The paper introduces CTQW-GNN, a graph neural network that uses Continuous‑Time Quantum Walks (CTQW) to address two common GNN problems: low‑pass bias on heterophilic graphs and over‑smoothing with deep layers. By exploiting the unitary nature of the CTQW propagator, the model preserves high‑frequency signals and maintains feature norms across layers. Three aggregation modules—CTQW‑based, CTQW‑attention, and a low‑pass GAT branch—combine to handle both heterophilic and homophilic graph structures, supported by spectral‑gap analysis and a Lieb–Robinson‑type bound for walk‑time selection.
arXiv:2606. 26873v1 Announce Type: cross Abstract: Graphs provide a natural language for relational data in chemistry, biology and optimisation.
arXiv:2503.24111v4 Announce Type: replace-cross Abstract: Graph Neural Networks (QGNNs) offer a promising approach to combining quantum computing with graph-structured data processing. While classica...
The paper implements two quantum graph neural network architectures—Simplified Graph Convolution (SGC) and Linear Graph Convolution (LGC)—and evaluates them on benchmark graph datasets for semi‑supervised learning using quantum simulation. It compares their predictive performance and optimization behavior to classical baselines, finding that the quantum models achieve competitive results with fewer parameters. Additionally, the study provides a cost‑gradient analysis to identify trainable tasks and a classical simulability investigation to determine regimes where the circuits remain robust during training.
arXiv:2602. 16018v2 Announce Type: replace-cross Abstract: Graph neural networks (GNNs) are a powerful framework for learning representations from graph-structured data, but their direct implementation on near-term quantum hardware remains challenging due to circuit depth, multi-qubit interactions, and qubit scalability constraints.
arXiv:2608.20660v1 Announce Type: cross Abstract: Simulating a continuous-time quantum walk (CTQW) on a graph in the circuit model of quantum computing requires decomposing its Hamiltonian into terms...
QGPINNs is a PyTorch-based physics-informed neural network framework for solving nonlocal differential equations on quantum graphs. It approximates the solution on each edge with a neural network and uses a unified graph‑based loss to enforce governing equations, initial, boundary, and vertex transmission conditions, including continuity, Kirchhoff‑Neumann, and Dirichlet conditions. The framework supports multi‑order fractional elliptic problems and time‑fractional evolution equations, incorporates graph‑adapted learning strategies such as soft/hard constraints, dynamic loss balancing, Fourier feature embeddings, and a learnable singularity‑capturing feature, and extends to inverse problems for identifying fractional orders and physical parameters from noisy data, as validated on benchmark and real‑world networks such as the IEEE 14‑bus system and an agricultural drainage network.
arXiv:2601. 02451v2 Announce Type: replace-cross Abstract: Graph Neural Networks (GNNs) suffer from over-smoothing in deep architectures and expressiveness bounded by the 1-Weisfeiler-Leman (1-WL) test.
arXiv:2602. 09258v2 Announce Type: replace Abstract: Deployed graph neural networks (GNNs) are frozen at deployment yet must fit clean data, generalize under distribution shifts, and remain stable to perturbations.
arXiv:2605. 13268v2 Announce Type: replace-cross Abstract: Trotter Suzuki product formulas are the standard route to Hamiltonian evolution on noisy intermediate-scale quantum (\NISQ{}) hardware, but their accuracy depends on three coupled choices: term grouping, product-formula order, and time-step allocation.
The paper introduces RGC‑Net, a Reservoir‑Based Graph Convolutional Network that combines fixed‑random reservoir dynamics with a structured convolutional framework for graph learning. It addresses limitations of existing reservoir‑based GNNs by adding a leaky integrator for better feature retention and a robust, adaptable architecture for graph classification and generation. Experiments demonstrate state‑of‑the‑art performance on classification and generative tasks, including dynamic brain connectivity, with faster convergence and reduced over‑smoothing.
arXiv:2608. 09596v1 Announce Type: cross Abstract: Graph Neural Networks (GNNs) suffer from two fundamental limitations: over-smoothing, where node representations become indistinguishable with depth, and over-squashing, where long-range information is compressed through limited message-passing channels.
arXiv:2605. 21916v2 Announce Type: replace-cross Abstract: Dynamic link prediction is important for modeling evolving interactions in social, communication, financial, and transportation networks.