In quantum computing, the quantum phase estimation algorithm (also referred to as quantum eigenvalue estimation algorithm), is a quantum algorithm to estimate the phase (or eigenvalue) of an eigenvector of a unitary operator. More precisely, given a unitary matrix and a quantum state such that , the algorithm estimates the value of with high probability within additive error , using qubits (without counting the ones used to encode the eigenvector state) and controlled-U operations. The algorithm was initially introduced by Alexei Kitaev in 1995.