  $SU(N_c)$ gauge theories in the strong coupling limit can be described by
integer variables representing monomers, dimers and baryon loops. We
demonstrate how the D-wave quantum annealer can perform importance sampling on
$U(N_c)$ gauge theory in the strong coupling formulation of this theory. In
addition to causing a sign problem in importance sampling, baryon loops induce
a complex QUBO matrix which cannot be optimized by the D-Wave annealer. Instead
we show that simulating the sign-problem free quenched action on the D-Wave is
sufficient when combined with a sign reweighting method. As the first test on
$SU(3)$ gauge theory, we simulate on $2 \times 2$ lattice and compare the
results with its analytic solutions.
