Programmable quantum simulations of spin systems with trapped ions

Trapped ions have always been among the leading contenders for the realization of a quantum computer. This review reports on progress in the use of these current-day quantum machines for the simulation of hard problems in spin dynamics of one-dimensional chain systems. Considerable acrobatics are needed to hide the real ion-spectroscopy physics and transform it into the quantum dynamics of the condensed matter system; this quantum computer is equally capable of simulating equilibrium spin physics and nonequilibrium dynamics. Prospects for scaling beyond 100 qubits are real, and the exploration of topological phases is on the horizon.