  We consider two-component fermions on the lattice in the unitarity limit.
This is an idealized limit of attractive fermions where the range of the
interaction is zero and the scattering length is infinite. Using Euclidean time
projection, we compute the ground state energy using four computationally
different but physically identical auxiliary-field methods. The best
performance is obtained using a bounded continuous auxiliary field and a
non-local updating algorithm called hybrid Monte Carlo. With this method we
calculate results for 10 and 14 fermions at lattice volumes 4^3, 5^3, 6^3, 7^3,
8^3 and extrapolate to the continuum limit. For 10 fermions in a periodic cube,
the ground state energy is 0.292(12) times the ground state energy for
non-interacting fermions. For 14 fermions the ratio is 0.329(5).
