  The quantum Monte Carlo algorithm is arguably one of the most powerful
computational many-body methods, enabling accurate calculation of many
properties in interacting quantum systems. In the presence of the so-called
sign problem, the algorithm typically relies on trial wave functions to
eliminate the exponential decay of signal-to-noise ratio, usually at the
expense of a bias in the result. The quality of the trial state therefore is
critical for accurate simulations. In this work, benchmark results of the
ground state auxiliary-field quantum Monte Carlo method are reported for the
Hubbard model on several geometries. We demonstrate that when multi-determinant
generalized Hartree-Fock states are used as trial wave functions, the
systematic errors can be systematically reduced to a low level and the results
compare favorably with the exact diagonalization data.
