BH approaches consist of consecutive perturbation and relaxation steps (see flow chart in Fig. in SI), which allow hopping to different basins and finding the minimum within a basin, respectively. Our implementation of BH uses the optimal-exchange relaxation for the latter minimization steps. The success of BH furthermore depends on a judicious choice of perturbation steps, as very destabilizing perturbations are often immediately reverted by the local optimization. An optimal perturbation should therefore allow escaping a basin while keeping the energy of the system low.