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.
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