  Universal control over a bosonic degree of freedom is key in the quest for
quantum-based technologies. Such universal control requires however the ability
to perform demanding non-Gaussian gates -- namely, higher-than-quadratic
interactions at the level of the bosonic operators. Here we consider a single
ancillary two-level system, interacting with the bosonic mode of interest via a
driven quantum Rabi model, and show that it is sufficient to induce the
deterministic realization of a large class of Gaussian and non-Gaussian gates,
which in turn provide universal bosonic control. This scheme reduces the
overhead of previous ancilla-based methods where long gate-sequences are
required to generate highly populated targets. In fact, our method naturally
yields the high-fidelity preparation of multi-squeezed states -- i.e., the
high-order generalization of displaced and squeezed states -- which feature
large phase-space Wigner negativities. The universal control is further
illustrated by generating a cubic-phase gate. Finally, we address the
resilience of the method in the presence of realistic noise. Due to the
ubiquity of the considered interaction, our scheme might open new avenues in
the design, preparation, and control of bosonic states in different setups.
