  We present an extensive numerical study of the Sherrington-Kirkpatrick model
in transverse field. Recent numerical studies of quantum spin-glasses have
focused on exact diagonalization of the full Hamiltonian for small systems
($\approx$ 20 spins). However, such exact numerical treatments are difficult to
apply on larger systems. We propose making an approximation by using only a
subspace of the full Hilbert space spanned by low-lying excitations consisting
of one-spin flipped and two-spin flipped states. The approximation procedure is
carried out within the theoretical framework of Hartree-Fock approximation and
Configuration Interaction. Although not exact, our approach allows us to study
larger system sizes comparable to that achievable by state of the art Quantum
Monte Carlo simulations. We calculate two quantities of interest due to recent
advances in quantum annealing, the ground-state energy and the energy gap
between the ground and first excited state. For the energy gap, we derive a
novel formula that enables it to be calculated using just the ground-state
wavefunction, thereby circumventing the need to diagonalize the Hamiltonian. We
calculate the scalings of the energy gap and the leading correction to the
extensive part of the ground-state energy with system size, which are difficult
to obtain with current methods.
