QUANTUM COMPLEXITY OF THE APPROXIMATION FOR THE CLASSES Β(Wpr([0, 1]d)) AND Β(Hpr([0, 1]d))

doi:10.1016/S0252-9602(10)60174-9

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (5): 1808-1818.doi: 10.1016/S0252-9602(10)60174-9

QUANTUM COMPLEXITY OF THE APPROXIMATION FOR THE CLASSES Β(W_p^r([0, 1]^d)) AND Β(H_p^r([0, 1]^d))

叶培新, 胡晓菲

School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China; College of Mathematical, Syracuse University, |NY 13210, USA

收稿日期:2006-03-03 修回日期:2008-10-10 出版日期:2010-09-20 发布日期:2010-09-20
基金资助:
Supported by the Natural Science Foundation of China (10501026, 60675010,10971251).

QUANTUM COMPLEXITY OF THE APPROXIMATION FOR THE CLASSES Β(W_p^r([0, 1]^d)) AND Β(H_p^r([0, 1]^d))

YE Pei-Xin, HU Xiao-Fei

School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China; College of Mathematical, Syracuse University, |NY 13210, USA

Received:2006-03-03 Revised:2008-10-10 Online:2010-09-20 Published:2010-09-20
Supported by:
Supported by the Natural Science Foundation of China (10501026, 60675010,10971251).

摘要/Abstract

摘要：

We study the approximation of functions from anisotropic Sobolev classes B(W_p^r}([0, 1]^d)) and H\"{o}lder-Nikolskii classes B(H_p^r}([0, 1]^d)) in the L_q([0, 1]^d) norm with q ≤ p in the quantum model of computation. We determine the quantum query complexity of this problem up to logarithmic factors. It shows that the quantum algorithms are significantly better than the classical deterministic or randomized algorithms.

关键词: quantum approximation, anisotropic classes, minimal query error

Abstract:

Key words: quantum approximation, anisotropic classes, minimal query error

中图分类号:

41A55

叶培新, 胡晓菲. QUANTUM COMPLEXITY OF THE APPROXIMATION FOR THE CLASSES Β(W_p^r([0, 1]^d)) AND Β(H_p^r([0, 1]^d))[J]. 数学物理学报(英文版), 2010, 30(5): 1808-1818.

YE Pei-Xin, HU Xiao-Fei. QUANTUM COMPLEXITY OF THE APPROXIMATION FOR THE CLASSES Β(W_p^r([0, 1]^d)) AND Β(H_p^r([0, 1]^d))[J]. Acta mathematica scientia,Series B, 2010, 30(5): 1808-1818.

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QUANTUM COMPLEXITY OF THE APPROXIMATION FOR THE CLASSES Β(W_p^r([0, 1]^d)) AND Β(H_p^r([0, 1]^d))

QUANTUM COMPLEXITY OF THE APPROXIMATION FOR THE CLASSES Β(W_p^r([0, 1]^d)) AND Β(H_p^r([0, 1]^d))

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