Quantum simulations with trapped ions

In the field of quantum simulation, methods and tools are explored for simulating the dynamics of a quantum system of interest with another system that is easier to control and measure. Systems of trapped atomic ions can be accurately controlled and manipulated, a large variety of interactions can be engineered with high precision and measurements of relevant observables can be obtained with nearly 100% efficiency. Here, we discuss prospects for quantum simulations using systems of trapped ions, and review the available set of quantum operations and first proof-of-principle experiments for both analog and digital quantum simulations with trapped ions.