  Quantum computing is currently limited by the cost of two-qubit entangling
operations. In order to scale up quantum processors and achieve a quantum
advantage, it is crucial to economize on the power requirement of two-qubit
gates, make them robust to drift in experimental parameters, and shorten the
gate times. In this paper, we present two methods, one exact and one
approximate, to construct optimal pulses for entangling gates on a pair of ions
within a trapped ion chain, one of the leading quantum computing architectures.
Our methods are direct, non-iterative, and linear, and can construct
gate-steering pulses requiring less power than the standard method by more than
an order of magnitude in some parameter regimes. The power savings may
generally be traded for reduced gate time and greater qubit connectivity.
Additionally, our methods provide increased robustness to mode drift. We
illustrate these trade-offs on a trapped-ion quantum computer.
