  It is proven that the ground state in the transverse field Edwards-Anderson
model is unique for a sufficiently weak transverse field in a $d$-dimensional
finite cubic lattice. On the basis of a recently obtained result for the low
energy states in the Edwards-Anderson model, the Kirkwood-Thomas expansion
method developed by Datta-Kennedy enables us to show that the uniqueness of
ground state is preserved against a sufficiently small transverse field in the
transverse field Edwards-Anderson model.
