Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for implementing Monte Carlo procedures using quantum circuits, focusing on the potential to obtain a quantum advantage in the computational speed of these procedures. We revisit the quantum algorithms that could replace classical Monte Carlo and then consider both the existing quantum algorithms and the potential quantum realizations that include adaptive enhancements as alternatives to the classical procedure.

翻译：蒙特卡洛采样是一套强大的算法工具箱，广泛应用于各类需要估计含噪量或其汇总统计量的场景。本文综述了利用量子线路实现蒙特卡洛过程的相关文献，重点关注这些过程在计算速度方面获得量子优势的潜力。我们重新审视了可能替代经典蒙特卡洛方法的量子算法，进而探讨了现有量子算法及包含自适应增强的潜在量子实现方案，以作为经典蒙特卡洛过程的替代选择。