Background As graph datasets—including social networks, supply chains, and bioinformatics data—grow in size and complexity, researchers are driven to search for solutions enhancing model efficiency and speed. One avenue that may provide a solution is Quantum Graph Learning (QGL), a subfield of Quantum Machine Learning (QML) that applies machine learning inspired or powered by quantum computing to graph learning tasks. Methods We reevaluate Quantum Feature Embeddings (QFE), a QGL methodology published by Xu et al. earlier this year. QFE uses Variational Quantum Circuits to preprocess node features and then sends them to a classical Graph Neural Network (GNN), with the goal of increasing performance and/or decreasing total model size. Xu et al. evaluated this methodology by comparing its performance with the performance of variously-sized classical models on the benchmark datasets PROTEINS and ENZYMES, and they report success. Our core methodology and learning task remain unchanged. However, we have made several changes to the experimental design that enhance the rigor of the study: 1) we include the testing of models with no embedder; 2) we conduct a thorough hyperparameter search using a state-of-the-art optimization algorithm; and 3) we conduct stratified five-fold cross-validation, which mitigates the bias produced by our small datasets and provides multiple test statistics from which we can calculate a confidence interval. Results We produce classical models that perform comparably to QFE and significantly outperform the small classical models used in Xu et al.’s comparison. Notably, many of our classical models achieve this using fewer parameters than the QFE models we trained. Xu et al. do not report their total model sizes. Conclusion Our study sheds doubt on the efficacy of QFE by demonstrating that small, well-tuned classical models can perform just as well as QFE, highlighting the importance of hyperparameter tuning and rigorous experimental design.
Background As graph datasets—including social networks, supply chains, and bioinformatics data—grow in size and complexity, researchers are driven to search for solutions enhancing model efficiency and speed. One avenue that may provide a solution is Quantum Graph Learning (QGL), a subfield of Quantum Machine Learning (QML) that applies machine learning inspired or powered by quantum computing to graph learning tasks. Methods We reevaluate Quantum Feature Embeddings (QFE), a QGL methodology published by Xu et al. earlier this year. QFE uses Variational Quantum Circuits to preprocess node features and then sends them to a classical Graph Neural Network (GNN), with the goal of increasing performance and/or decreasing total model size. Xu et al. evaluated this methodology by comparing its performance with the performance of variously-sized classical models on the benchmark datasets PROTEINS and ENZYMES, and they report success. Our core methodology and learning task remain unchanged. However, we have made several changes to the experimental design that enhance the rigor of the study: 1) we include the testing of models with no embedder; 2) we conduct a thorough hyperparameter search using a state-of-the-art optimization algorithm; and 3) we conduct stratified five-fold cross-validation, which mitigates the bias produced by our small datasets and provides multiple test statistics from which we can calculate a confidence interval. Results We produce classical models that perform comparably to QFE and significantly outperform the small classical models used in Xu et al.’s comparison. Notably, many of our classical models achieve this using fewer parameters than the QFE models we trained. Xu et al. do not report their total model sizes. Conclusion Our study sheds doubt on the efficacy of QFE by demonstrating that small, well-tuned classical models can perform just as well as QFE, highlighting the importance of hyperparameter tuning and rigorous experimental design.
Quantum computing offers a promising avenue to reduce growing machine learning model complexity as required in large language models and simulation models for weather forecasts, financial forecasts, or engineering. Graph neural networks are a particular class of machine learning models that have garnered much attention for their ability to deal well with structured data. We investigate how to enhance existing GNNs and find through the inductive bias that quantum circuits are used best to encode node features. The proposed Quantum Feature Embeddings (QFEs) turn raw input features into quantum states, enabling non-linear and entangled representations. In particular, QFEs provide normalized, non-redundant weight matrices in an exponentially larger feature space and require much fewer qubits than fully quantum graph neural networks. On standard graph benchmark datasets, we showcase that for the same parameter count QFEs perform better than their classical counterpart, and are able to match the performance of an exponentially larger model. Finally, we study the potential benefit of using a hybrid quantum graph neural network over a classic alternative on a concrete use case, laser cutting. We find that the proposed model has the performance and thus the near-term potential to uplift these business applications.
Quantum computing offers a promising avenue to reduce growing machine learning model complexity as required in large language models and simulation models for weather forecasts, financial forecasts, or engineering.Graph neural networks are a particular class of machine learning models that have garnered much attention for their ability to deal well with structured data.We investigate how to enhance existing GNNs and find through the inductive bias that quantum circuits are used best to encode node features.The proposed Quantum Feature Embeddings (QFEs) turn raw input features into quantum states, enabling non-linear and entangled representations.In particular, QFEs provide normalized, non-redundant weight matrices in an exponentially larger feature space and require much fewer qubits than fully quantum graph neural networks.On standard graph benchmark datasets, we showcase that for the same parameter count QFEs perform better than their classical counterpart, and are able to match the performance of an exponentially larger model.Finally, we study the potential benefit of using a hybrid quantum graph neural network over a classic alternative on a concrete use case, laser cutting.We find that the proposed model has the performance and thus the near-term potential to uplift these business applications.
Accurate prediction of molecular properties is crucial for accelerating the development of new drugs, and quantum machine learning (QML) holds great promise in this domain. A typical QML pipeline comprises two core stages: encoding classical data into quantum representations followed by training and prediction using quantum computing-based machine learning (ML) models. In this article, we focus on the initial encoding stage and propose an effective quantum feature extraction approach for molecular graph data, introducing quantum node embedding and quantum edge embedding methods. We developed a hybrid quantum-classical ML framework and implemented several quantum-embedded graph neural network (QEGNN) models to evaluate the proposed method. Experiments conducted on three benchmark data sets with diverse molecular property prediction tasks demonstrate that QEGNN models consistently achieve higher accuracy, improved stability, and significantly reduced parameter complexity─hallmarks of quantum advantage. Furthermore, we validate the reliability of the quantum embedding approach on the superconducting quantum processor "Wukong," showing that the models retain stable performance even under the constraints of current noisy quantum hardware. This work highlights the potential of QML and paves the way for the development of universal QML models.
Node embeddings act as the information interface for graph neural networks, yet their empirical impact is often reported under mismatched backbones, splits, and training budgets. This paper provides a controlled benchmark of embedding choices for graph classification, comparing classical baselines with quantum-oriented node representations under a unified pipeline. We evaluate two classical baselines alongside quantum-oriented alternatives, including a circuit-defined variational embedding and quantum-inspired embeddings computed via graph operators and linear-algebraic constructions. All variants are trained and tested with the same backbone, stratified splits, identical optimization and early stopping, and consistent metrics. Experiments on five different TU datasets and on QM9 converted to classification via target binning show clear dataset dependence: quantum-oriented embeddings yield the most consistent gains on structure-driven benchmarks, while social graphs with limited node attributes remain well served by classical baselines. The study highlights practical trade-offs between inductive bias, trainability, and stability under a fixed training budget, and offers a reproducible reference point for selecting quantum-oriented embeddings in graph learning.
To accelerate the process of materials design, materials science has increasingly used data driven techniques to extract information from collected data. Specially, machine learning (ML) algorithms, which span the ML discipline, have demonstrated ability to predict various properties of materials with the level of accuracy similar to explicit calculation of quantum mechanical theories, but with significantly reduced run time and computational resources. Within ML, graph neural networks have emerged as an important algorithm within the field of machine learning, since they are capable of predicting accurately a wide range of important physical, chemical and electronic properties due to their higher learning ability based on the graph representation of material and molecular descriptors through the aggregation of information embedded within the graph. In parallel with the development of state of the art classical machine learning applications, the fusion of quantum computing and machine learning have created a new paradigm where classical machine learning model can be augmented with quantum layers which are able to encode high dimensional data more efficiently. Leveraging the structure of existing algorithms, we developed a unique and novel gradient free hybrid quantum classical convoluted graph neural network (HyQCGNN) to predict formation energies of perovskite materials. The performance of our hybrid statistical model is competitive with the results obtained purely from a classical convoluted graph neural network, and other classical machine learning algorithms, such as XGBoost. Consequently, our study suggests a new pathway to explore how quantum feature encoding and parametric quantum circuits can yield drastic improvements of complex ML algorithm like graph neural network.
In recent years, the field of machine learning has witnessed a paradigm shift with the emergence of hybrid quantum-classical neural networks. These networks combine the power of classical neural networks with the computational advantages offered by quantum variational circuits. This study presents a comprehensive survey of hybrid quantum-classical machine learning algorithms, focusing on their architecture, performance, and hyperparameter optimization techniques. Introducing the concept of hybrid quantum-classical machine learning and its significance in contemporary image classification tasks. It explores the theoretical foundations of quantum variational circuits and their integration with classical neural network architectures. Special attention is given to prominent algorithms such as Quantum Convolutional Neural Networks, Quanvolutional Neural Networks, and Quantum ResNet, each offering unique advantages in image classification tasks. A major aspect covered in this study is the hyperparameter optimization techniques employed in hybrid quantum-classical machine learning. The chapter discusses quantum-inspired optimization methods tailored for efficiently tuning the hyperparameters of complex neural network models. Through comparative analysis, the effectiveness of these optimization techniques is demonstrated in reducing computational overhead and improving model performance. Moreover, the study also delves into experimental results obtained from benchmarking hybrid quantum-classical models against traditional classical approaches. It highlights the accuracy variations observed across different quantum architectures and explores the impact of architectural permutations on model convergence. Insights gained from these experiments provide valuable guidance for researchers and practitioners seeking to leverage hybrid quantum-classical neural networks in real-world applications.