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A Lower Bound for Quantum Phase Estimation

Arvid J. Bessen
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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 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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Arvid J. Bessen. 2005-01-26. A Lower Bound for Quantum Phase Estimation. https://doi.org/10.1103/physreva.71.042313

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