  New generations of ultracold-atom experiments are continually raising the
demand for efficient solutions to optimal control problems. Here, we apply
Bayesian optimization to improve a state-preparation protocol recently
implemented in an ultracold-atom system to realize a two-particle fractional
quantum Hall state. Compared to manual ramp design, we demonstrate the superior
performance of our optimization approach in a numerical simulation - resulting
in a protocol that is 10x faster at the same fidelity, even when taking into
account experimentally realistic levels of disorder in the system. We
extensively analyze and discuss questions of robustness and the relationship
between numerical simulation and experimental realization, and how to make the
best use of the surrogate model trained during optimization. We find that
numerical simulation can be expected to substantially reduce the number of
experiments that need to be performed with even the most basic transfer
learning techniques. The proposed protocol and workflow will pave the way
toward the realization of more complex many-body quantum states in experiments.
