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First I will present the first experimental quantum simulation of "unphysical'" operations beyond the regime of unitary and dissipative evolutions through the embedding of the dynamics in the electronic multi-levels of an Yb 171 ion.The implementation of fundamental useful anti-linear operations such as the complex conjugate in a quantum device is considered to be impossible due to the linear character of quantum mechanics.We successfully observe the dynamics of the Majorana equation in a physical system and perform anti-unitary symmetry operators such as time reversal and charge conjugation.Our approach offers the possibility to add "unphysical" operations to the toolbox of quantum simulation and quantum computation,therefore providing a new route to efficiently compute otherwise intractable quantities as entanglement monotones or time correlation functions.Then I will report on the first experimental quantum simulation of interacting quantum field modes with trapped ions,using a model of a fermion and an anti-fermion field modes interacting via bosonic field modes.