量子近似I.有限维L_p空间的嵌入
Quantum Approximation I. Embeddings of Finite Dimensional L_p Spaces
摘要：
研究量子计算模型中有限维L_p空间之间嵌入的逼近问题。对于这个问题的量子查询的复杂性匹配（对数因子）的上限和下限。结果表明，对于参数域的某些区域，量子计算可以从根本上提高经典确定性或随机近似的收敛速度，而在其他区域，所有三种设置的最佳可能速率一致。这些结果作为一个重要的积木分析函数空间中的逼近在随后的文件。
英文摘要：
We study approximation of embeddings between finite dimensional L_p spaces in the quantum model of computation. For the quantum query complexity of this problem matching (up to logarithmic factors) upper and lower bounds are obtained. The results show that for certain regions of the parameter domain quantum computation can essentially improve the rate of convergence of classical deterministic or randomized approximation, while there are other regions where the best possible rates coincide for all three settings. These results serve as a crucial building block for analyzing approximation in function spaces in a subsequent paper.
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。
