  In principe, General Relativity seems to allow the existence of closed
timelike curves (CTC). However, when quantum effects are considered, it is
likely that their existence is prevented by some kind of chronological
protection mechanism, as Hawking conjectured. Confirming or refuting the
conjecture would require a full quantum theory of gravity. Meanwhile, the use
of simulations could shed some light on this issue. We propose simulations of
CTCs in a quantum system as well as in a classical one. In the quantum
simulation, some restrictions appear that are not present in the classical
setup, which could be interpreted as an analogue of a chronology protection
mechanism.
