  Digital quantum simulation uses the capabilities of quantum computers to
determine the dynamics of quantum systems, which are beyond the computability
of modern classical computers. A notoriously challenging task in this field is
the description of non-equilibrium dynamics in quantum many-body systems. Here
we use the IBM quantum computers to simulate the non-equilibrium dynamics of
few spin and fermionic systems. Our results reveal, that with a combination of
error mitigation, noise extrapolation and optimized initial state preparation,
one can tackle the most important drawbacks of modern quantum devices. The
systems we simulate demonstrate the potential for large scale quantum
simulations of light-matter interactions in the near future.
