  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.
