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

TL;DR

This paper enhances QAOA efficiency for MaxCut problems by combining parameter transfer initialization with targeted-single-layer optimization and regularization, achieving near-optimal results with significant speedup and reduced performance variability.

Contribution

It introduces a novel approach combining parameter transfer and targeted-single-layer optimization with regularization to improve QAOA efficiency and robustness.

Findings

Achieved 98.88% optimal performance with 8.06x speedup on unweighted graphs.

Targeted-single-layer optimization outperformed full optimization in 8.92% of cases.

Regularization reduced sub-optimal local minima from 8.92% to 3.81%.

Abstract

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.