  Microwave control of trapped ions can provide an implementation of
high-fidelity two-qubit gates free from errors induced by photon scattering.
Furthermore, microwave conductors may be embedded into a scalable trap
structure, providing the chip-level integration of control that is desirable
for scaling. Recent developments have demonstrated how amplitude modulation of
the gate drive can permit a two-qubit entangling operation to become robust
against motional mode noise and other experimental imperfections. Here, we
discuss a method for the numerical optimization of the microwave pulse envelope
to produce gate pulses with improved resilience, faster operation and higher
energy efficiency.
