量子计算模型中的Sobolev近似

2011 Fourth International Conference on Intelligent Computation Technology and Automation Pub Date : 2011-03-28 DOI:10.1109/ICICTA.2011.69

Peixin Ye, Xiuhua Yuan

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引用次数: 0

摘要

使用一种新的优雅的约简方法，我们推导了从各向异性Sobolev类B(Wrp([0,1]d))到各向异性Sobolev空间Wsp([0,1]d)的嵌入近似的量子复杂性的下界。P q ?当p ?我们通过推导匹配的上界来证明这个界是最优的。在这种情况下，量子算法并不明显优于经典的确定性或随机算法。

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Sobolev Approximation in the Quantum Computation Model

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(Wrp([0,1]d)) to anisotropic Sobolev space Wsp([0,1]d) for all 1 ? p, q ? ?, When p ? q we show this bound is optimal by deriving the matching upper bound. In this case the quantum algorithms are not significantly better than the classical deterministic or randomized algorithms.

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2011 Fourth International Conference on Intelligent Computation Technology and Automation

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