Abstract
We study the approximation of the integration of multivariate functions classes in the quantum model of computation. We first obtain a lower bound of the n-th minimal query error for integration on anisotropic Sobolev-Slobodezkii classes. Then combining our previous results we determine the optimal bound of n-th minimal query error for anisotropic Hölder-Nikolskii class and Sobolev class. The results show that for these two type of classes the quantum algorithms give significant speed up over classical deterministic and randomized algorithms.
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Ye, P., He, Q. (2007). Quantum Integration Error on Some Classes of Multivariate Functions. In: Huang, DS., Heutte, L., Loog, M. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Contemporary Intelligent Computing Techniques. ICIC 2007. Communications in Computer and Information Science, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74282-1_52
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DOI: https://doi.org/10.1007/978-3-540-74282-1_52
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74281-4
Online ISBN: 978-3-540-74282-1
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