  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.
