Superadiabatic multi-photon Landau-Zener-Stückelberg-Majorana effect in a transmon qudit

The recently observed two-photon Landau-Zener-Stückelberg-Majorana (LZSM) effect in superconducting circuits 2025 Phys. Rev. Lett. 134 060602 provides a robust pathway for high-fidelity population transfer in qudit systems, but its adiabatic nature necessitates long operation times that are vulnerable to decoherence. Here, we present a practical acceleration scheme based on the superadiabatic (SUAD) framework that overcomes this fundamental limitation. Crucially, our approach is tailored to the multi-photon LZSM process. By constructing modified pulse envelopes for the existing drive field, without introducing any auxiliary counterdiabatic controls, we achieve accelerated high-fidelity state transfer from the ground state to the target excited state. For the two-photon case, our protocol reduces the operation time by over fourfold compared to the adiabatic reference while maintaining a fidelity of 0.998. We further generalize this to the three-photon regime, demonstrating a speedup factor exceeding three. Our SUAD LZSM scheme exhibits superior resilience to decoherence, offering a ready-to-implement solution for fast and reliable control in multi-level quantum hardware.