QPE circuit — eigenphase φ estimation via QFT, precision scales as 1/2ⁿ
QPE uses n ancilla qubits to estimate the eigenphase φ of a unitary U where U|ψ⟩=e^(2πiφ)|ψ⟩. After applying controlled-U^(2^k) gates and the inverse QFT, measuring the ancillas gives φ̃ ∈ {0,1,...,2ⁿ−1}/2ⁿ with probability |∑ₖ e^(2πi(φ−φ̃)k)|²/4ⁿ. Precision is 1/2ⁿ; success probability for best estimate exceeds 8/π² ≈ 0.81.