Quantum Simulators, Spin Systems, and Trapped Ions

Many-quantum-spin systems cannot be efficiently simulated on classical computers as they require exponentially large resources. Yet many such systems can be simulated efficiently with quantum simulators (QS) that do not require universal control like quantum computers. Following the work of Porras and Cirac [Phys. Rev. Lett. 92, 207901-1 (2004)] we discuss current experimental efforts at Los Alamos to implement a QS for Ising-like and Heisenberg-like models with trapped ion qubit ``spins''. The states of the QS follow nearly the same equations of motion as the systems of interest, and unlike with real materials, the experimenter has the advantage of direct access to and control over the spins. We will discuss progress towards proof-of-principle investigations of two-ion simulations in a single-well trap, in which we use state-selective optical forces to induce ion-ion interactions.