Red-QAOA: Efficient Variational Optimization through Circuit Reduction

Abstract: The Quantum Approximate Optimization Algorithm (QAOA) addresses combinatorial optimization challenges by converting inputs to graphs. However, the optimal parameter searching process of QAOA is greatly affected by noise. Larger problems yield bigger graphs, requiring more qubits and making their outcomes highly noise-sensitive. This paper introduces Red-QAOA, leveraging energy landscape concentration via a simulated annealing-based graph reduction. Red-QAOA creates a smaller (distilled) graph with nearly identical parameters to the original graph. The distilled graph produces a smaller quantum circuit and thus reduces noise impact. At the end of the optimization, Red-QAOA employs the parameters from the distilled graph on the original graph and continues the parameter search on the original graph. Red-QAOA outperforms state-of-the-art Graph Neural Network (GNN)-based pooling techniques on 3200 real-world problems. Red-QAOA reduced node and edge counts by 28% and 37%, respectively, with a mean square error of only 2%.