Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Communications in computer and information science

Quantum Integration Error on Some Classes of Multivariate Functions

Peixin Ye, Qing He

Published Jan 1, 2007• 0 citations
Publisher
DOI
10.1007/978-3-540-74282-1_52

Related papers

Integration error for multivariate functions from anisotropic classes

Fang Gensun, Peixin Ye

Journal of Complexity•Apr 4, 2003•20 citations

Error analysis and tractability for multivariate integration and approximation

F HUANG

•Jan 1, 2004•0 citations

Quantum Integration Error for Some Sobolev Classes

Peixin Ye, Hu Xiaofei

Lecture notes in computer science•Jan 1, 2006•2 citations

Lower Bound for Quantum Integration Error on Some Sobolev Classes

Peixin Ye

We study the approximation of the integration of multivariate functions in the quantum model of computation. Using a new reduction approach we obtain a lower bound of the n-th minimal query error on anisotropic Sobolev classes B(Wpr([0, 1]d)), (r isin R+d). Then combining our previous results we determine the optimal bound of nth minimal query error for anisotropic Holder-Nikolskii class B(Hinfinr([0, 1]d)), (r isin R+d) and Sobolev class B(Wpr([0, 1]d)) (r isin Nd). The results show the quantum algorithms give speed up over classical algorithms.

International Conference on Natural Computation (ICNC)•Jan 1, 2008•0 citations

Cubature and Reconstruction of Smooth Isotropic Random Functions

K. Ritter, G.W. Wasilkowski

We propose isotropic probability measures defined on classes of smooth multivariate functions. These provide a natural extension of the classical isotropic Wiener measure to multivariate functions from C 2r . We show that in the corresponding average case setting the minimal errors of algorithms that use n function values are Θ (n -(d+4r+1)/2d ) and Θ (n -(4r+1)/2d ) for the integration and L 2 -approximation problems respectively. Here d is the number of variables of the corresponding class of functions. This means that the minimal average errors depend essentially on the number d of variables. In particular, for d large relative to r, the L 2 -approximation problem is intractable. The integration and L 2 -approximation problems have been recently studied with measures whose covariance kernels are tensor products. The results for these measures and for isotropic measures differ significantly.

•Jan 1, 1997•0 citations

The Evaluation of Quantum Integrals

Edwin C. Kemble

Proceedings of the National Academy of Sciences•Oct 1, 1921•4 citations
We study the approximation of the integration of multivariate functions in the quantum model of computation. Using a new reduction approach we obtain a lower bound of the n-th minimal query error on anisotropic Sobolev classes B(Wpr([0, 1]d)), (r isin R+d). Then combining our previous results we determine the optimal bound of nth minimal query error for anisotropic Holder-Nikolskii class B(Hinfinr([0, 1]d)), (r isin R+d) and Sobolev class B(Wpr([0, 1]d)) (r isin Nd). The results show the quantum algorithms give speed up over classical algorithms.
We propose isotropic probability measures defined on classes of smooth multivariate functions. These provide a natural extension of the classical isotropic Wiener measure to multivariate functions from C 2r . We show that in the corresponding average case setting the minimal errors of algorithms that use n function values are Θ (n -(d+4r+1)/2d ) and Θ (n -(4r+1)/2d ) for the integration and L 2 -approximation problems respectively. Here d is the number of variables of the corresponding class of functions. This means that the minimal average errors depend essentially on the number d of variables. In particular, for d large relative to r, the L 2 -approximation problem is intractable. The integration and L 2 -approximation problems have been recently studied with measures whose covariance kernels are tensor products. The results for these measures and for isotropic measures differ significantly.