Quantum Integration in Sobolev Classes
Abstract
We study high dimensional integration in the quantum model of computation. We develop quantum algorithms for integration of functions from Sobolev classes Wrp([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 H\"older classes.
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