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Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
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Quantum-enhanced learning: Leveraging von Neumann entropy for enhanced graph neural network performance.

Muhammad Awais1, Octavian Adrian Postolache1, Sancho Moura Oliveira1

  • 1Iscte-Instituto Universitário de Lisboa, Av. das Forças Armadas, Lisbon, 1649-026, Portugal; Instituto de Telecomunicações, Av. Rovisco Pais, Lisbon, 1049-001, Portugal.

Neural Networks : the Official Journal of the International Neural Network Society
|April 12, 2026
PubMed
Summary

Quantum-Inspired Graph Neural Networks (QGNNs) overcome over-squashing limitations in Graph Neural Networks (GNNs). A novel Quantum Entanglement Loss (QEL) enables efficient long-range dependency modeling in complex graph data.

Keywords:
Graph neural networksOver-smoothingOver-squashingQuantum information theoryvon Neumann entropy

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Area of Science:

  • Graph Neural Networks
  • Quantum Computing
  • Machine Learning

Background:

  • Graph Neural Networks (GNNs) excel at learning from graph data but struggle with long-range dependencies due to over-squashing.
  • Over-squashing compresses neighborhood information, limiting the modeling of distant relationships.

Purpose of the Study:

  • Introduce a Quantum-Inspired Graph Neural Network (QGNN) to address the over-squashing problem.
  • Develop a novel Quantum Entanglement Loss (QEL) function for improved long-range dependency modeling.

Main Methods:

  • QGNN utilizes a Quantum Entanglement Loss (QEL) function.
  • QEL minimizes von Neumann entropy of the node embedding correlation matrix, preserving global patterns.
  • This creates direct information pathways between distant, functionally related nodes.

Main Results:

  • QGNN demonstrated significant improvements on the Long Range Graph Benchmark (LRGB) datasets.
  • Achieved 37.6% relative MAE reduction on Peptides-struct and 97% better performance than GCN for nodes 7+ hops apart.
  • Outperformed Graph Transformers (GraphGPS) by 4.0% while being computationally efficient.

Conclusions:

  • Entropy-based regularization is a principled and efficient method for long-range dependency modeling in graphs.
  • QGNN offers substantial performance gains with manageable computational overhead.
  • QGNN effectively bypasses multi-hop bottlenecks inherent in traditional GNNs.