Abstract

I improve the tight bound on quantum searching [4] to a matching bound, thus showing that for any probability of success Grover’s quantum searching algorithm is optimal. E.g. for near certain success we have to query the oracle π/4 √ 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. 1 Quantum searching Imagine we have N cases of which only one fulfills our conditions. E.g. we have a function which gives 1 only for one of N possible input values and gives 0 otherwise. Often an analysis of the algorithm for calculating the function will allow us to find the input value for which the output is 1. Here we consider the case where we don’t know better than to repeatedly calculate the function

Citations

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