Universal speeded-up adiabatic geometric quantum computation in three-level systems via counterdiabatic driving

Universal speeded-up adiabatic geometric quantum computation~(SAGQC) is studied in $\Lambda$-type three-level system with different coupling cases, i.e., time-dependent detuning, large detuning and one-photon resonance couplings, respectively. In these cases, the counterdiabatic driving method is used to speed up the universal quantum computation. These schemes in $\Lambda$-type three-level system are feasible in experiment because additional unaccessible ground-state-coupling is not needed. Only the shapes and phases of the initial adiabatic classical-field pulse are modified with the aid of effective two-level systems based on the counterdiabatic driving. The speed and robustness against decay of these schemes are discussed and compared. In addition, our work enriches the study of the speeded-up geometric computation in $\Lambda$-type three-level system and can be applied to various experimental platforms with different coupling features.