  In this work, we study the real-time evolution of periodically driven
(Floquet) systems on a quantum computer using IBM quantum devices. We consider
a driven Landau-Zener model and compute the transition probability between the
Floquet steady states as a function of time. We find that for this simple
one-qubit model, Floquet states can develop in real-time, as indicated by the
transition probability between Floquet states. Next, we model light-driven spin
chains and compute the time-dependent antiferromagnetic order parameter. We
consider models arising from light coupling to the underlying electrons as well
as those arising from light coupling to phonons. For the two-spin chains, the
quantum devices yield time evolutions that match the effective Floquet
Hamiltonian evolution for both models once readout error mitigation is
included. For three-spin chains, zero-noise extrapolation yields a time
dependence that follows the effective Floquet time evolution. Therefore, the
current IBM quantum devices can provide information on the dynamics of small
Floquet systems arising from light drives once error mitigation procedures are
implemented.
