  We present a general framework to study quantum disordered systems in the
context of the Kikuchi's Cluster Variational Method (CVM). The method relies in
the solution of message passing-like equations for single instances or in the
iterative solution of complex population dynamic algorithms for an average case
scenario. We first show how a standard application of the Kikuchi's Cluster
Variational Method can be easily translated to message passing equations for
specific instances of the disordered system. We then present an "ad-hoc"
extension of these equations to a population dynamic algorithm representing an
average case scenario. At the Bethe level, these equations are equivalent to
the dynamic population equations that can be derived from a proper Cavity
Ansatz. However, at the plaquette approximation, the interpretation is more
subtle and we discuss it taking also into account previous results in classical
disordered models. Moreover, we develop a formalism to properly deal with the
average case scenario using a Replica-Symmetric ansatz within this CVM for
quantum disordered systems. Finally, we present and discuss numerical solutions
of the different approximations for the Quantum Transverse Ising model and the
Quantum Random Field Ising model in two dimensional lattices.
