On the Power of Quantum Algorithms for Vector Valued Mean Computation

Abstract

We study computation of the mean of sequences with values in finite dimensional normed spaces and compare the computational power of classical randomized with that of quantum algorithms for this problem. It turns out that in contrast to the known superiority of quantum algorithms in the scalar case, in high dimensional $L_p^M$ spaces classical randomized algorithms are essentially as powerful as quantum algorithms.

Paper submitted to 'Monte Carlo Methods and Applications', 18 pages