Fast M{\o}lmer-S{\o}rensen gates in trapped-ion quantum processors with compensated carrier transition

Carrier transition is one of the major factors hindering the high-speed implementation of M{\o}lmer-S{\o}rensen gates in trapped-ion quantum processors. We present an approach to design laser pulse shapes for M{\o}lmer-S{\o}rensen 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, we demonstrate that our approach allows to reach the infidelity below $10^{-4}$ while keeping the gate duration below 100 $\mu$s.