A method of performing simultaneous entangling gate operations in a trapped-ion quantum computer includes selecting a gate duration value and a detuning frequency of pulses to be individually applied to a plurality of participating ions in a chain of trapped ions to simultaneously entangle a plurality of pairs of ions among the plurality of participating ions by one or more predetermined values of entanglement interaction, determining amplitudes of the pulses, based on the selected gate duration value, the selected detuning frequency, and the frequencies of the motional modes of the chain of trapped ions, generating the pulses having the determined amplitudes, and applying the generated pulses to the plurality of participating ions for the selected gate duration value. Each of the trapped ions in the chain has two frequency-separated states defining a qubit, and motional modes of the chain of trapped ions each have a distinct frequency.