Quantum Phase Estimation

Quantum Phase Estimation (QPE) is a fundamental quantum algorithmic building block used as a subroutine in quantum algorithms such as Shor’s algorithm.

Given a unitary operator U and one of its eigenstates |ψ⟩, QPE estimates the corresponding phase θ, where:

U|ψ⟩ = e^{^}(2πiθ)|ψ⟩

Because U is unitary, its eigenvalues have magnitude 1 and can therefore be expressed in the form e^{^}(2πiθ), where θ is a real-valued phase.