Improving the efficiency of QAOA using efficient parameter transfer initialization and targeted-single-layer regularized optimization with minimal performance degradation

Quantum approximate optimization algorithm (QAOA) have promising applications in combinatorial optimization problems (COPs). We investigated the MaxCut problem in three different families of graphs using QAOA ansats with parameter transfer initialization followed by targeted single layer optimization. For 3 regular (3R), Erdos Renyi (ER), and Barabasi Albert (BA) graphs, the parameter transfer approach achieved mean approximation ratios of 0.9443 for targeted-single layer optimization as compared to 0.9551 of full optimization. It represents 98.88 percent optimal performance, with 8.06 times computational speedup in unweighted graphs. But, in weighted graph families, optimal performance is relatively low (less than 90 percent) for higher nodes graph, suggesting parameter transfer followed by targeted-single-layer optimization is not ideal for weighted graph families, however, we find that for some weighted families (weighted 3-regular) this approach works perfectly. In 8.92 percent test cases, targeted single layer optimization outperformed the full optimization, indicating that complex parameter landscape can trap full optimization in sub-optimal local minima. To mitigate this inconsistency, ridge (L2) regularization is used to smoothen the solution landscape, which helps the optimizer to find better optimum parameters during full optimization and reduces these inconsistent test cases from 8.92 percent to 3.81 percent. This work demonstrates that efficient parameter initialization and targeted-single-layer optimization can improve the efficiency of QAOA with minimal performance degradation.