Time-dependent Pancharatnam phases and quantum correlations for coupling superconducting two-qubit system with dissipative environment

Two coupling superconducting qubits are studied for the quantum concurrence, discord, and Pancharatnam phase, for the X and Y states under the dephasing and instantaneous decay environment as well as their couplings. We find that the X and Y states are special mixed states according to the Bloch radius. In general, the larger the environment and phonon number are at the larger region of time, the larger the quantum concurrence and discord are. But we find that the environment correlations are helpful to implement the quantum computation. The Pancharatnam phases provide a way to distinguish the X and Y states.