量子均值估计算法研究进展

Research Advances of Quantum Mean Estimation Algorithms

随机变量的均值估计问题一直是经典数据分析中研究的热点,均值估计算法的目的是通过对随机变量尽可能少地采样从而获得尽可能准确的均值估计值。量子计算作为一项革命性的技术,在一些问题上具有超越经典计算的优势。量子算法在均值估计问题上相对于经典算法具有平方加速,展现了量子计算的优越性。该文系统梳理了量子均值估计算法的发展历程,详细介绍了各阶段的算法流程及其优缺点,并对其主要应用场景进行了展示,最后讨论了量子均值估计算法的潜在发展方向。

The problem of estimating the mean of a random variable has long been a focal point of research in classical data analysis.The objective of mean estimation algorithms is to obtain an accurate estimate of the mean with as few samples of the random variable as possible.Quantum computing,as a revolutionary technology,offers advantages over classical computing in certain problems.Quantum algorithms provide a quadratic speedup in the problem of mean estimation,demonstrating the superiority of quantum computing in this aspect.This paper systematically reviews the development of quantum mean estimation algorithms,providing a detailed introduction to the algorithmic processes at each stage,along with their advantages and disadvantages.Furthermore,the primary application scenarios of these algorithms are presented.Finally,potential future directions for the development of quantum mean estimation algorithms are discussed.