关键词: trapped ion quantum computing, robust optimization, high-fidelity quantum gates, magnus expansion

Abstract: Trapped ion hardware has made significant progress recently and is now one of the leading platforms for quantum computing. To construct two-qubit gates in trapped ions, experimental manipulation approaches for ion chains are becoming increasingly prevalent. Given the restricted control technology, how implementing high-fidelity quantum gate operations is crucial. Many works in current pulse design optimization focus on ion-phonon and effective ion-ion couplings while ignoring the first-order derivative terms expansion impacts of these two terms brought on by experiment defects. This paper proposes a novel robust quantum control optimization method in trapped ions. By introducing the first-order derivative terms caused by the error into the optimization cost function, we generate an extremely robust Mølmer-Sørensen gate with infidelity below $10^{-3}$ under a drift noise range of $\pm 10 $ kHz, the relative robustness achieves a tolerance of $\pm 5$%, compared to the 200-kHz frequency spacing between phonon modes, and for time noise drift, the tolerance reached to 2%. Our work reveals the vital role of the first-order derivative terms of coupling in trapped ion pulse control optimization, especially the first-order derivative terms of ion-ion coupling. It provides a robust optimization scheme for realizing more efficient entangled states in trapped ion platforms.

Key words: trapped ion quantum computing, robust optimization, high-fidelity quantum gates, magnus expansion