Stabilizer Approximation III: Maximum Cut

Abstract: We apply the stabilizer formalism to the Maximum Cut problem, and obtain a new greedy construction heuristic. It turns out to be an elegant synthesis of the edge-contraction and differencing edge-contraction approaches. Utilizing the relation between the Maximum Cut problem and the Ising model, the approximation ratio of the heuristic is easily found to be at least $1/2$. Moreover, numerical results show that the heuristic has very nice performance for graphs with about 100 vertices.