  We introduce the adiabatic quantum Monte Carlo (AQMC) method, where we
gradually crank up the interaction strength, as an amelioration of the sign
problem. It is motivated by the adiabatic theorem and will approach the true
ground-state if the evolution time is long enough. We demonstrate that the AQMC
enhances the average sign exponentially such that low enough temperatures can
be accessed and ground-state properties probed. It is a controlled
approximation that satisfies the variational theorem and provides an upper
bound for the ground-state energy. We first benchmark the AQMC vis-\`a-vis the
undoped Hubbard model on the square lattice which is known to be
sign-problem-free within the conventional quantum Monte Carlo formalism. Next,
we test the AQMC against the density-matrix-renormalization-group approach for
the doped four-leg ladder Hubbard model and demonstrate its remarkable
accuracy. As a nontrivial example, we apply our method to the Hubbard model at
$p=1/8$ doping for a $16\times 8$ system and discuss its ground-state
properties. We finally utilize our method and demonstrate the emergence of
$U(1)_2\sim SU(2)_1$ topological order in a strongly correlated Chern
insulator.
