Fig. 2: Scaling performance of the PRIS.

(a, top) Ground state energy versus graph order of random spin glasses. A sample graph is shown as an inset in (a, bottom): a fully-connected spin glass with uniformly-distributed continuous couplings in [−1, 1]. N_{iter, 99%} versus graph size for spin glasses (a, bottom) and MAX-CUT graphs (b). c N_{iter, 99%} versus graph density for MAX-CUT graphs and N = 75. The graph density is defined as d = 2∣E∣∕(N(N − 1)), ∣E∣ being the number of undirected edges. RCG denotes Random Cubic Graphs, for which ∣E∣ = 3N∕2. Ground states are determined with the exact solver BiqMac⁵⁷ (see Methods section). In this analysis, we set α = 0, and for each set of density and graph order we ran 10 graph instances 1000 times. The number of iterations to find the ground state is measured for each run and N_{iter, q} is defined as the q-th quantile of the measured distribution.