Amplitude estimation without phase estimation

TL;DR

This paper introduces a quantum amplitude estimation algorithm that avoids complex controlled operations by using maximum likelihood estimation, making it more feasible for near-term quantum computers while maintaining near-optimal speedup.

Contribution

The paper presents a novel amplitude estimation method that eliminates the need for controlled operations, simplifying implementation on current quantum hardware.

Findings

Achieves near-optimal quantum speedup asymptotically

Reduces circuit complexity compared to traditional methods

Demonstrates effectiveness through numerical simulations

Abstract

This paper focuses on the quantum amplitude estimation algorithm, which is a core subroutine in quantum computation for various applications. The conventional approach for amplitude estimation is to use the phase estimation algorithm, which consists of many controlled amplification operations followed by a quantum Fourier transform. However, the whole procedure is hard to implement with current and near-term quantum computers. In this paper, we propose a quantum amplitude estimation algorithm without the use of expensive controlled operations; the key idea is to utilize the maximum likelihood estimation based on the combined measurement data produced from quantum circuits with different numbers of amplitude amplification operations. Numerical simulations we conducted demonstrate that our algorithm asymptotically achieves nearly the optimal quantum speedup with a reasonable circuit length.