Quantum simulations of time-dependent Hamiltonians beyond the quasistatic approximation

Existing approaches to analog 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 multimode Fourier expansion. The potential of the quantum simulations that can be achieved with our approach is demonstrated with the pedagogical example of a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi mathvariant="normal">Λ</a:mi></a:math> system and the quench in finite time through a quantum phase transition of a Chern insulator in a driven noninteracting Hubbard system. The example of the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi mathvariant="normal">Λ</c:mi></c:math> system demonstrates the ability of our approach to describe situations beyond the validity of adiabatic approximations. Published by the American Physical Society 2024