  We analyze the efficiency of quantum simulations of fermionic and bosonic
models in trapped ions. In particular, we study the optimal time of entangling
gates and the required number of total elementary gates. Furthermore, we
exemplify these estimations in the light of quantum simulations of quantum
field theories, condensed-matter physics, and quantum chemistry. Finally, we
show that trapped-ion technologies are a suitable platform for implementing
quantum simulations involving interacting fermionic and bosonic modes, paving
the way for overcoming classical computers in the near future.
