Information-efficient belief propagation for closed-loop control and model learning of solid-state quantum emitters

Characterization and control of large arrays of optically active qubits is crucial for achieving large-scale quantum networks but is challenging due to the vast number of distinct parameters of each emitter. Here, accurate tracking and belief propagation of the measured parameters is essential for characterization, control, and model learning. Existing methods, however, are mostly heuristic-based, require extensive manual interaction, and can lead to loss of information about parameters and uncertainties.

We address this challenge by developing a Reinforcement Learning (RL)-based belief propagation network founded on Bayesian principles that evolves alongside the real experiment. The network reflects the known parameters of the system and is continuously updated with each new measured datapoint. By generalizing parameter tracking under one framework, we achieve closed-loop characterization, control, and model learning of SnV emitters in diamond. Information gain is optimized through exploration of the parameter space by RL agents, and Bayesian inference techniques allow us to uncover interdependencies between parameters for model learning. By leveraging this synthesis of Bayesian digital twins and intelligent decision-making, our framework not only reduces the need for manual intervention but also provides a robust, autonomous approach to characterizing, controlling, and understanding medium-scale quantum systems involving complex, multi-parameter dynamics.