  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%.
