# HHL phase estimation step

I have got an HHL circuit that looks as follows:

In the phase estimation part we are trying to find the eigenvalues of the matrix A. But what is the role of the piece of circuit hightlighted below?

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 $$\pi / 2^n$$?

• This step should be the phase estimation step. Typically, you would see controlled-U's to exponentiated matrices $U$ such as $U^{2^0}, U^{2^1}, U^{2^2}$, with each $U = e^{i A t}$. In the description, the $t$ is then chosen such that the eigenvalues map to full integers. So I don't know why there would be those fractions of $\pi$ in your circuit. Does it work? Here is my implementation of that paper. Mar 10 at 6:34