Superadiabatic Multiphoton Landau-Zener-Stückelberg-Majorana Effect in a Transmon Qudit

The recently observed two-photon Landau-Zener-Stückelberg-Majorana (LZSM) effect in superconducting circuits Phys. Rev. Lett. 134 060602 (2025) has provided a robust pathway for high-fidelity population transfer in qudit systems, but its adiabatic nature necessitates long operation times, which are vulnerable to decoherence. In this paper, we present a practical acceleration scheme based on a superadiabatic (SUAD) framework that overcomes these fundamental limitations. Our approach is tailored to a multiphoton LZSM process. By constructing modified pulse envelopes for the existing drive field without introducing auxiliary counterdiabatic controls, we achieve accelerated high-fidelity state transfer from the ground state to the target excited state. For the twophoton case, our protocol reduces the operation time by more than four times compared with 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 the fast and reliable control of multilevel quantum hardware.