A Lower Bound for Quantum Phase Estimation
Arvid J. Bessen
Abstract
We obtain a query lower bound for quantum algorithms solving the phase estimation problem. Our analysis generalizes existing lower bound approaches to the case where the oracle Q is given by controlled powers Qp of Q, as it is for example in Shor's order finding algorithm. In this setting we will prove a log (1/epsilon) lower bound for the number of applications of Qp1, Qp2, ... This bound is tight due to a matching upper bound. We obtain the lower bound using a new technique based on frequency analysis.
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