Hybrid quantum-classical algorithms for approximate graph coloring

We show how to apply the recursive quantum approximate optimization algorithm (RQAOA) MAX-k-CUT, problem of finding an k-vertex coloring a graph. compare this proposal best known classical and hybrid classical-quantum algorithms. First, we that standard (non-recursive) QAOA fails solve for most regular bipartite graphs at any constant level xmlns:mml="http://www.w3.org/1998/Math/MathML">p: approximation ratio achieved by is hardly better than assigning colors vertices random. Second, construct efficient simulation which simulates level-1 RQAOA arbitrary graphs. In particular, these algorithms give rise algorithms, no benefit arising from use mechanics be expected. Nevertheless, they provide suitable testbed assessing potential algorithm: perform large-scale with up xmlns:mml="http://www.w3.org/1998/Math/MathML">300 qutrits applied ensembles randomly generated xmlns:mml="http://www.w3.org/1998/Math/MathML">3-colorable constant-degree find surprisingly competitive: considered, its ratios are often higher those generic based on rounding SDP relaxation. This suggests intriguing possibility higher-level may potentially useful NISQ devices.