  We develop a superoperator coupled cluster method for nonequilibrium open
many-body quantum systems described by the Lindblad master equation. The method
is universal and applicable to systems of interacting fermions, bosons or their
mixtures. We present a general theory and consider its application to the
problem of quantum transport through the system with electron-phonon
correlations. The results are assessed against the perturbation theory and
nonequilibrium configuration interaction theory calculations.
