  We combine quantum optimal control with a variational ansatz based on
non-Gaussian states for fast, non-adiabatic preparation of quantum many-body
states. We demonstrate this on the example of the spin-boson model, and use a
multi-polaron ansatz to prepare near-critical ground states. For one mode, we
achieve a reduction in infidelity of up to $\approx 60$ ($\approx 20$) times
compared to linear (optimised local adiabatic) ramps respectively; for many
modes we achieve a reduction in infidelity of up to $\approx 5$ times compared
to non-adiabatic linear ramps. Further, we show that the typical control
quantity, the leakage from the variational manifold, provides only a loose
bound on the state's fidelity. Instead, in analogy to the bond dimension of
matrix product states, we suggest a controlled convergence criterion based on
the number of polarons. Finally, motivated by the possibility of realizations
in trapped ions, we study the dynamics of a system with bath properties going
beyond the paradigm of (sub/super) Ohmic couplings. We apply the ansatz to the
study of the out-of-time-order-correlator (OTOC) of the bath modes in a
non-perturbative regime. The scrambling time is found to be a robust feature
only weakly dependent on the details of the coupling between the bath and the
spin.
