GROVER'S QUANTUM SEARCHING ALGORITHM IS OPTIMAL

I show that for any number of oracle lookups up to about {pi}/4thinsp{radical} (N) , Grover{close_quote}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. {copyright} {ital 1999} {ital The American Physical Society}