用可微分方法同时优化图划分和参数初始化，提升量子优化性能。
Neural QAOA$^{2}$: Differentiable Joint Graph Partitioning and Parameter Initialization for Quantum Combinatorial Optimization
- 联合生成图分区与初始参数，通过梯度反传优化
- 在183个实例上优于启发式基线，101个排名第一
- 支持跨图结构零样本泛化，适合大规模量子优化
量子近似优化算法（QAOA）在组合优化中前景广阔，但受限于量子比特数量。尽管像QAOA²这样的分治框架通过将图划分为子图来提升可扩展性，现有方法仍存在两大根本局限：一是启发式划分指标与量子优化目标不一致；二是拓扑无关的参数初始化导致优化冷启动。为此，我们提出Neural QAOA²，一个端到端可微分框架，联合生成图分区与初始参数。通过集成生成评估网络（GEN），该方法利用可微分量子评估器作为高保真性能代理，提供直接梯度指导，使联合生成器学习从图拓扑到高质量分区与参数配置的内在映射。在183个QUBO、Ising和MaxCut实例（变量数21至1000）上的大量实验表明，我们的梯度驱动方法广泛优于启发式基线，在101个实例上排名第一。该方法表现出跨分布外图拓扑的零样本泛化能力并具备可扩展性。
原文摘要 · Abstract (English)
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.
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