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arXiv:2203.03251

Novel Architecture of Parameterized Quantum Circuit for Graph Convolutional Network

Yanhu Chen, Cen Wang, Hongxiang Guo, Jianwu

Published Mar 7, 2022• 1 citation
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Abstract

Recently, the implementation of quantum neural networks is based on noisy intermediate-scale quantum (NISQ) devices. Parameterized quantum circuit (PQC) is such the method, and its current design just can handle linear data classification. However, data in the real world often shows a topological structure. In the machine learning field, the classical graph convolutional layer (GCL)-based graph convolutional network (GCN) can well handle the topological data. Inspired by the architecture of a classical GCN, in this paper, to expand the function of the PQC, we design a novel PQC architecture to realize a quantum GCN (QGCN). More specifically, we first implement an adjacent matrix based on linear combination unitary and a weight matrix in a quantum GCL, and then by stacking multiple GCLs, we obtain the QGCN. In addition, we first achieve gradients decent on quantum circuit following the parameter-shift rule for a GCL and then for the QGCN. We evaluate the performance of the QGCN by conducting a node classification task on Cora dataset with topological data. The numerical simulation result shows that QGCN has the same performance as its classical counterpart, the GCN, in contrast, requires less tunable parameters. Compared to a traditional PQC, we also verify that deploying an extra adjacent matrix can significantly improve the classification performance for quantum topological data.

DOI
10.48550/arxiv.2203.03251

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Recently, the implementation of quantum neural networks is based on noisy intermediate-scale quantum (NISQ) devices. Parameterized quantum circuit (PQC) is such the method, and its current design just can handle linear data classification. However, data in the real world often shows a topological structure. In the machine learning field, the classical graph convolutional layer (GCL)-based graph convolutional network (GCN) can well handle the topological data. Inspired by the architecture of a classical GCN, in this paper, to expand the function of the PQC, we design a novel PQC architecture to realize a quantum GCN (QGCN). More specifically, we first implement an adjacent matrix based on linear combination unitary and a weight matrix in a quantum GCL, and then by stacking multiple GCLs, we obtain the QGCN. In addition, we first achieve gradients decent on quantum circuit following the parameter-shift rule for a GCL and then for the QGCN. We evaluate the performance of the QGCN by conducting a node classification task on Cora dataset with topological data. The numerical simulation result shows that QGCN has the same performance as its classical counterpart, the GCN, in contrast, requires less tunable parameters. Compared to a traditional PQC, we also verify that deploying an extra adjacent matrix can significantly improve the classification performance for quantum topological data.
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.
Processing graph-structured data in Green Internet of Things (IoT) applications demands a dual focus on analytical accuracy and energy efficiency. While Quantum Graph Neural Networks (QGNNs) present a promising computational paradigm, the parameterized quantum circuits (PQC) they rely on often require excessive depth and lack robustness, hindering their use in resource-constrained environments. The core problem addressed in this paper is how to design a quantum-inspired GCN that balances expressive power with shallow, energy-efficient circuit design, making it viable for sustainable Green IoT deployment. Our main contributions are threefold. First, we design the Intelligent Parameterized Quantum Circuit (IPQC) as a compact, 15-parameter bidirectional-control quantum convolutional block that enhances expressive power while maintaining parameter efficiency and noise tolerance. Second, building on this block, we develop the Quantum Graph Convolutional Network with Residual Injection (QGCN-RI), a residual-injection-driven network that integrates two-stage normalization and amplitude encoding to significantly improve optimization stability. Third, we conduct comprehensive experiments on citation network benchmarks. Results demonstrate that QGCN-RI achieves performance competitive with strong classical baselines like GAT, reaching 83.3% accuracy on Cora. More critically, our quantitative analysis indicates that the model’s shallow circuit design allows it to achieve this competitive accuracy with a lower estimated energy consumption. By showing that a compact QGCN can approximate the performance of its classical counterparts with reduced resource costs, our work validates the feasibility of quantum graph learning for developing sustainable and resource-aware Green IoT solutions.
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 (GNNs) achieve state-of-the-art performance on graph-structured data, but training and inference on large graphs are often bottlenecked by memory constraints and sparse linear-algebra workloads. Quantum computing offers an alternative set of primitives that may improve scalability for graph learning. Building on the quantum graph neural network (QGNN) framework of Liao \textit{et al.}, this work implements two representative architectures --- the Simplified Graph Convolution (SGC) and Linear Graph Convolution (LGC) models --- and evaluates them on open benchmark graph datasets and semi-supervised learning tasks using quantum simulation. We compare predictive performance and optimization behavior against classical baselines, showing that the quantum models achieve competitive performance with fewer parameters. Finally, we present a cost gradient analysis that identifies the tasks for which the models showcased are trainable. This is followed by a classical simulability study to find regimes in which the proposed circuits remain robust during training.
Image classification is a core task in the field of computer vision, with significant implications for applications such as medical imaging and autonomous driving. Classical neural network architectures face numerous challenges when dealing with high-dimensional and complex data, particularly in terms of feature extraction and data processing capabilities, limiting their performance in certain applications. Quantum computing offers promising new approaches to processing high-dimensional complex data, most notably through Parameterized Quantum Circuits (PQC) as quantum hybrid neural networks for image classification. In this paper, we propose a hybrid neural network featuring a specific PQC structure designed to generate entanglement in accordance with sample images. This PQC structure utilizes the adjacency matrix of the corresponding graph of the sample image, embedding adjacency relationships among nodes into the entanglement module, thereby generating entanglement aligned with the features of specific images. Numerical results validate the effectiveness of our PQC model across various image classification tasks, enhancing the efficiency of feature learning and representation. Our model demonstrates significant advantages in classification accuracy and learning efficiency on classical datasets. Our research not only advances the theoretical understanding of hybrid quantum networks but also paves the way for practical implementations in real-world scenarios.
Graph Convolutional Networks (GCNs) have been widely used to learn from graph structured data, but GCNs suffer from a high complexity in the handling of large-scale graphs, since processing large graphs demands recursive aggregation of features and high dimensional node embeddings. Scalability can become a tight bottleneck in traditional CPU/GPU implementations, which detracts from their ability to be used in real-time and resource-constrained settings. In this study, Quantum-assisted GCN (QGCN) is proposed as a quantum-assisted GCN model with the help of quantum logic gates, thereby speeding up the graph convolution operation. The idea proposed in the paper is to represent the queries and graph features as qubits and use a sequence of both single and multi-qubit gates such as Hadamard, CNOT and rotation gates with learned parameters to convolute a graph over qubits simultaneously. Once measured, the quantum state is represented classically, in the form of features, which are then used to feed downstream node classification tasks. On the benchmark datasets Cora, PubMed, and Citeseer, experiments show that the quantum-assisted GCN delivers substantial speed-up over a classical implementation, approaches the performance of the GPU-optimized implementation, and maintains classification within a 0.5–1% margin. If NISQ simulators are to scale up to very large graphs, there are resource utilization issues, which is manageable for current simulators given the number of qubits and gate depth. These results show concrete compromises between acceleration, accuracy preservation, and quantum resource efficiency. The results of this study could be useful for designing hybrid quantum-classical graph learning architectures and represent one possible method for performing faster GCN operations in both academic research and applications. Extensions and developments are focused on multi-layer quantum GCNs as well as hybrid architectures for large-scale GWs and real-time deployment strategies.