qubits with controlled operation, Controlled-A. How can I implement this gate? This is the paper from which I got matrices A and B and they have implemented Controlled-A gate. I am curious how they did that. I tried to read the references they provided but couldn't get anything related to this.
Any hints or approaches would be helpful.