Experimental techniques for quantum simulation and computation using trapped ions

Quantum technologies, such as trapped atomic ions, have advanced to the point of carrying out proof-of-principle demonstrations of quantum computing and quantum simulation. A current focus of interest is exploring how quantum simulation tools can be exploited for nuclear physics related problems, such as the simulation of lattice gauge theories. This talk will present a broad overview of trapped ion quantum simulation experiments, describing the tools and techniques that have been demonstrated in a laboratory setting, and the current challenges in extending these results to more complex systems. Trapped ions are well suited for both ``digital'' quantum simulations, in which quantum logic gates are used to construct a unitary operator of interest, as well as ``analog'' simulations, in which the trapped ions are induced to obey dynamics analogous to a quantum system of interest, such as a spin chain. I will review existing protocols for using trapped ions to simulate spin-like and boson-like degrees of freedom and to control their interactions, as well as giving an outlook on near-term efforts to expand the capabilities of such experiments.