Fig. 3: Optimization performance with low rank approximated coupling matrices.
a The energy of approximate solutions is plotted against the rank of the approximate coupling matrix. The exact interaction matrix represents a random, unweighted, undirected graph with 1000 vertices, all with anti-ferromagnetic couplings. The coupling strengths are rounded to the nearest 2−8 in the approximation. b The energy of approximate solutions is plotted against the precision of the approximate coupling matrix. A full-rank (R = 1000) matrix and two low-rank approximations with ranks R = 256 and R = 64 are used for each precision level. c, d follow the same structure as (a) and (b), but the exact interaction matrix represents a random 3-regular graph, again with all non-zero couplings being anti-ferromagnetic. The semi-transparent bands in (b) and (d) show the 95% confidence interval on mean energy values. Data used to plot this figure can be found in the data tables given in the “Figure 3ab” tab of Supplementary Data 1 file.
