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From Graphs to Qubits: A Critical Review of Quantum Graph Neural Networks
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From Graphs to Qubits: A Critical Review of Quantum Graph Neural Networks
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Quantum Graph Neural Networks (QGNNs) represent a novel fusion of quantum computing and Graph Neural Networks (GNNs), aimed at overcoming the computational and scalability challenges inherent in classical GNNs 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 QGNNs, 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 QGNNs, including noise, decoherence, and scalability issues, proposing potential strategies to mitigate these problems. This comprehensive review aims to provide a foundational understanding of QGNNs, fostering further research and development in this promising interdisciplinary field.
Forward citations
Cited by 7 Pith papers
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Scalable Message-Passing Quantum Graph Neural Networks in the Weisfeiler-Leman Hierarchy
The work constructs a permutation-equivariant quantum GNN that implements message passing at selectable Weisfeiler-Leman levels, supports pre-training on small graphs, and demonstrates readout scalability with simulat...
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Analog Quantum Asynchronous Event-Based Graph Neural Network
Proposes a hybrid quantum-classical framework for running event-based graph neural networks on neutral-atom processors by mapping events to atoms and programming the Rydberg Hamiltonian to realize message passing.
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Quantum Injection Pathways for Implicit Graph Neural Networks
Independent quantum signal injection into graph DEQs yields higher test accuracy and fewer solver iterations than state-dependent or backbone-dependent injection and classical equilibrium models on NCI1, PROTEINS, and...
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Pattern Formation in Quantum Hierarchical Cellular Neural Networks
Wick rotation of p-adic hierarchical CNNs produces nonlinear p-adic Schrödinger QNNs with graph discretizations, local solutions, and simulations of open-system pulse response and habituation.
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Spectral Geometry and Bosonic-Bloch Probes: Explorations in Quantum Learning
Training in graph-regularized quantum networks increases spectral dimension by 0.23 and enables anomaly detection via Bloch drift (ROC-AUC ≥0.9) while bosonic enhancement correlates with Fiedler splits (r=-0.50).
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Spectral Geometry and Bosonic-Bloch Probes: Explorations in Quantum Learning
Learning-induced spectral structure in hybrid quantum models is diagnosed by edge-resolved two-boson interference correlated with Fiedler cuts and by absolute Bloch drift that separates anomalies from benign states.
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Spectral Geometry and Bosonic-Bloch Probes: Explorations in Quantum Learning
Training reorganizes output similarity graphs in quantum networks, increasing spectral dimension by 0.23, with bosonic interference correlations and Bloch drift enabling high-ROC-AUC anomaly detection via a proposed s...
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