Neural networks for Bayesian quantum many-body magnetometry

. Entangled quantum many-body systems can be used as sensors that enable the estimation of parameters with a precision larger than that achievable with ensembles of individual quantum detectors. Typically, the parameter estimation strategy requires the microscopic modelling of the quantum many-body system, as well as a an accurate description of its dynamics. This entails a complexity that can hinder the applicability of Bayesian inference techniques. In this work we show how to circumvent these issues by using neural networks that faithfully reproduce the dynamics of quantum many-body sensors, thus allowing for an e ﬃ cient Bayesian analysis. We exemplify with an XXZ model driven by magnetic ﬁelds, and show that our method is capable to yield an estimation of ﬁeld parameters beyond the standard quantum limit scaling. Our work paves the way for the practical use of quantum many-body systems as black-box sensors exploiting quantum resources to improve precision estimation.