Research Advances of Quantum Mean Estimation Algorithms

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.