Quantum complexity of the approximation for the classes B(Wp ([0, 1])) and B(Hp ([0, 1])) |
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| Authors: | Ye Peixin Hu Xiaofei |
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| Institution: | 1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China;2. College of Mathematical, Syracuse University, NY 13210, USA |
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| Abstract: | We study the approximation of functions from anisotropic Sobolev classes B(Wrp(0,1]d)) and Hölder-Nikolskii classes B(Hrp(0,1]d)) in the Lq(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. |
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| Keywords: | quantum approximation anisotropic classes minimal query error |
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