Geometric phases and quantum correlations of superconducting two-qubit system with dissipative effect

• We find that the Pancharatnam phases include the information of quantum correlations.
• We show that the sudden died and alive phenomena of quantum entanglement is original in the transition of Pancharatnam phase.
• We find that the faster the Pancharatnam phases change, the slower the quantum correlations decay.
• We find that a subspace of quantum entanglement can exist in the Y-state.
• Our results provide a useful approach experimentally to implement the time-dependent geometric quantum computation.

We investigate time-dependent Pancharatnam phases and the relations between such geometric phases and quantum correlations, i.e., quantum discord and concurrence, of superconducting two-qubit coupling system in dissipative environment with the mixture effects of four different eigenstates of density matrix. We find that the time-dependent Pancharatnam phases not only keep the motion memory of such a two-qubit system, but also include the information of quantum correlations. We show that the sudden died and alive phenomena of quantum entanglement are intrinsic in the transition of Pancharatnam phase in the X-state and the complex oscillations of Pancharatnam phase in the Y-state. The faster the Pancharatnam phases change, the slower the quantum correlations decay. In particular, we find that a subspace of quantum entanglement can exist in the Y-state by choosing suitable coupling parameters between two-qubit system and its environment, or initial conditions.