  We propose a quantum bosonic qubit model on a fcc lattice to obtain mimetic
dark matter. The general relativity contribution is implemented similarly to
other works but it differs strongly on the implementation of the constraint
equations and their meaning. Different theories as mimetic dark matter, the
vector mimetic dark mater, and tensor-vector-scalar models are implemented on
the lattice. In all these cases, a generalized Gauss' law incorporates an
additional topological defect depending on the type of generalization, but
always fitting in the structure of the topological defects from general
relativity contribution.
