Standard quantum amplitude estimation algorithms provide quadratic speedup to Monte-Carlo simulations but require a circuit depth that scales as inverse of the estimation error. In view of the shallow depth in near-term devices, the precision achieved by these algorithms would be low. In this paper we bypass this limitation by performing the classical Monte-Carlo method on the quantum algorithm itself, achieving a higher than classical precision using low-depth circuits. We require the quantum algorithm to be weakly biased in order to avoid error accumulation during this process. Our method is parallel and can be as weakly biased as the constituent algorithm in some cases.

翻译：标准量子振幅估计算法为蒙特卡洛模拟提供了二次加速，但要求电路深度随估计误差的倒数而缩放。考虑到近期设备的浅层深度特性，这些算法所能达到的精度将受到限制。本文通过对量子算法本身执行经典蒙特卡洛方法，绕过了这一限制，从而在低深度电路条件下实现了超越经典方法的精度。为避免在此过程中误差累积，我们要求量子算法具有弱偏差特性。本方法具有并行性，且在特定情况下可实现与组成算法同等程度的弱偏差。