TITLE:  Realizing Feynman's dream of a quantum computer with trapped ions

ABSTRACT:  Feynman proposed that well controlled systems of quantum particles can simulate quantum systems better than anything else. I will discuss some recent progress in ion traps quantum simulations which show what types of problems can be simulated and what are the challenges faced with scaling machines up to large sizes. In particular, I have been involved in working with experimental groups at both University of Maryland and NIST Boulder on simulating spin systems. I will describe the different types of experiments that are undertaken and the different types of information that can be extracted from them. These results go beyond the standard adiabatic state preparation into examining low-energy excitation and spectroscopy of these simulations.