Non-Abelian braiding in three-fold degenerate subspace and the acceleration

Non-Abelian braiding operations of quantum states have attracted substantial attention due to their great potentials for realizing topological quantum computations. The adiabatic version of quantum braiding is robust against systematic errors, yet will suffer from decoherence and dephasing effects due to a long evolution time. In this paper, we propose to realize the braiding process in a three-fold degenerate subspace of a seven-level system, where the non-Abelian effect can be detected by changing the orders of the braiding. We accelerate the adiabatic control through adding auxiliary coupling terms according to a shortcut to adiabatic theory for the non-Abelian case. Furthermore, by generalizing the parallel adiabatic passages, adiabatic control can be accelerated through only reshaping the original control waveforms and the effective pulses area will be significantly reduced. Therefore, the proposed schemes may provide an experimentally feasible way to investigate the non-Abelian braiding in atomic systems and the waveguide systems.