# Which angle is estimated by the phase estimation algorithm?

Is it $$\theta$$ or $$\varphi$$ as usually depicted on the Bloch sphere? In other words, is it the angle projected on the $$xy$$-plane or is it the one on a plane that intersects the $$z$$-axis of the Bloch sphere? How could I have answered this myself?

Phase estimation algorithm does not estimate a property of a qubit state (and the angles $$\theta$$ and $$\varphi$$ in your question are exactly that - a property of a given qubit state).
Rather, it estimates the eigenvalue of a given unitary $$U$$ that corresponds to the given eigenvector $$|\psi\rangle$$ - the angle $$\alpha$$ in the following equation:
$$U|\psi\rangle = e^{2i\pi\alpha}|\psi\rangle$$