Abstract
We proposed an efficient scheme for constructing a quantum controlled phase-shift gate and generating the cluster states with rf superconducting quantum interference devices (SQUIDs) coupled to a microwave cavity through adiabatic evolution of dark eigenstates. During the operation, the spontaneous emission is suppressed since the rf SQUIDs are always in the three lowest flux states. Considering the influence from the cavity decay with achievable experimental parameters, we numerically analyze the success probability and the fidelity for generating the two-SQUID maximally entangled state and the controlled phase-shift gate by adiabatic passage.