A machine learning approach to Bayesian parameter estimation

TL;DR

This paper introduces a neural network-based method for Bayesian parameter estimation in quantum sensors, reducing calibration demands and improving sensitivity, especially with limited calibration data.

Contribution

It formulates Bayesian estimation as a classification problem and demonstrates neural networks can efficiently perform this task, surpassing standard methods with limited calibration data.

Findings

Neural networks accurately estimate parameters within the quantum sensor's sensitivity limit.

The method outperforms traditional calibration techniques with limited measurements.

It enables adaptive and complex quantum sensing applications.

Abstract

Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its use to proof-of-principle experiments. In this theoretical study, we formulate parameter estimation as a classification task and use artificial neural networks to efficiently perform Bayesian estimation. We show that the network's posterior distribution is centered at the true (unknown) value of the parameter within an uncertainty given by the inverse Fisher information, representing the ultimate sensitivity limit for the given apparatus. When only a limited number of calibration measurements are available, our machine-learning based procedure outperforms standard calibration methods. Thus, our work paves the way for Bayesian quantum sensors which can benefit from efficient optimization methods, such as in adaptive schemes, and take advantage of complex non-classical states. These capabilities can significantly enhance the sensitivity of future devices.