  Existing approaches to analogue quantum simulations of time-dependent quantum
systems rely on perturbative corrections to quantum simulations of
time-independent quantum systems. We overcome this restriction to perturbative
treatments with an approach based on flow equations and a multi-mode Fourier
expansion. The potential of the quantum simulations that can be achieved with
our approach is demonstrated with the pedagogical example of a Lambda-system
and the quench in finite time through a quantum phase transition of a Chern
insulator in a driven non-interacting Hubbard system. The example of the
Lambda-system demonstrates the ability of our approach to describe situations
beyond the validity of adiabatic approximations.
