What if QPE input is not an exact eigenstate?

Question: Standard Quantum Phase Estimation is applied to a state |ψ⟩ that is a superposition of eigenstates of U. What happens ideally? A) The algorithm always returns the arithmetic mean of all eigenphases B) The algorithm fails because QPE requires a classically known eigenvector C) The algorithm measures an eigenphase with probability related to the squared overlap of |ψ⟩ with the corresponding eigenstate D) The inverse QFT converts the superposition into a single deterministic phase bitstring Correct: C Explanation: If the input is not one eigenstate, it decomposes into eigencomponents. Phase estimation correlates the phase register with those components, and measurement samples an eigenphase according to the input state's spectral weight. Topic: advanced quantum computing / phase estimation / spectral sampling