  A quantum simulator is a device engineered to reproduce the properties of an
ideal quantum model. It allows the study of quantum systems that cannot be
efficiently simulated on classical computers. While a universal quantum
computer is also a quantum simulator, only particular systems have been
simulated up to now. Still, there is a wealth of successful cases, such as spin
models, quantum chemistry, relativistic quantum physics and quantum phase
transitions. Here, we show how to design a quantum simulator for the Majorana
equation, a non-Hamiltonian relativistic wave equation that might describe
neutrinos and other exotic particles beyond the standard model. The simulation
demands the implementation of charge conjugation, an unphysical operation that
opens a new front in quantum simulations, including the discrete symmetries
associated with complex conjugation and time reversal. Finally, we show how to
implement this general method in trapped ions.
