selecting, by a classical computer, a gate duration of a pulse to be applied to two trapped ions in a quantum processor, comprising a plurality of trapped ions, wherein each of the trapped ions has two frequency-separated states defining a qubit, and the pulse is generated by one or more lasers;

selecting, by the classical computer, an amount of infidelity that is allowed in an entangling operation between the two trapped ions;

computing, by the classical computer, a first set of values of an amplitude and a detuning frequency of the pulse based on the selected gate duration, the selected amount of infidelity, and a phase-space condition for states of the plurality of trapped ions to remain unchanged at the end of the gate duration;

selecting, by the classical computer, a second set of values of the amplitude and the detuning frequency of the pulse among the first set of values based on a gate angle condition for entangling interaction between the two trapped ions to be a selected value;

generating, by the classical computer, the pulse based on the second set of values of the amplitude and the detuning frequency of the pulse;

applying, by use of a system controller and the one or more lasers, the generated pulse to each of the two trapped ions to perform the entangling operation between the two trapped ions;

measuring, by use of the system controller, a population of gubit states in the quantum processor; and

outputting, by the classical computer, the measured population of qubit states.