Trapped ions are very suitable candidates for realizing quantum simulators because they provide us with excellent control over all quantum degrees of freedom: we can repeatedly and reliably prepare a quantum state, control its dynamic evolution, generate entangled states and carry out quantum measurements with high efficiency. In our experiment, we encode spin-1/2 particles into the electronic states of a string of trapped calcium ions. Laser beams are used to generate variable-range effective spin-spin interactions and a tightly focused laser beam allows for high-fidelity single-spin control.
In the first part of my presentation I will introduce the experimental setup and its capabilities, and explain how we engineer tunable-range spin-spin interactions. The second part focuses on properties of the realized interaction dynamics [1, 2], and presents a study of quantum transport under the influence of disorder and dephasing . Finally, I discuss how we can apply our tunable-range interaction and single-qubit control to perform variational quantum simulation of lattice models with up to 20 sites .
 N. Friis, O. Marty, et al., PRX 8, 021012 (2018)
 T. Brydges, A. Elben et al., Science 364, 260 (2019)
 C. Maier et al., Phys. Rev. Lett. 122, 050501 (2019)
 C. Kokail, C. Maier, R. van Bijnen et al., Nature 569, 355 (2019)