Bayesian optimization for state engineering of quantum gases

State engineering of quantum objects is a central requirement in most implementations. In the cases where the quantum dynamics can be described by analytical solutions or simple approximation models, optimal state preparation protocols have been theoretically proposed and experimentally realized. For more complex systems, however, such as multi-component quantum gases, simplifying assumptions do not apply anymore and the optimization techniques become computationally impractical. Here, we propose Bayesian optimization based on multi-output Gaussian processes to learn the quantum state's physical properties from few simulations only. We evaluate its performance on an optimization study case of diabatically transporting a Bose-Einstein condensate while keeping it in its ground state, and show that within only few hundreds of executions of the underlying physics simulation, we reach a competitive performance with other protocols. While restricting this benchmarking to well known approximations for straightforward comparisons, we expect a similar performance when employing more involving models, which are computationally more challenging. This paves the way to efficient state engineering of complex quantum systems.