Random-depth Quantum Amplitude Estimation

TL;DR

This paper introduces a modified quantum amplitude estimation algorithm that employs random depths to improve accuracy and robustness, approaching the Heisenberg limit more effectively than previous methods.

Contribution

The paper proposes a novel random-depth approach to enhance the MLAE algorithm, reducing bias and improving convergence to the Heisenberg limit.

Findings

The random-depth MLAE is approximately unbiased.

The new algorithm approaches the Heisenberg limit more closely.

Numerical experiments validate the improved performance.

Abstract

The maximum likelihood amplitude estimation algorithm (MLAE) is a practical solution to the quantum amplitude estimation problem with Heisenberg limit error convergence. We improve MLAE by using random depths to avoid the so-called critical points, and do numerical experiments to show that our algorithm is approximately unbiased compared to the original MLAE and approaches the Heisenberg limit better.