  We reveal the existence of polariton soliton solutions in the array of weakly
coupled optical cavities, each containing an ensemble of interacting qubits. An
effective complex Ginzburg-Landau equation is derived in the continuum limit
taking into account the effects of cavity field dissipation and qubit
dephasing. We have shown that an enhancement of the induced nonlinearity can be
achieved by two order of the magnitude with a negative interaction strength
which implies a large negative qubit-field detuning as well. Bright solitons
are found to be supported under perturbations only in the upper (optical)
branch of polaritons, for which the corresponding group velocity is controlled
by tuning the interacting strength. With the help of perturbation theory for
solitons, we also demonstrate that the group velocity of these polariton
solitons is suppressed by the diffusion process.
