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 two-photon 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.