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