  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.
