An optimal quantum algorithm to approximate the mean and its application for approximating the median of a set of points over an arbitrary distance

Details An optimal quantum algorithm to approximate the mean and its application for approximating the median of a set of points over an arbitrary distance An optimal quantum algorithm to approximate the mean and its application for approximating the median of a set of points over an arbitrary distance

2011-06-21

arxiv.org/abs/1106.4267v1

Physics

Quantum Physics

Ten pages, no figures, three algorithms

Scientific paper

We describe two quantum algorithms to approximate the mean value of a black-box function. The first algorithm is novel and asymptotically optimal while the second is a variation on an earlier algorithm due to Aharonov. Both algorithms have their own strengths and caveats and may be relevant in different contexts. We then propose a new algorithm for approximating the median of a set of points over an arbitrary distance function.

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