Implementation of Quantum Fourier Transforms via Counter-Diabatic Acceleration in a Four-Dimensional System

<jats:p>Counter-diabatic Shortcut to Adiabaticity (CDSTA) has been explored in implementing qudit quantum Fourier transforms (QFT) via stimulated Raman adiabatic passage (STIRAP) to suppress non-adiabatic leakage. While direct CD driving may introduce unwanted global microwave couplings, seeking an approach without explicit CD fields is highly desirable. By employing rotating-frame absorption, we implement an all-optical STA strategy to synthesize the QFT. Our systematic comparison of qubit and quartit encodings across Average Gate Fidelity, peak amplitude, and energy cost elucidates the practical advantages brought by qudit architecture and CD driving, demonstrating an acceleration factor of at least 7. Furthermore, we extend our evaluation to open quantum systems. Based on the trade-off analysis, optimized parameters are selected, revealing that the all-optical strategy maintains significant advantages against amplitude noise, pure dephasing, and spontaneous emission, improving robustness against infidelity by an order of magnitude.</jats:p>