This proposal is framed in the timely and novel field of quantum simulations of relativistic and quantum field theory systems. In the field of quantum information, quantum simulations of physical systems difficult to measure in the lab, with other, controllable, quantum systems, appear as one of the most promising avenues. Due to the difficulty to analyze some physical systems in the lab, or the limitations of classical simulations of quantum systems with standard computers, quantum simulations have raised much interest in the quantum information science. Simulating quantum relativistic systems with quantum optics setups, could shed much light on the fundamental properties of these relevant systems. In addition, it could establish interesting analogies and differences between the relativistic and the quantum optics systems, making a very multidisciplinary study. Prominent examples of already proposed scenarios are Dirac equation simulation in a single trapped ion, or black hole radiation in a Bose-Einstein condensate. Here, further interesting quantum relativistic systems, like Dirac fermions in interaction, quantum fields, exotic topological effects, or rotating and charged black holes, are proposed for their simulation in trapped ions, electrons in Penning traps, or cold atoms. Soon-to-be-made quantum simulations will already be able to overcome classical simulations with even the fastest classical supercomputers. Europe has maintained a leading position both in high energy physics and in quantum information, and this project will contribute to maintain this leadership from a modern and multidisciplinary approach.