arXiv quant-ph/01121532001-12-23quant-ph

Sobolev类中的量子积分

Quantum Integration in Sobolev Classes

Stefan Heinrich

备注：: Paper submitted to the Journal of Complexity. 28 pages

摘要：

我们研究量子计算模型中的高维积分。我们开发了Sobolev类函数积分的量子算法$W^r_p([0,1]^d)$，并分析了它们的收敛速度。我们还证明了下界表明，所提出的算法，在许多情况下，最佳的量子计算的设置内。这扩展了最近的结果诺瓦克整合功能从霍德尔类。

英文摘要：

We study high dimensional integration in the quantum model of computation. We develop quantum algorithms for integration of functions from Sobolev classes $W^r_p([0,1]^d)$ and analyze their convergence rates. We also prove lower bounds which show that the proposed algorithms are, in many cases, optimal within the setting of quantum computing. This extends recent results of Novak on integration of functions from Hölder classes.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。