  We present an implementation of Quantum Annealing (QA) via lattice Green's
function Monte Carlo (GFMC), focusing on its application to the Ising
spin-glass in transverse field. In particular, we study whether or not such
method is more effective than the Path-Integral Monte Carlo (PIMC) based QA, as
well as classical simulated annealing (CA), previously tested on the same
optimization problem. We identify the issue of importance sampling, i.e., the
necessity of possessing reasonably good (variational) trial wavefunctions, as
the key point of the algorithm. We have considered two possible classes of
trial wavefunctions, a mean-field single-site one -- whose optimization is
however a very difficult task -- and a Boltzmann-like choice. We performed
GFMC-QA runs using such a Boltzmann-like trial wavefunction, finding results
for the residual energies that are qualitatively similar to those of CA (but at
a much larger computational cost), and definitely worse than PIMC-QA. We
conclude that, at present, without a serious effort in constructing reliable
importance sampling variational wavefunctions for a quantum glass, GFMC-QA is
not a true competitor of PIMC-QA.
