Quantum integration in Sobolev classes
نویسنده
چکیده
We study high dimensional integration in the quantum model of computation. We develop quantum algorithms for integration of functions from Sobolev classes W r p ([0, 1] ) 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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عنوان ژورنال:
- J. Complexity
دوره 19 شماره
صفحات -
تاریخ انتشار 2003