Let U be a unitary operator that operates on m qubits with an eigenvector | \psi \rangle, such that U| \psi\rangle = e^{ 2\pi i \theta}\left|\psi \right\rangle , 0 \leq \theta < 1 .
We would like to find the eigenvalue e^{2 \pi i \theta} of |\psi\rangle , which in this case is equivalent to estimating the phase \theta, to a finite level of precision.