All interactions between atoms (spins and ancillas) that are not part of a common plaquette are at least two orders of magnitude smaller than the interactions within a plaquette. This allows us to restrict the sum in equation (4) to pairs of atoms belonging to the same plaquette, thus realizing of equation (3) for the optimal parameters α=2 and β=1. For the above system parameters, we obtain a final energy gap Δ□=−2π × 20 kHz. Note that the energy gap is negative, which can be easily accounted for by a sign change of all local fields and making the annealer adiabatically follow the maximum energy state, instead of the minimum.