Quantum machine learning is a fast-emerging field that aims to tackle machine learning using quantum algorithms and quantum computing. Due to the lack of physical qubits and an effective means to map real-world data from Euclidean space to Hilbert space, most of these methods focus on quantum analogies or process simulations rather than devising concrete architectures based on qubits. In this paper, we propose a novel hybrid quantum-classical algorithm for graph-structured data, which we refer to as the Ego-graph based Quantum Graph Neural Network (egoQGNN). egoQGNN implements the GNN theoretical framework using the tensor product and unity matrix representation, which greatly reduces the number of model parameters required. When controlled by a classical computer, egoQGNN can accommodate arbitrarily sized graphs by processing ego-graphs from the input graph using a modestly-sized quantum device. The architecture is based on a novel mapping from real-world data to Hilbert space. This mapping maintains the distance relations present in the data and reduces information loss. Experimental results show that the proposed method outperforms competitive state-of-the-art models with only 1.68\% parameters compared to those models.

翻译：量子机器学习是一个快速发展的新兴领域，旨在利用量子算法和量子计算来解决机器学习问题。由于缺乏物理量子比特以及将现实世界数据从欧几里得空间映射到希尔伯特空间的有效方法，大多数方法侧重于量子类比或过程模拟，而非基于量子比特设计具体架构。本文提出了一种针对图结构数据的新型量子-经典混合算法，称为基于自我中心图的量子图神经网络（egoQGNN）。egoQGNN利用张量积和单位矩阵表示实现了GNN理论框架，大幅减少了所需模型参数数量。在经典计算机控制下，该算法可通过处理输入图中的自我中心图，使用小规模量子设备适应任意大小的图。其架构基于一种从现实世界数据到希尔伯特空间的新型映射方法，该方法能保持数据中的距离关系并减少信息损失。实验结果表明，所提方法仅需1.68%的参数量即可超越具有竞争力的最新模型。