Demonstration of machine-learning-enhanced Bayesian quantum state estimation

TL;DR

This paper demonstrates an experimental approach where machine learning is used to automatically tune prior distributions for Bayesian quantum state estimation, improving convergence times and incorporating prior knowledge effectively.

Contribution

The authors introduce a method for defining ML-tuned prior distributions that enhance Bayesian quantum state estimation, addressing computational and conceptual challenges.

Findings

ML-defined priors reduce convergence times

Enhanced incorporation of prior knowledge

Validated with simulated and experimental data

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 use with Bayesian quantum state estimation methods. Previously, researchers have looked to Bayesian quantum state tomography due to its unique advantages like natural 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.