A machine learning approach to Bayesian parameter estimation

Year: 2021

Authors: Nolan S.; Smerzi A.; Pezze L.

Autors Affiliation: QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, Firenze, 50125, Italy

Abstract: Bayesian estimation is a powerful theoretical paradigm for the operation of the approach to parameter estimation. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its use to systems that can be explicitly modeled. 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. Our machine-learning-based procedure is model independent, and is thus well suited to “”black-box sensors””, which lack simple explicit fitting models. Thus, our work paves the way for Bayesian quantum sensors that can take advantage of complex nonclassical quantum states and/or adaptive protocols. These capabilities can significantly enhance the sensitivity of future devices.


Volume: 7 (1)      Pages from: 169-1  to: 169-8

More Information: We would like to thank V. Gebhart for useful discussions. We acknowledge funding from the project EMPIR-USOQS, EMPIR projects are co-funded by the European Unions Horizon2020 research and innovation program and the EMPIR Participating States. We also acknowledge financial support from the European Union´s Horizon 2020 research and innovation program -Qombs Project, FET Flagship on Quantum Technologies grant no. 820419, and from the H2020 QuantERA ERA-NET Cofund in Quantum Technologies projects QCLOCKS and CEBBEC.
KeyWords: quantum; states
DOI: 10.1038/s41534-021-00497-w