Abstract: A system includes a controller configured to reconstitute a continuous waveform to a discrete analogue version. The system includes a numerical optimizer configured to determine frequencies of a pulse sequence. The numerical optimizer uses radial motional mode frequencies and a desired gate time. The numerical optimizer generates the pulse sequence by closing phase-space trajectories, disentangling spins and motions, and constraining a Rabi frequency for motional sideband transitions. The system also includes a display configured to illustrate a discrete frequency modulation pulse sequence based on the determined frequencies.