  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.
