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In this work, we design and implement frequency-robust Molmer-Sorensen gateson a linear chain of trapped ions, using Gaussian amplitude modulation and aconstant laser frequency. We select this frequency to balance the entanglementaccumulation of all motional modes during the gate to produce a strongrobustness to frequency error, even for long ion chains. We demonstrate thistechnique on a three-ion chain, achieving $<\,1\%$ reduction from peak fidelityover a $20\,$kHz range of frequency offset, and we analyze the performance ofthis gate design through numerical simulations on chains of two to 33 ions.

Frequency-robust M{\o}lmer-S{\o}rensen gates via balanced contributions of multiple motional modes