Rotation equivariant quantum graph neural networks with trainable compression encoder and entanglement-enhanced...

Area of Science:

• Quantum Machine Learning
• Graph Neural Networks
• Computational Chemistry

Background:

• Equivariant Quantum Graph Neural Networks (EQGNNs) improve generalization on graph data.
• Current QGNNs lack rotational equivariance, and large graphs increase qubit demands.
• Processing large-scale graph data presents computational challenges in quantum computing.

Purpose of the Study:

• To introduce a novel Rotationally Equivariant Quantum Graph Neural Network (REQGNN).
• To address limitations in existing QGNNs regarding rotational equivariance and computational complexity.
• To develop a model that effectively handles large-scale graph data with reduced qubit requirements.

Main Methods:

• Proposed a REQGNN featuring a trainable compression encoder and an entanglement-enhanced aggregation mechanism.
• Utilized a quantum autoencoder with quantum fidelity for feature dimensionality compression, reducing qubit needs.
• Introduced an entanglement-enhanced layer incorporating node distance and angle information for rotational equivariance and an auxiliary entanglement layer to combat over-smoothing.

Main Results:

• REQGNN demonstrated superior performance in graph classification across four datasets compared to GIN, Gra+QSVM, and Gra+QCNN.
• Achieved better accuracy than egoGQNN on the PTC dataset for graph classification.
• Outperformed classical models EGNN and EquiformerV2 in graph regression tasks, reducing the MAE of the C_v task by 20% on average compared to QGCNN.

Conclusions:

• The proposed REQGNN effectively achieves rotational equivariance and addresses computational complexity in QGNNs.
• This work offers a novel perspective on incorporating symmetry in graph neural networks.
• REQGNN provides an effective solution for enhancing generalization and performance in graph-based quantum machine learning tasks.