Permutation-Invariant Quantum Graph Neural Network Based on Variational Quantum Algorithms

Area of Science:

• Quantum Computing
• Machine Learning
• Graph Representation Learning

Background:

• Graph Neural Networks (GNNs) excel at graph representation learning but face scalability and efficiency challenges.
• Existing Quantum GNNs (QGNNs) often underutilize edge information, demand significant quantum resources, and struggle with permutation invariance.

Purpose of the Study:

• To propose a novel permutation-invariant quantum GNN (PIQGNN) that addresses the limitations of current GNNs and QGNNs.
• To develop an efficient and scalable quantum framework for graph learning.

Main Methods:

• Introduced a low-qubit-cost quantum encoding strategy embedding node, edge, and topology information using n qubits for n nodes.
• Designed a symmetry-aware variational quantum neural network (QNN) for end-to-end permutation-invariant learning.
• Utilized Bayesian optimization for hyperparameter tuning to mitigate barren plateau effects and enhance training stability.

Main Results:

• PIQGNN achieved competitive performance against classical GNNs with fewer trainable parameters.
• Compared to existing QGNNs, PIQGNN demonstrated higher accuracy and required fewer quantum resources.
• PIQGNN exhibited enhanced robustness in noisy conditions, indicating practical potential for the NISQ era.

Conclusions:

• PIQGNN presents an efficient, scalable, and noise-resilient quantum framework for graph learning.
• The model effectively handles permutation invariance and integrates diverse graph information using minimal qubits.
• PIQGNN shows significant promise for real-world applications in the noisy intermediate-scale quantum (NISQ) era.