  We describe and discuss a recently proposed quantum Monte Carlo algorithm to
compute the ground-state properties of various systems of interacting fermions.
In this method, the ground state is projected from an initial wave function by
a branching random walk in an over-complete basis of Slater determinants. By
constraining the determinants according to a trial wave function
$|\psi_T\rangle$, we remove the exponential decay of signal-to-noise ratio
characteristic of the sign problem. The method is variational and is exact if
$|\psi_T\rangle$ is exact. We illustrate the method by describing in detail its
implementation for the two-dimensional one-band Hubbard model. We show results
for lattice sizes up to $16\times 16$ and for various electron fillings and
interaction strengths. Besides highly accurate estimates of the ground-state
energy, we find that the method also yields reliable estimates of other
ground-state observables, such as superconducting pairing correlation
functions. We conclude by discussing possible extensions of the algorithm.
