Grover’s quantum searching algorithm is optimal

Abstract

I show that for any number of oracle lookups up to about $\ensuremath{\pi}/4\sqrt{N},$ Grover's quantum searching algorithm gives the maximal possible probability of finding the desired element. I explain why this is also true for quantum algorithms which use measurements during the computation. I also show that unfortunately quantum searching cannot be parallelized better than by assigning different parts of the search space to independent quantum computers.