Quantum independent-set problem and non-Abelian adiabatic mixing

We present an efficient quantum algorithm for independent-set problems in graph theory, based on non-Abelian adiabatic mixing. We illustrate the performance of our algorithm with analysis and numerical calculations for two different types of graphs, with the number of edges proportional to the number of vertices or its square. Our quantum algorithm is compared to the corresponding quantum circuit algorithms and classical algorithms. Non-Abelian adiabatic mixing can be a general technique to aid exploration in a landscape of near-degenerate ground states.