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Machine learning (ML) has found broad applicability in quantum informationscience in topics as diverse as experimental design, state classification, andeven studies on quantum foundations. Here, we experimentally realize anapproach for defining custom prior distributions that are automatically tunedusing ML for use with Bayesian quantum state estimation methods. Previously,researchers have looked to Bayesian quantum state tomography due to its uniqueadvantages like natural uncertainty quantification, the return of reliableestimates under any measurement condition, and minimal mean-squared error.However, practical challenges related to long computation times and conceptualissues concerning how to incorporate prior knowledge most suitably canovershadow these benefits. Using both simulated and experimental measurementresults, we demonstrate that ML-defined prior distributions reduce netconvergence times and provide a natural way to incorporate both implicit andexplicit information directly into the prior distribution. These resultsconstitute a promising path toward practical implementations of Bayesianquantum state tomography.

Demonstration of machine-learning-enhanced Bayesian quantum state estimation