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IEEE International Conference on Computer Design: VLSI in Computers and Processors (ICCD)

On the Design of Quantum Graph Convolutional Neural Network in the NISQ-Era and Beyond

Zhirui Hu, Jinyang Li, Zhenyu Pan, Shanglin Zhou, Lei Yang, Caiwen Ding, Omer Khan, Tong Geng, Weiwen Jiang

Published Oct 1, 2022• 28 citations
Publisher

Abstract

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.

DOI
10.1109/iccd56317.2022.00050

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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.
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.
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.
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.
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.
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 high energy physics (HEP) community has a long history of dealing with large-scale datasets. To manage such voluminous data, classical machine learning and deep learning techniques have been employed to accelerate physics discovery. Recent advances in quantum machine learning (QML) have indicated the potential of applying these techniques in HEP. However, there are only limited results in QML applications currently available. In particular, the challenge of processing sparse data, common in HEP datasets, has not been extensively studied in QML models. This research provides a hybrid quantum-classical graph convolutional network (QGCNN) for learning HEP data. The proposed framework demonstrates an advantage over classical multilayer perceptron and convolutional neural networks in the aspect of number of parameters. Moreover, in terms of testing accuracy, the QGCNN shows comparable performance to a quantum convolutional neural network on the same HEP dataset while requiring less than 50%50\%50% of the parameters. Based on numerical simulation results, studying the application of graph convolutional operations and other QML models may prove promising in advancing HEP research and other scientific fields.