Demonstration of machine-learning-enhanced Bayesian quantum state estimation

Abstract

Machine learning (ML) has found broad applicability in quantum information science in topics as
diverse as experimental design, state classification, and even studies on quantum foundations. Here, we experimentally realize an approach for defining custom prior distributions that are automatically tuned using ML for Bayesian quantum state estimation methods that generally better conform to the physical properties of the underlying system than standard fixed prior distributions. Previously, researchers have looked to Bayesian quantum state tomography for advantages like uncertainty quantification, the return of reliable estimates under any measurement condition, and minimal mean-squared error. However, practical challenges related to long computation times and conceptual issues concerning how to incorporate prior knowledge most suitably can overshadow these benefits. Using both simulated and experimental measurement results, we demonstrate that ML-defined prior distributions reduce net convergence times and provide a natural way to incorporate both implicit and explicit information directly into the prior distribution. These results constitute a promising path toward practical implementations of Bayesian quantum state tomography.

A Bayesian quantum state tomography along with adaptive frameworks based on linear minimum mean square error criterion

“…It does not assume that the quantum state itself will vary following a prior. Recently, performance improvement of machine learning-based QST and Bayesian QST with limited prior distribution has been discussed in [27,28]. Moreover, experimental realization of adaptive tomography has been demonstrated in [29].…”