Quantum-enhanced learning: Leveraging von Neumann entropy for enhanced graph neural network performance

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.