As I understant, what are we doing here is to try apply a gate that affects the same as a matrix A multiplied on some angle $\pi / 2^n$. And due to the phase kickback, the q1-q3 qubits stores some phases. What these phases stand for? I read somewhere that this is "phase representation of the eigenvalues" - but why is it so? And why do we need this anlge $\pi / 2^n$?