Quantum phase estimation algorithm

Quantum phase estimation algorithm is a quantum algorithm used as a subroutine in several applications such as order finding, factoring and discrete logarithm.

This algorithm makes it possible to estimate the phase that a unitary transformation adds to one of its eigenvectors.

Let U be a unitary operator that operates on m qubits with an eigenvector ${\displaystyle |\psi \rangle ,}$ such that ${\displaystyle U|\psi \rangle =e^{2\pi i\theta }\left|\psi \right\rangle ,0\leq \theta <1}$.

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