Speeding up adiabatic method has attracted much attention with the wide applications in quantum information processing. In this paper, two kinds of methods, Lewis-Riesenfeld invariant-based inverse engineering and transitionless quantum driving are applied to implement speeding up adiabatic state conversion in optomechanical system. The perfect population transfer can be achieved within a short time. At last, the energetic cost is analysed for the transitionless quantum driving.

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An experimentally feasible strong coupling system between a spin ensemble and a superconducting qubit is studied. The coupling strength can be exponentially enhanced by applying the squeezing transformations to the system. By means of the two spin ensembles commonly coupled to a superconducting qubit, a set of universal nonadiabatic holonomic single-qubit quantum gates can be realized in a decoherence-free subspace. Furthermore, this proposal is robust with respect to decay of the system parameters, and it is experimentally feasible with currently available technology.

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