Quantum Phase Estimation Algorithm

QPE estimates the eigenphase φ of a unitary U: U|ψ⟩ = e^{2πiφ}|ψ⟩. Using t ancilla qubits and the QFT, it achieves precision 1/2ᵗ. QPE underlies Shor's algorithm, quantum chemistry simulation, and the HHL algorithm for linear systems.

True phase φ0.333
Ancilla qubits t4
Noise level ε0.000
True phase φ
0.333
Estimated φ̂
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Error |φ−φ̂|
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