Quantum theory has shown its superiority in enhancing machine learning. However, facilitating quantum theory to enhance graph learning is in its infancy. This survey investigates the current advances in quantum graph learning (QGL) from three perspectives, i.e., underlying theories, methods, and prospects. We first look at QGL and discuss the mutualism of quantum theory and graph learning, the specificity of graph-structured data, and the bottleneck of graph learning, respectively. A new taxonomy of QGL is presented, i.e., quantum computing on graphs, quantum graph representation, and quantum circuits for graph neural networks. Pitfall traps are then highlighted and explained. This survey aims to provide a brief but insightful introduction to this emerging field, along with a detailed discussion of frontiers and outlook yet to be investigated.
Quantum theory has shown its superiority in enhancing machine learning. However, facilitating quantum theory to enhance graph learning is in its infancy. This survey investigates the current advances in quantum graph learning (QGL) from three perspectives, i.e., underlying theories, methods, and prospects. We first look at QGL and discuss the mutualism of quantum theory and graph learning, the specificity of graph-structured data, and the bottleneck of graph learning, respectively. A new taxonomy of QGL is presented, i.e., quantum computing on graphs, quantum graph representation, and quantum circuits for graph neural networks. Pitfall traps are then highlighted and explained. This survey aims to provide a brief but insightful introduction to this emerging field, along with a detailed discussion of frontiers and outlook yet to be investigated.
Graph and network theory play a fundamental role in quantum computer sciences, including quantum information and computation. Random graphs and complex network theory are pivotal in predicting novel quantum phenomena, where entangled links are represented by edges. Quantum algorithms have been developed to enhance solutions for various network problems, giving rise to quantum graph computing and quantum graph learning (QGL). In this review, we explore graph theory and graph learning methods as powerful tools for quantum computers to generate efficient solutions to problems beyond the reach of classical systems. We delve into the development of quantum complex network theory and its applications in quantum computation, materials discovery, and research. We also discuss quantum machine learning (QML) methodologies for effective image classification using qubits, quantum gates, and quantum circuits. Additionally, the paper addresses the challenges of QGL and algorithms, emphasizing the steps needed to develop flexible QGL solvers. This review presents a comprehensive overview of the fields of QGL and QML, highlights recent advancements, and identifies opportunities for future research.
Abstract Quantum Machine Learning (QML) is an emerging interdisciplinary field that merges quantum computing with classical machine learning (ML) to enhance computational efficiency, scalability, and accuracy in data-driven tasks. By leveraging quantum properties such as superposition, entanglement, and quantum parallelism, QML has the potential to solve complex problems that are intractable for classical models. This survey provides a comprehensive, systematic review of recent advancements in QML, conducted following the PRISMA 2020 guidelines and covering fundamental encoding techniques that enable quantum computers to process classical data, as well as essential tools, datasets, and evaluation metrics used in quantum model development. Furthermore, it explores various QML approaches, including supervised, semi-supervised, unsupervised, and reinforcement learning, alongside quantum deep learning (QDL) models such as Quantum Neural Networks (QNNs) and Variational Quantum Circuits (VQCs). The paper also discusses the challenges in QML, including hardware limitations, scalability issues, and the need for improved quantum error correction. A dual-axis taxonomy simultaneously classifies algorithms by learning paradigm and quantum-classical integration level – a structure not found in prior surveys. The survey also covers Quantum Transfer Learning, Quantum Graph Neural Networks, and hardware-aware encoding selection, and introduces the first structured adversarial robustness taxonomy and Explainable QML treatment in a comprehensive QML survey. Together, these contributions position this work as both a reference and a methodological guide for advancing QML research and applications.
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.
Quantum computing (QC) is a new computational paradigm whose foundations relate to quantum physics. Notable progress has been made, driving the birth of a series of quantum-based algorithms that take advantage of quantum computational power. In this paper, we provide a targeted survey of the development of QC for graph-related tasks. We first elaborate the correlations between quantum mechanics and graph theory to show that quantum computers are able to generate useful solutions that can not be produced by classical systems efficiently for some problems related to graphs. For its practicability and wide-applicability, we give a brief review of typical graph learning techniques designed for various tasks. Inspired by these powerful methods, we note that advanced quantum algorithms have been proposed for characterizing the graph structures. We give a snapshot of quantum graph learning where expectations serve as a catalyst for subsequent research. We further discuss the challenges of using quantum algorithms in graph learning, and future directions towards more flexible and versatile quantum graph learning solvers.
This paper introduces a novel approach to graph neural networks (GNNs) – the 'Quantum Adaptive Graph Neural Network' – leveraging quantum self-adaptation to enhance both expressiveness and computational efficiency. Traditional GNNs often struggle with the inherent complexities of graph data and require substantial computational resources. We propose a new architecture that employs quantum mechanics to simulate graph structures, allowing the network to learn more robust representations. This approach, dubbed Quantum Adaptive Graph Neural Network (QAGNN), utilizes quantum machine learning algorithms to improve the network's ability to capture intricate relationships within the graph. The paper details the core mechanism, its mathematical foundations, and preliminary experimental results demonstrating significant improvements in various graph classification tasks compared to traditional GNNs. We present a comprehensive analysis of the QAGNN's performance and discuss potential future research directions.
Quantum Machine Learning (QML) has emerged as a promising interdisciplinary field that combines quantum computing with machine learning to address complex computational problems. This survey provides a comprehensive overview of the theoretical foundations, unified taxonomy, and key methodologies in QML. We discuss quantum data encoding techniques, variational quantum models, neural-inspired quantum architectures, and quantum data learning approaches, along with their associated challenges and limitations. The survey further examines evaluation strategies, the concept of quantum advantage, and the role of current quantum hardware and software platforms in advancing QML research. In addition, major application domains and the growing importance of trustworthy QML, including interpretability, robustness, and security, are explored. Finally, we highlight open challenges and future research directions to provide insights into the evolving landscape of Quantum Machine Learning.