Mitigating Experimental Imperfections with Frequency-Modulated Pulses for High-Fidelity Two-Qubit Gates in Ion Chains*

High-fidelity two-qubit gates are essential in many quantum information processing tasks. In a trapped-ion quantum computer, collective motional modes of the ion chain are used to entangle the internal states of two ions. The quality of the gates suffers when the experimental parameters such as trap frequency and laser intensity differ from the ideal case or fluctuate over time. Here we present two methods of improving the fidelity of frequency-modulated Mølmer-Sørensen gates under experimental imperfections. First, we achieve robustness to motional mode frequency offsets by optimizing average performance over a range of systematic errors using batch optimization. Next, we mitigate dephasing of the motional modes under a known noise spectrum by designing the filter function of the pulse. We present theoretical methods and experimental results [Kang, M. et al., Phys. Rev. Applied 16, 024039 (2021)].