Lower bounds of a quantum search for an extreme point
Abstract
We show that DurrHoyer's quantum algorithm of searching for extreme point of integer function can not be sped up for functions chosen randomly. Any other algorithm acting in substantially shorter time $o(\sqrt{2^n})$ gives incorrect answer for the functions with the single point of maximum chosen randomly with probability converging to 1. The lower bound as $\Omega (\sqrt{2^n /b})$ was established for the quantum search for solution of equations $f(x)=1$ where $f$ is a Boolean function with $b$ such solutions chosen at random with probability converging to 1.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 June 1999
 DOI:
 10.1098/rspa.1999.0397
 arXiv:
 arXiv:quantph/9806001
 Bibcode:
 1999RSPSA.455.2165O
 Keywords:

 Quantum Physics
 EPrint:
 Some minor changes