Figure 3

Number of ties per iteration of RQAOA (average over 200 runs) for \((3,8)\)-cage graph (30 vertices, 45 edges, edge weights \((\{-1, +1\})\). We chose \(n_{c}=8\) in our simulations where RQAOA achieved a mean approximation ratio of \(0.955 \pm 0.036\) and the probability to reach the ground state was 33.5%. The y-axis (Number of Ties) is log-scaled. The black crosses depict the mean values, with the error bar showing the 95% confidence interval of 200 independent runs. The figure illustrates that one would invariably encounter a constant fraction of ties between maximal two-correlations no matter whatever path is chosen in the search tree, implying an exponential blow-up in the size of the search tree to be explored by RQAOA