Quantum Simulations with Trapped Ions

I will review the research we have been developing at UPV/EHU Bilbao regarding quantum simulations in trapped ions. I will explain the possibility to simulate relativistic quantum mechanics in trapped ions, including the Dirac equation and Zitterbewegung [1,2], Klein's paradox [3,4], two interacting Dirac particles [5], and the Majorana equation [6]. Then, I will describe a scalable approach towards the simulation of quantum field theories in trapped ions [7], and also the realization of interacting fermion lattice models in an efficient manner [8,9]. Finally, I will propose an implementation of protected qubits in trapped ions by means of Majorana fermions [10], and the research lines I intend to pursue in the future.

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