Fig. 6: p = 2 QAOA cut fraction guarantees under different assumptions.

Dashed and solid lines plot with high probability the lower and upper bounds on cut fractions, respectively, assuming only graph theoretic typicality on the number of subgraphs. Dotted plots are the ensemble median over an ensemble of 3 regular graphs; for N ≤ 16 (dots); this includes all graphs, while for N > 16, this is an ensemble of 1000 graphs for each size. We used 32 sizes between 16 and 256. Dark black fill plots the variance in the cut fraction over the ensemble, and light black fill plots the extremal values over the ensemble. The median serves as a proxy of performance, assuming QAOA typicality. Given a particular cut from a classical solver, there may be different regions of advantage, shown by the four colors and discussed in the text.