Abstract
We construct a novel Λ-type system via the dressed states formed by the coupling between a superconducting qubit and a transmission line resonator (TLR). Compared with the conventional three-level structure, our model averts the decay of excited states. We choose the two lowest energy dressed states as the logical states. The single qubit quantum gate can be realized by the adiabatic passage and three-step operation method, respectively. Based on realistic parameters, the feasibility of the adiabatic passage method is discussed. Also, we calculate the fidelity (0.9996) of realizing the single qubit gate with the three-step operation method.