Quantum computers & simulators promise access to previously inaccessible states and properties of many-body quantum systems with potential use in fields ranging from material science to pharmaceutical chemistry. Current experimental investigations are mainly focused on analog quantum simulations as full quantum error correction is still under development.
In this talk, I will first introduce the trapped-ion platform and present its capabilities in the context of quantum gates and analog simulations. Next, I will report on work in which we investigate the dynamical behavior of one-dimensional spin chains. Building on recent experiments that examined how entanglement and information travels around an interacting quantum system , we have implemented a new spectroscopy technique to directly measure the system’s dispersion relation and reveal interactions between the emergent quasi-particles . I will briefly touch upon ongoing work on ways to efficiently characterize  such quantum systems with up to 20 particles.
Lastly, I will describe a recent experiment in which we realized a novel quantum chemistry algorithm  in a fully scalable way. Here, we joined quantum and classical resources in a hybrid approach, which allows us to simulate properties of small molecular systems on a noisy quantum processor without error correction using a small number of quantum gates.
 P. Jurcevic et al, Nature 511, 202 (2014).
 P. Jurcevic et al, PRL 115, 100501 (2015).
 M. Cramer et al, Nat. Commun. 1, 149 (2010).
 A. Peruzzo et al. Nat. Commun. 5, 4213 (2014).