A method of performing a computation using a quantum computer includes modulating motional mode structures of a plurality of trapped ions, each of the plurality of trapped ions having two frequency-separated states defining a qubit, computing a detuning frequency function and an amplitude function of a laser pulse to cause entangling interaction between a pair of trapped ions of the plurality of trapped ions, and performing a quantum computation in the quantum computer by applying a laser pulse having the computed detuning frequency function and the amplitude function to the pair of trapped ions for a gate duration.