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.
Author: | S. Heinrich |
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URN: | urn:nbn:de:hbz:386-kluedo-49444 |
Series (Serial Number): | Interner Bericht des Fachbereich Informatik (312) |
Document Type: | Report |
Language of publication: | English |
Date of Publication (online): | 2017/10/25 |
Year of first Publication: | 2001 |
Publishing Institution: | Technische Universität Kaiserslautern |
Date of the Publication (Server): | 2017/10/25 |
Page Number: | 48 |
Faculties / Organisational entities: | Kaiserslautern - 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) |