Figure 4

Boxplot visualization of ratios to optimal angles’ expectation value per clustering method and depth on MaxCut (a) and dense QUBOs (b), when using the angle values. We show also the boxplots when computing the median angle values, yielding a median ratio of 0.524307 for MaxCut and 0.671572 for QUBOs. The median ratios are respectively 0.990579, 0.995610 and 0.998293 for 3, 5 and 10 clusters. For QUBOs, we get 0.956099, 0.970842, and 0.984787 taking the same number of clusters. With reference to the optimal angles’ expectation value, this corresponds on average to a less than 1–2% reduction in performances when using 10 clusters. For MaxCut, we had to use the closest data point in the dataset to the cluster, as it results in better performances. For instance, with 3 clusters at \(p=3\), the median ratio was 0.618275