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A Lower Bound for Quantum Phase Estimation

Bessen, Arvid J.

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 Q^p 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 Q^p1, Q^p2, ... 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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Academic Units
Computer Science
Publisher
Department of Computer Science, Columbia University
Series
Columbia University Computer Science Technical Reports, CUCS-011-05
Published Here
April 26, 2011
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