A Heuristic for Minimizing Resource Requirement for Quantum Graph Neural Networks

Quantum graph neural networks (QGNNs) utilize qubit entanglement and superposition for better representation of the graph data, but they are limited by the number of qubits available on the quantum hardware. To offset this limitation, we propose an approach called hybrid quantum-classical GNNs (QCGNNs) involving graph clustering algorithms for partitioning the nodes of a graph into clusters and learning representation of clusters using QGNNs for subsequent graph classification. QCGNNs require lesser number of qubits and runs on quantum hardware in comparison to existing QGNNs without significantly impacting accuracy. Suitability of different clustering algorithms for implementing QCGNNs was also assessed in this research attempt. Experimental results show an 81.33% reduction in qubit requirement on the MUTAG dataset. All the experiments reported in this paper are performed on the SV1 quantum simulator provided by Amazon Braket environment.