Programmable 2D Arrays of Interacting Quantum Spins Using Trapped Ions

This document summarizes the advances in research performed under AFOSR YIP award FA9550-16-1-0277. The scope of this work spanned both theory and experimental developments. On the theory side, three publications proposed (1) new approaches to quantum simulation in two dimensional ion arrays,(2) a new method to achieve string-order in ion systems by periodically driving the interactions, and (3) the first proposal for realizing full Heisenberg interactions in an ion lattice. Experimentally, this work started from a vacant laboratory, and built up a full suite of laser systems, ion traps, and vacuum chambers. In the final year of this project, these efforts culminated in the trapping of Yb+ within a two-dimensional array as well as quantum manipulation of these ion configurations