Matrix-power energy-landscape transformation for finding spin-glass ground states

A method for solving binary optimization problems was proposed by Karandashev and Kryzhanovsky that can be used for finding ground states of spin glass models. By taking a power of the bond matrix the energy landscape of the system is transformed in such a way, that the global minimum should become easier to find. In this paper we test the combination of the new approach with various algorithms, namely simple random search, a cluster algorithm by Houdayer and Martin, and the common approach of parallel tempering. We apply these approaches to find ground states of the three-dimensional Edwards-Anderson model, which is an NP-hard problem, hence computationally challenging. To investigate whether the power-matrix approach is useful for such hard problems, we use previously computed ground states of this model for systems of size 103 spins. In particular we try to estimate the difference in needed computation time compared to plain parallel tempering.