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

Published 2011-06-21Version 1

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.