We introduce a geometric framework for efficient few-parameter pulse optimization in multi-level quantum systems, enabling high-fidelity state transfer beyond the adiabatic limit. Our method interpolates smoothly between adiabatic and diabatic dynamics to minimize unwanted excitations and maximize desired transitions even within a multi-level structure. Crucially, for single-parameter pulse control, the optimization reduces to solving a first-order ordinary differential equation. We showcase the flexibility of our diabatic-adiabatic protocols through two examples in spin-based quantum information processing: state initialization and qubit state transfer.
@article{arxiv.2602.14756,
title = {Multi-level spectral navigation with geometric diabatic-adiabatic control},
author = {Christian Ventura-Meinersen and Edmondo Valvo and Stefano Bosco and Maximilian Rimbach-Russ},
journal= {arXiv preprint arXiv:2602.14756},
year = {2026}
}