Neural QAOA$^{2}$: Differentiable Joint Graph Partitioning and Parameter Initialization for Quantum Combinatorial Optimization

TL;DR

Neural QAOA$^{2}$ introduces an end-to-end differentiable framework that jointly optimizes graph partitioning and parameters for quantum combinatorial optimization, improving scalability and performance.

Contribution

It presents a novel neural, differentiable approach with a generative network and quantum evaluator to better align partitioning and optimization goals.

Findings

Outperforms heuristic baselines on 183 instances

Ranks first on 101 instances

Shows zero-shot generalization across graph topologies

Abstract

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.