A hybrid quantum-classical neural network for learning to route
Abstract
This work studies hybrid quantum-classical neural networks for learning routing heuristics. Specifically, this paper asks whether small quantum neural networks can replace parameter-heavy modules inside a competitive attention-based routing model while maintaining solution quality. For the capacitated vehicle routing problem, encoder feed-forward replacement emerges as the most promising design: it reduces the number of model parameters by 56.6% while keeping the hybrid model close to the classical neural baseline at small and medium instance sizes, although the gap grows for larger instances. This work also compares to classical routing algorithms, which remain highly competitive and often superior on the fixed Euclidean test sets. Our results therefore do not indicate quantum advantage or solver dominance, but identify encoder feed-forward replacement as a viable hybrid-module compression strategy for neural combinatorial optimization.
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BibTeX
@misc{ritt2026hybrid,
title = {{A hybrid quantum-classical neural network for learning to route}},
author = {Marcus Rolf Peter Ritt and Alexsandro Santos da Rosa Júnior and Marcos Vinicius Reballo and Cesar Augusto do Amaral and Fernando Augusto Caletti de Barros},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00489},
eprint = {2609.00489},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00489},
}
RIS
TY - UNPB
TI - A hybrid quantum-classical neural network for learning to route
AU - Marcus Rolf Peter Ritt
AU - Alexsandro Santos da Rosa Júnior
AU - Marcos Vinicius Reballo
AU - Cesar Augusto do Amaral
AU - Fernando Augusto Caletti de Barros
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00489
UR - https://arxiv.org/abs/2609.00489
AB - This work studies hybrid quantum-classical neural networks for learning routing heuristics. Specifically, this paper asks whether small quantum neural networks can replace parameter-heavy modules inside a competitive attention-based routing model while maintaining solution quality. For the capacitated vehicle routing problem, encoder feed-forward replacement emerges as the most promising design: it reduces the number of model parameters by 56.6% while keeping the hybrid model close to the classical neural baseline at small and medium instance sizes, although the gap grows for larger instances. This work also compares to classical routing algorithms, which remain highly competitive and often superior on the fixed Euclidean test sets. Our results therefore do not indicate quantum advantage or solver dominance, but identify encoder feed-forward replacement as a viable hybrid-module compression strategy for neural combinatorial optimization.
ER -