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From Graphs to Qubits: A Critical Review of Quantum Graph Neural Networks

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arxiv 2408.06524 v1 pith:DF7LO2N7 submitted 2024-08-12 quant-ph cs.LG

classification quant-phcs.LG
keywords quantumqgnnscomputationalgraphnetworksneuralapplicationschallenges
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Pattern Formation in Quantum Hierarchical Cellular Neural Networks

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    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.

  2. Spectral Geometry and Bosonic-Bloch Probes: Explorations in Quantum Learning

    quant-ph 2026-06 unverdicted novelty 5.0 of 10

    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...

  3. Learnable quantum spectral filters for hybrid graph neural networks

    quant-ph 2025-07 reject novelty 5.0 of 10

    A parameterized quantum Fourier circuit with graph-derived gate connections acts as a convolution plus pooling layer in a hybrid quantum-classical graph neural network, achieving benchmark accuracies comparable to som...

  4. Entanglement in Quantum Systems Based on Directed Graphs

    quant-ph 2025-09 conditional novelty 4.0 of 10

    For a class of graph states with commuting controlled-rotation gates, the Fubini-Study entanglement distance depends only on the vertex degree sequence, and this paper works out explicit formulas for four example grap...

  5. Clique detection using symmetry-restricted quantum circuits

    quant-ph 2025-06 reject novelty 4.0 of 10

    Permutation-invariant quantum circuits label cliques in small random graphs more accurately than cyclic-invariant or standard ansatze in simulation.

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