We implement faster-than-adiabatic two-qubit phase gates using smooth state-dependent forces. The forces are designed to leave no final motional excitation, independently of the initial motional state in the harmonic, small-oscillations limit. They are simple, explicit functions of time and the desired logical phase of the gate, and are based on quadratic invariants of motion and Lewis-Riesenfeld phases of the normal modes.
@article{arxiv.1609.01892,
title = {Fast phase gates with trapped ions},
author = {M. Palmero and S. Martínez-Garaot and D. Leibfried and D. J. Wineland and J. G. Muga},
journal= {arXiv preprint arXiv:1609.01892},
year = {2017}
}