Low depth amplitude estimation without really trying

TL;DR

This paper introduces a quantum amplitude estimation method that achieves higher precision with low-depth circuits by integrating classical Monte-Carlo techniques, suitable for near-term quantum devices.

Contribution

It proposes a novel hybrid quantum-classical approach that bypasses depth limitations of standard amplitude estimation algorithms.

Findings

Achieves higher precision with shallow quantum circuits.

Requires the quantum algorithm to be weakly biased.

Method is parallel and adaptable to different biases.

Abstract

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.