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Quantum Summation with an Application to Integration

  • We study summation of sequences and integration in the quantum model of computation. We develop quantum algorithms for computing the mean of sequences which satisfy a \(p\)-summability condition and for integration of functions from Lebesgue spaces \(L_p([0,1]^d)\) 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 Brassard, Høyer, Mosca, and Tapp (2000) on computing the mean for bounded sequences and complements results of Novak (2001) on integration of functions from Hölder classes.

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Author:S. Heinrich
URN (permanent link):urn:nbn:de:hbz:386-kluedo-49444
Serie (Series number):Interner Bericht des Fachbereich Informatik (312)
Document Type:Report
Language of publication:English
Publication Date:2017/10/25
Year of Publication:2001
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2017/10/25
Number of page:48
Faculties / Organisational entities:Fachbereich Informatik
DDC-Cassification:0 Allgemeines, Informatik, Informationswissenschaft / 004 Informatik
Licence (German):Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0)