Unconventional Geometric Phase-Shift Gates Based on Superconducting Quantum Interference Devices Coupled to a Single-Mode Cavity

We present a scheme to realize geometric phase-shift gate for twosuperconducting quantum interference device (SQUID) qubits coupled to asingle-mode microwave field. The geometric phase-shift gate operation isperformed in two lower flux states, and the excited state |2〉wouldnot participate in the procedure. The SQUIDs undergo no transitions duringthe gate operation. Thus, the docoherence due to energy spontaneous emission based on the levels of SQUIDs are suppressed. The gate is insensitive to the cavity decay throughout the operation since the cavity mode is displaced along a circle in the phase space, acquiring a phase conditional upon the two lower flux states of the SQUID qubits, and the cavity mode is still in the original vacuum state. Based on the SQUID qubits interacting with the cavity mode, our proposed approach may open promising prospects for quantum logic in SQUID-system.