Elsevier

Journal of Complexity

Volume 19, Issue 1, February 2003, Pages 19-42
Journal of Complexity

Quantum integration in Sobolev classes

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Abstract

We study high-dimensional integration in the quantum model of computation. We develop quantum algorithms for integration of functions from Sobolev classes Wpr([0,1]d) and analyze their convergence rates. We also prove lower bounds which show that the proposed algorithms are, in many cases, optimal within the setting of quantum computing. This extends recent results of Novak on integration of functions from Hölder classes.

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