Lower bound for quantum phase estimation

@article{Bessen2005LowerBF,
  title={Lower bound for quantum phase estimation},
  author={Arvid J. Bessen},
  journal={Physical Review A},
  year={2005},
  volume={71},
  pages={042313}
}
  • A. J. Bessen
  • Published 1 December 2004
  • Computer Science
  • Physical Review A
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 $\ensuremath{\Omega}(\mathrm{log}\phantom{\rule{0.2em}{0ex}}1∕ϵ)$ lower bound for the number of applications of ${Q}^{{p}_{1}}$, ${Q}^{{p}_{2}},\dots{}$. This bound is tight due to… 

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