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Complexity for the approximation of Sobolev imbeddings in the quantum computation model

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3 Author(s)
Jingfan Long ; Beijing Information Science and Technology University, 100101, China ; Peixin Ye ; Xiuhua Yuan

Using a new and elegant reduction approach we derive a lower bound of quantum complexity for the approximation of imbeddings from anisotropic Sobolev classes B(Wpr([0, 1]d)) to anisotropic Sobolev space Wps([0, 1]d) for all 1 ≤ p, q ≤ ∞. When p ≥ q this bound is optimal. In this case the quantum algorithms are not significantly better than the classical deterministic or randomized algorithms. When p ≥ q we conjecture that quantum algorithms bring speed-up over the classical deterministic and randomized ones. This conjecture was confirmed in the situation s = 0.

Published in:

Control Conference (CCC), 2011 30th Chinese

Date of Conference:

22-24 July 2011