  We investigate the properties of quantum annealing applied to the random
field Ising model in one, two and three dimensions. The decay rate of the
residual energy, defined as the energy excess from the ground state, is find to
be $e_{res}\sim \log(N_{MC})^{-\zeta}$ with $\zeta$ in the range $2...6$,
depending on the strength of the random field. Systems with ``large clusters''
are harder to optimize as measured by $\zeta$. Our numerical results suggest
that in the ordered phase $\zeta=2$ whereas in the paramagnetic phase the
annealing procedure can be tuned so that $\zeta\to6$.
