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We present a robust quantum optimal control framework for implementing fastentangling gates on ion-trap quantum processors. The framework leveragestailored laser pulses to drive the multiple vibrational sidebands of the ionsto create phonon-mediated entangling gates and, unlike the state of the art,requires neither weak-coupling Lamb-Dicke approximation nor perturbationtreatment. With the application of gradient-based optimal control, it enablesfinding amplitude- and phase-modulated laser control protocols that work beyondthe Lamb-Dicke regime, promising gate speed at the order of microsecondscomparable to the characteristic trap frequencies. Also, robustnessrequirements on the temperature of the ions and initial optical phase can beconveniently included to pursue high-quality fast gates against experimentalimperfections. Our approach represents a step in speeding up quantum gates toachieve larger quantum circuits for quantum computation and simulation, andthus can find applications in near-future experiments.

Fast Ion Gates Outside the Lamb-Dicke Regime by Robust Quantum Optimal Control