Quantum simulations of time-dependent Hamiltonians beyond the quasi-static approximation

Existing approaches to analogue quantum simulations of time-dependent quantum systems rely on perturbative corrections to the time-independence of the systems to be simulated. We overcome this restriction to perturbative approaches and demonstrate the potential of achievable quantum simulations 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 Hubbard system.