Parameter estimation by learning quantum correlations in continuous photon-counting data using neural networks

TL;DR

This paper introduces a neural network-based method for estimating parameters from quantum photon-counting data, achieving near-optimal precision with lower computational costs and robustness to imperfections.

Contribution

The paper presents a novel neural network approach for quantum parameter estimation using photon-counting data, outperforming traditional methods in efficiency and robustness.

Findings

Achieves near-Bayesian optimal precision in parameter estimation.

Reduces computational costs compared to Bayesian inference.

Demonstrates robustness against measurement and training data imperfections.

Abstract

We present an inference method utilizing artificial neural networks for parameter estimation of a quantum probe monitored through a single continuous measurement. Unlike existing approaches focusing on the diffusive signals generated by continuous weak measurements, our method harnesses quantum correlations in discrete photon-counting data characterized by quantum jumps. We benchmark the precision of this method against Bayesian inference, which is optimal in the sense of information retrieval. By using numerical experiments on a two-level quantum system, we demonstrate that our approach can achieve a similar optimal performance as Bayesian inference, while drastically reducing computational costs. Additionally, the method exhibits robustness against the presence of imperfections in both measurement and training data. This approach offers a promising and computationally efficient tool for quantum parameter estimation with photon-counting data, relevant for applications such as quantum sensing or quantum imaging, as well as robust calibration tasks in laboratory-based settings.