Quantum Integration in Sobolev Classes

Details Quantum Integration in Sobolev Classes Quantum Integration in Sobolev Classes

2001-12-23

arxiv.org/abs/quant-ph/0112153v1

Physics

Quantum Physics

Paper submitted to the Journal of Complexity. 28 pages

Scientific paper

We study high dimensional integration in the quantum model of computation. We develop quantum algorithms for integration of functions from Sobolev classes $W^r_p([0,1]^d)$ 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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