Neural QAOA$^{2}$: Differentiable Joint Graph Partitioning and Parameter Initialization for Quantum Combinatorial Optimization
This work addresses the scalability and performance bottlenecks of QAOA for combinatorial optimization by aligning partitioning and initialization with quantum optimization objectives.
Neural QAOA$^{2}$ introduces an end-to-end differentiable framework that jointly learns graph partitioning and parameter initialization for QAOA, outperforming heuristic baselines on 101 out of 183 instances across QUBO, Ising, and MaxCut problems (21-1000 variables).
The quantum approximate optimization algorithm (QAOA) holds promise for combinatorial optimization but is constrained by limited qubits. While divide-and-conquer frameworks like QAOA$^{2}$ address scalability by partitioning graphs into subgraphs, existing methods suffer from two fundamental limitations: i) misalignment between heuristic partitioning metrics and quantum optimization goals, and ii) topology-blind parameter initialization that leads to optimization cold starts. To bridge these gaps, we propose Neural QAOA$^{2}$, an end-to-end differentiable framework that jointly generates graph partitions and initial parameters. By integrating a generative evaluative network (GEN), our method utilizes a differentiable quantum evaluator as a high-fidelity performance surrogate to provide direct gradient guidance, enabling the joint generator to learn the intrinsic mapping from graph topology to high-quality partition and parameter configurations. Extensive experiments on 183 QUBO, Ising, and MaxCut instances (21 to 1000 variables) demonstrate that our gradient-driven approach broadly outperforms heuristic baselines, ranking first on 101 instances. It exhibits zero-shot generalization across out-of-distribution graph topologies and scales.