  We develop a quantum Monte Carlo method to estimate the ground-state energy
of a fermionic many-particle system in the configuration-interaction shell
model approach. The fermionic sign problem is circumvented by using a guiding
wave function in Fock space. The method provides an upper bound on the
ground-state energy whose tightness depends on the choice of the guiding wave
function. We argue that the antisymmetric geminal product class of wave
functions is a good choice for guiding wave functions. We demonstrate our
method for the trapped two-species fermionic cold atom system in the unitary
regime of infinite scattering length using the particle-number projected
Hartree-Fock-Bogoliubov wave function as the guiding wave function. We estimate
the ground-state energy and energy-staggering pairing gap as a function of the
number of particles. Our results compare favorably with exact numerical
diagonalization results and with previous coordinate-space Monte Carlo
calculations.
