Trapped ion quantum simulators can in principle simulate an arbitrarily connected spin model. This requires precise programming of the ions with laser beams. In this paper, we numerically show that modern machine learning methods can be employed to program a trapped ion quantum simulator to simulate spin Hamiltonians on an arbitrary lattice geometry. This work is a collaboration with Prof. Roger Melko’s group.

Abstract: Trapped ions have emerged as one of the highest quality platforms for the quantum simulation of interacting spin models of interest to various fields of physics. In such simulators, two effective spins can be made to interact with arbitrary strengths by coupling to the collective vibrational or phonon states of ions, controlled by precisely tuned laser beams. However, the task of determining laser control parameters required for a given spin-spin interaction graph is a type of inverse problem, which can be highly mathematically complex. In this paper, we adapt a modern machine learning technique developed for similar inverse problems to the task of finding the laser control parameters for a number of interaction graphs. We demonstrate that typical graphs, forming regular lattices of interest to physicists, can easily be produced for up to 50 ions using a single GPU workstation. The scaling of the machine learning method suggests that this can be expanded to hundreds of ions with moderate additional computational effort.