  Direct experimental access to some of the most intriguing quantum phenomena
is not granted due to the lack of precise control of the relevant parameters in
their naturally intricate environment. Their simulation on conventional
computers is impossible, since quantum behaviour arising with superposition
states or entanglement is not efficiently translatable into the classical
language. However, one could gain deeper insight into complex quantum dynamics
by experimentally simulating the quantum behaviour of interest in another
quantum system, where the relevant parameters and interactions can be
controlled and robust effects detected sufficiently well. We report on the
progress in experimentally simulating quantum many-body physics with trapped
ions.
