Quantum phase estimation

Given access to the controlled version of an $n$-qubit unitary $U$ and its eigenstate $\ket{\psi}$ such that $U\ket{\psi}=e^{2\pi i\theta}\ket{\psi}$, there is a quantum algorithm that estimates $\theta$ up to precision $2^{-n_a}$ and failure probability at most $1-4/\pi^2$, using $n_a$ ancilla qubits, $\mathcal{O}(2^{n_a})$ queries to controlled-$U$, and $\mathcal{O}(n_a^2)$ single-qubit gates and CNOT gates.