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

The counter-diabatic shortcut to adiabaticity (CDSTA) has been explored in implementing qudit quantum Fourier transforms (QFTs) 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 CDSTA strategy to synthesize the QFT. Direct CD driving (STIRSAP) removes the adiabatic time floor of STIRAP and sets the acceleration upper bound; the all-optical scheme reproduces this acceleration with a peak-amplitude overhead below 5% in the working regime while eliminating the microwave coupling. The quartit encoding further reduces the integrated energy by a factor of 3 relative to the two-qubit decomposition. Extending to open quantum systems, the all-optical strategy shows improved robustness against amplitude noise and spontaneous emission.