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We present an extensive numerical study of the Sherrington-Kirkpatrick modelin transverse field. Recent numerical studies of quantum spin-glasses havefocused on exact diagonalization of the full Hamiltonian for small systems($\approx$ 20 spins). However, such exact numerical treatments are difficult toapply on larger systems. We propose making an approximation by using only asubspace of the full Hilbert space spanned by low-lying excitations consistingof one-spin flipped and two-spin flipped states. The approximation procedure iscarried out within the theoretical framework of Hartree-Fock approximation andConfiguration Interaction. Although not exact, our approach allows us to studylarger system sizes comparable to that achievable by state of the art QuantumMonte Carlo simulations. We calculate two quantities of interest due to recentadvances in quantum annealing, the ground-state energy and the energy gapbetween the ground and first excited state. For the energy gap, we derive anovel formula that enables it to be calculated using just the ground-statewavefunction, thereby circumventing the need to diagonalize the Hamiltonian. Wecalculate the scalings of the energy gap and the leading correction to theextensive part of the ground-state energy with system size, which are difficultto obtain with current methods.

Effects of low-lying excitations on ground-state energy and energy gap of Sherrington-Kirkpatrick model in transverse field