Quantum logical gates with four-level SQUIDs coupled to a superconducting resonator

We propose a way for realizing a two-qubit controlled phase gate with superconducting quantum interference devices (SQUIDs) coupled to a superconducting resonator. In this proposal, the two lowest levels of each SQUID serve as the logical states and two intermediate levels of each SQUID are used for the gate realization. We show that neither adjustment of SQUID level spacings during the gate operation nor uniformity in SQUID parameters is required by this proposal. In addition, this proposal does not require the adiabatic passage or a second-order detuning and thus the gate is much faster.