Fast Mølmer-Sørensen gates in trapped-ion quantum processors with compensated carrier transition

Carrier transition is one of the major factors hindering the high-speed implementation of the Mølmer-Sørensen gates in trapped-ion quantum processors. We present an approach to design laser pulse shapes for the Mølmer-Sørensen gate in ion chains which accounts for the effect of carrier transition on qubit-phonon dynamics. We show that the fast-oscillating carrier term effectively modifies the spin-dependent forces acting on ions, and this can be compensated by a simple nonlinear transformation of a laser pulse. Using numerical simulations for short ion chains and perturbation theory for longer chains up to $20$ ions, we demonstrate that our approach allows to reach the infidelity below ${10}^{-4}$ while keeping the gate duration of the order of tens of microseconds.