量子近似II。Sobolev嵌入
Quantum Approximation II. Sobolev Embeddings
摘要：
从量子计算的角度考虑逼近论的一个基本问题，Sobolev空间W_p^r（[0，1]^d）中的函数在L_q（[0，1]^d）范数下的逼近.我们确定这个问题的量子查询复杂性（对数因子）。事实证明，在参数p，q，r，d的域的某些区域，量子计算可以达到经典确定性或随机近似方法的收敛速度的近似平方。还有其他地区是最好的可能率符合所有三个设置。
英文摘要：
A basic problem of approximation theory, the approximation of functions from the Sobolev space W_p^r([0,1]^d) in the norm of L_q([0,1]^d), is considered from the point of view of quantum computation. We determine the quantum query complexity of this problem (up to logarithmic factors). It turns out that in certain regions of the domain of parameters p,q,r,d quantum computation can reach a speedup of roughly squaring the rate of convergence of classical deterministic or randomized approximation methods. There are other regions were the best possible rates coincide for all three settings.
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