A machine learned model for quick access to analytic solutions of a QIS system

For quantum information ion systems, the calculation of analytic solutions describing a state of interest can become computationally expensive even for systems with a relatively small number of ions. This can become a big constriction when attempting to quickly access specific states of a quantum ion system for manipulation. Here we describe the implementation of a Machine Learning algorithm to determine the equilibrium positions of a linear chain of ions, an ideal configuration of ions in a Paul trap or a storage ring with a crystalline beam. Specifically, given the solutions of this system for a relatively small amount of ions, our ML predicts the partial equilibrium solution of the system with a higher number of ions where the numerical approach takes longer calculating time with increasing number of ions.