  We study a fermionic version of the Sherrington-Kirkpatrick model including
nearest-neighbor hopping on a $\infty$-dimensional simple cubic lattices. The
problem is reduced to one of free fermions moving in a dynamical effective
random medium. By means of a CPA method we derive a set of self-consistency
equations for the spin glass order parameter and for the Fourier components of
the local spin susceptibility. In order to solve these equations numerically we
employ an approximation scheme which restricts the dynamics to a feasible
number of the leading Fourier components. From a sequence of systematically
improved dynamical approximations we estimate the location of the quantum
critical point.
