An optimal quantum algorithm to approximate the mean and its application for approximating the median of a set of points over an arbitrary distance
Abstract
We describe two quantum algorithms to approximate the mean value of a blackbox 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2011
 DOI:
 10.48550/arXiv.1106.4267
 arXiv:
 arXiv:1106.4267
 Bibcode:
 2011arXiv1106.4267B
 Keywords:

 Quantum Physics;
 Computer Science  Data Structures and Algorithms
 EPrint:
 Ten pages, no figures, three algorithms