This paper proposes a new Quantum Spatial Graph Convolutional Neural Network (QSGCNN) model that can directly learn a classification function for graphs of arbitrary sizes. Unlike state-of-the-art Graph Convolutional Neural Network (GCNN) models, the proposed QSGCNN model incorporates the process of identifying transitive aligned vertices between graphs and transforms arbitrary sized graphs into fixed-sized aligned vertex grid structures. In order to learn representative graph characteristics, a new quantum spatial graph convolution is proposed and employed to extract multi-scale vertex features, in terms of quantum information propagation between grid vertices of each graph. Since the quantum spatial convolution preserves the grid structures of the input vertices (i.e., the convolution layer does not alter the original spatial position of vertices), the proposed QSGCNN model allows to directly employ the traditional convolutional neural network architecture to further learn from the global graph topology, providing an end-to-end deep learning architecture that integrates the graph representation and learning in the quantum spatial graph convolution layer and the traditional convolutional layer for graph classifications. We indicate the effectiveness of the proposed QSGCNN model in relation to existing state-of-the-art methods. Experiments on benchmark graph classification datasets demonstrate the effectiveness of the proposed QSGCNN model.
This paper proposes a new Quantum Spatial Graph Convolutional Neural Network (QSGCNN) model that can directly learn a classification function for graphs of arbitrary sizes. Unlike state-of-the-art Graph Convolutional Neural Network (GCNN) models, the proposed QSGCNN model incorporates the process of identifying transitive aligned vertices between graphs and transforms arbitrary sized graphs into fixed-sized aligned vertex grid structures. In order to learn representative graph characteristics, a new quantum spatial graph convolution is proposed and employed to extract multi-scale vertex features, in terms of quantum information propagation between grid vertices of each graph. Since the quantum spatial convolution preserves the grid structures of the input vertices (i.e., the convolution layer does not alter the original spatial position of vertices), the proposed QSGCNN model allows to directly employ the traditional convolutional neural network architecture to further learn from the global graph topology, providing an end-to-end deep learning architecture that integrates the graph representation and learning in the quantum spatial graph convolution layer and the traditional convolutional layer for graph classifications. We indicate the effectiveness of the proposed QSGCNN model in relation to existing state-of-the-art methods. Experiments on benchmark graph classification datasets demonstrate the effectiveness of the proposed QSGCNN model.
This paper proposes a novel Quantum Spatial Graph Convolutional Neural Network (QSGCNN) model that can directly learn a classification function for graphs of arbitrary sizes. The main idea is to define a new quantum-inspired spatial graph convolution associated with pre-transformed fixed-sized aligned grid structures of graphs, in terms of quantum information propagation between grid vertices of each graph. We show that the proposed QSGCNN model can significantly reduce either the information loss or the notorious tottering problem arising in existing spatially-based Graph Convolutional Network (GCN) models. Experiments on benchmark graph datasets demonstrate the effectiveness of the proposed QSGCNN model.
At present, there are a large number of quantum neural network models to deal with Euclidean spatial data, while little research have been conducted on non-Euclidean spatial data. In this paper, we propose a novel quantum graph convolutional neural network (QGCN) model based on quantum parametric circuits and utilize the computing power of quantum systems to accomplish graph classification tasks in traditional machine learning. The proposed QGCN model has a similar architecture as the classical graph convolutional neural networks, which can illustrate the topology of the graph type data and efficiently learn the hidden layer representation of node features as well. Numerical simulation results on a graph dataset demonstrate that the proposed model can be effectively trained and has good performance in graph level classification tasks.
The data generated from non-Euclidean domains and its graphical representation (with complex-relationship object interdependence) applications has observed an exponential growth. The sophistication of graph data has posed consequential obstacles to the existing machine learning algorithms. In this study, we have considered a revamped version of a semi-supervised learning algorithm for graph-structured data to address the issue of expanding deep learning approaches to represent the graph data. Additionally, the quantum information theory has been applied through Graph Neural Networks (GNNs) to generate Riemannian metrics in closed-form of several graph layers. In further, to pre-process the adjacency matrix of graphs, a new formulation is established to incorporate high order proximities. The proposed scheme has shown outstanding improvements to overcome the deficiencies in Graph Convolutional Network (GCN), particularly, the information loss and imprecise information representation with acceptable computational overhead. Moreover, the proposed Quantum Graph Convolutional Network (QGCN) has significantly strengthened the GCN on semi-supervised node classification tasks. In parallel, it expands the generalization process with a significant difference by making small random perturbations of the graph during the training process. The evaluation results are provided on three benchmark datasets, including Citeseer, Cora, and PubMed, that distinctly delineate the superiority of the proposed model in terms of computational accuracy against state-of-the-art GCN and three other methods based on the same algorithms in the existing literature.
The rapid growth in the size of Graph Convolutional Neural Networks (GCNs) encounters both computational- and memory-wall on classical computing platforms (e.g., CPU, GPU, FPGA, etc.). Quantum computing, on the other hand, provides extremely high parallelism for computation. Although quantum neural networks have been recently studied, the research on quantum graph neural networks is still in its infancy. The key challenge here is how to integrate both the graph topology information and the learning ability of GCNs into quantum circuits. In this work, we leverage the Givens rotations and its quantum implementation to encode graph information; in addition, we employ the widely used variational quantum circuit to bring the learnable parameters. On top of these, we present a full-quantum design of Graph Convolutional Neural Networks, namely "QuGCN", for semi-supervised learning on graph-structured data. Experiment results show our design is competitive with classical GCNs in terms of node classification accuracy on Cora sub-dataset. More importantly, we show the potential advantages that can be achieved by the proposed quantum GCN design when the number of features grows.
Graph Neural Networks (GNN) and Transformer-based architectures have achieved remarkable progress in graph learning, yet they still struggle to capture both global structural dependencies and model the dynamic information propagation. In this paper, we propose CTQWformer, a hybrid graph learning framework that integrates continuous-time quantum walks (CTQW) with GNN. CTQWformer employs a trainable Hamiltonian that fuses graph topology and node features, enabling physically grounded modeling of quantum walk dynamics that captures rich and intricate graph structure information. The extracted CTQW-based representations are incorporated into two complementary modules:(i) a Graph Transformer module that embeds final-time propagation probabilities as structural biases in the self-attention mechanism, and (ii) a Graph Recurrent Module that captures temporal evolution patterns with bidirectional recurrent networks. Extensive experiments on benchmark graph classification datasets demonstrate that CTQWformer outperforms graph kernel and GNN-based methods, demonstrating the potential of integrating quantum dynamics into trainable deep learning frameworks for graph representation learning. To the best of our knowledge, CTQWformer is the first hybrid CTQW-based Transformer, integrating CTQW-derived structural bias with temporal evolution modeling to advance graph learning.
This article proposes a quantum spatial graph convolutional neural network (QSGCN) model that is implementable on quantum circuits, providing a novel avenue to processing non-Euclidean type data based on the state-of-the-art parameterized quantum circuit (PQC) computing platforms. Four basic blocks are constructed to formulate the whole QSGCN model, including the quantum encoding, the quantum graph convolutional layer, the quantum graph pooling layer, and the network optimization. In particular, the trainability of the QSGCN model is analyzed through discussions on the barren plateau phenomenon. Simulation results from various types of graph data are presented to demonstrate the learning, generalization, and robustness capabilities of the proposed quantum neural network (QNN) model.