  The interpolation method for mean field spin glass models developed by Guerra
and Talagrand is extended to a quantum mean field spin glass model. This
extension enables us to obtain both replica-symmetric (RS) and one step
replica-symmetry breaking (1RSB) solutions of the free energy density in the
transverse field Sherrington-Kirkpatrick model. It is shown that the RS
solution is exact in the paramagnetic phase. We provide a sufficient condition
on coupling constants where the 1RSB solution gives better bound than the RS
one. This condition reduced to physical quantities in disordered single spin
systems allows a simple computer-assisted proof for the existence of the de
Almeida-Thouless-type instability.
