Quantum Phase Estimation (Kitaev)
QPE circuit: eigenphase extraction via QFT and controlled-U^(2^k) gates
Parameters
True phase φ (×2π):
0.375
Ancilla qubits n:
6
State noise ε:
0.00
Shots:
1000
Run QPE
Sweep φ
True φ:
—
Estimated φ̂:
—
Error:
—
Resolution 1/2ⁿ:
—
QPE algorithm:
1. Prepare n ancilla qubits in |0⟩, apply H
2. Controlled-U^(2^k) on target eigenstate
3. Inverse QFT on ancilla register
4. Measure: p(j) ∝ |sin(π(φ−j/2^n)·2^n)|²/|sin(π(φ−j/2^n))|²
Precision:
δφ = 1/2ⁿ with probability > 8/π² ≈ 81%
Used in Shor's algorithm (phase = k·ord/N) and quantum chemistry (eigenvalues of H).