Variational quantum amplitude estimation

TL;DR

This paper introduces a variational quantum algorithm for amplitude estimation using shallow circuits, combining it with maximum likelihood methods, and demonstrates its potential to outperform classical Monte Carlo sampling in small-scale simulations.

Contribution

It presents a novel variational quantum amplitude estimation (VQAE) method that reduces quantum circuit depth and computational cost, improving efficiency over previous approaches.

Findings

Shallow circuits can accurately perform amplitude amplification.

Adaptive VQAE can outperform classical Monte Carlo sampling in small qubit simulations.

Numerical results show potential advantages of the proposed method.

Abstract

We propose to perform amplitude estimation with the help of constant-depth quantum circuits that variationally approximate states during amplitude amplification. In the context of Monte Carlo (MC) integration, we numerically show that shallow circuits can accurately approximate many amplitude amplification steps. We combine the variational approach with maximum likelihood amplitude estimation [Y. Suzuki et al., Quantum Inf. Process. 19, 75 (2020)] in variational quantum amplitude estimation (VQAE). VQAE typically has larger computational requirements than classical MC sampling. To reduce the variational cost, we propose adaptive VQAE and numerically show in 6 to 12 qubit simulations that it can outperform classical MC sampling.