Quantum integration error for some sobolev classes

Authors:
Ye Peixin;Hu Xiaofei
Affiliations:
School of Mathematical Sciences and LPMC, Nankai University, Tianjin, China;College of Mathematical, Syracuse University, NY
Venue:
ICNC'06 Proceedings of the Second international conference on Advances in Natural Computation - Volume Part II
Year:
2006

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Abstract

Based on the quantum algorithms for approximating the mean of p-summable sequences, we develop quantum algorithms for approximating the integration from anisotropic and generalized Sobolev classes. Then we analyze query error of these algorithms and prove their optimality. It is proved that for these classes of functions the optimal convergence rates of quantum algorithms are essential smaller than those of classical deterministic and randomized algorithms. Our results extend recent works of Heinrich on classical Sobolev classes.