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arXiv · 1106.4267

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

Gilles Brassard·Frederic Dupuis·Sebastien Gambs·Alain Tapp
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Abstract

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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Gilles Brassard, Frederic Dupuis, Sebastien Gambs, Alain Tapp. 2011-06-21. An optimal quantum algorithm to approximate the mean and its application for approximating the median of a set of points over an arbitrary distance. https://arxiv.org/abs/1106.4267

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