From graphs to qubits: a critical review of quantum graph neural networks

Abstract Quantum Graph Neural Networks represent a novel fusion of quantum computing and Graph Neural Networks, aimed at overcoming the computational and scalability challenges inherent in classical models that are powerful tools for analyzing data with complex relational structures but suffer from limitations such as high computational complexity and over-smoothing in large-scale applications. Quantum computing, leveraging principles like superposition and entanglement, offers a pathway to enhanced computational capabilities. This paper critically reviews the state-of-the-art in Quantum Graph Neural Networks, exploring various architectures. We discuss their applications across diverse fields such as high-energy physics, molecular chemistry, finance and earth sciences, highlighting the potential for quantum advantage. Additionally, we address the significant challenges faced by Quantum Graph Neural Networks, including noise, decoherence, and scalability issues, proposing potential strategies to mitigate these problems. This comprehensive review aims to provide a foundational understanding of Quantum Graph Neural Networks, fostering further research and development in this promising interdisciplinary field.