  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.
