Decoherence and dissipation during a quantum XOR gate operation

The dynamics of a quantum XOR gate operation in a two-qubit system being coupled to a bath of quantum harmonic oscillators is investigated. Upon applying the numerical quasiadiabatic propagator path integral method, we obtain the numerically precise time-resolved evolution of this interacting two-qubit system in presence of time-dependent external fields without further approximations. We simulate the dissipative gate operation for characteristic experimental realizations of condensed matter qubits; namely, the flux and charge qubits realized in superconducting Josephson systems and qubits formed with semiconductor quantum dots. Moreover, we study systematically the quality of the XOR gate by determining the four characteristic gate quantifiers: fidelity, purity, the quantum degree, and the entanglement capability of the gate. Two different types of errors in the qubits have been modelled, i.e., bit-flip errors and phase errors. The dependence of the quality of the gate operation on the environmental temperature, on the friction strength stemming from the system-bath interaction, and on the strength of the interqubit coupling is systematically explored: Our main finding is that the four gate quantifiers depend only weakly on temperature, but are rather sensitive to the friction strength.