Quantum Algorithm for Approximating Maximum Independent Sets

We present a quantum algorithm for approximating maximum independent sets of graph based on non-Abelian adiabatic mixing in the sub-Hilbert space degenerate ground states, which generates annealing secondary Hamiltonian. For both sparse and dense random graphs G , numerical simulation suggests that our average finds an set size close to α ( ) low polynomial time. The best classical algorithms, by contrast, produce about half