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

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