Grover's quantum searching algorithm is optimal

Details Grover's quantum searching algorithm is optimal Grover's quantum searching algorithm is optimal

1997-11-26

arxiv.org/abs/quant-ph/9711070v2

Phys.Rev. A60 (1999) 2746-2751

Physics

Quantum Physics

13 pages, LaTeX, essentially published version

Scientific paper

10.1103/PhysRevA.60.2746

I improve the tight bound on quantum searching by Boyer et al. (quant-ph/9605034) to a matching bound, thus showing that for any probability of success Grovers quantum searching algorithm is optimal. E.g. for near certain success we have to query the oracle pi/4 sqrt{N} times, where N is the size of the search space. I also show that unfortunately quantum searching cannot be parallelized better than by assigning different parts of the search space to independent quantum computers. Earlier results left open the possibility of a more efficient parallelization.

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