A hybrid quantum-classical neural network for learning to route

The paper investigates hybrid quantum‑classical neural networks for learning routing heuristics, focusing on whether small quantum neural networks can replace parameter‑heavy modules in an attention‑based routing model without sacrificing solution quality. For the capacitated vehicle routing problem, replacing the encoder feed‑forward component with a quantum version reduces model parameters by 56.6% while maintaining performance close to the classical baseline on small and medium instances, though the gap widens for larger instances. The study also compares the hybrid approach to classical routing algorithms, finding that classical methods remain highly competitive and often superior on fixed Euclidean test sets, indicating no quantum advantage but highlighting encoder feed‑forward replacement as a viable compression strategy for neural combinatorial optimization.

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