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.
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.
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.
Abstract Quantum machine learning is a relatively new research field that aims to combine the dramatic performance advantage offered by quantum computing and the ability of machine learning algorithms to learn complex distributions of high-dimensional data. The primary focus of this domain is the implementation of classical machine learning algorithms in the quantum mechanical domain and study of the speedup due to quantum parallelism, which could enable the development of novel techniques for solving problems such as quantum phase recognition and quantum error correction optimization. In this paper, we propose a hybrid quantum machine learning pipeline for predicting the atomization energies of various molecules using the nuclear charges and atomic positions of the constituent atoms. Firstly, we will be using a deep convolutional auto-encoder model for the feature extraction of data constructed from the eigenvalues and eigenvector centralities of the pairwise distance matrix calculated from atomic positions and the unrolled upper triangle of each Coulomb matrix calculated from nuclear charges, and we will then be using a quantum regression algorithm such as quantum linear regression, quantum radial basis function neural network and, a quantum neural network for estimating the atomization energy. The hybrid quantum neural network models do not seem to provide any speedup over their classical counterparts. Before implementing a quantum algorithm, we will also be using state-of-the-art classical machine learning and deep learning models such as XGBoost, multilayer perceptron, deep convolutional neural network, and a long short-term memory network to study the correlation between the extracted features and corresponding atomization energies of molecules.
The pharmaceutical industry faces mounting challenges in drug discovery, where exploring a chemical space exceeding 10 60 possible compounds remains computationally prohibitive. Traditional in-silico screening approaches struggle to capture the quantum mechanical interactions that determine molecular behavior. To overcome these limitations, this study introduces a hybrid quantum–classical machine learning framework that uniquely integrates molecular graph theory with quantum-enhanced learning for accelerated drug discovery. Using the QM9 benchmark dataset containing 133,885 molecules of low-to-medium structural complexity, we extract Laplacian eigenvalue spectra as topological descriptors that preserve both connectivity and electronic information. These features are jointly processed by Random Forest (RF), Support Vector Machine (SVM), and a Variational Quantum Classifier (VQC) in a weighted ensemble architecture designed for balanced generalization. The Quantum Graph Neural Network (QGNN) component achieves 97.5% accuracy, while the hybrid ensemble attains 100.0% accuracy, confirming strong predictive reliability. Although quantum training requires roughly 3.2× longer computation, it captures high-dimensional correlations that classical methods overlook. Overall, the proposed framework bridges the gap between theoretical quantum computing and practical pharmaceutical modeling, providing a scalable, physics-inspired pathway toward intelligent molecular screening and next-generation drug discovery systems.
Graph Neural Networks (QGNNs) offer a promising approach to combining quantum computing with graph-structured data processing. While classical Graph Neural Networks (GNNs) are scalable and robust, existing QGNNs often lack flexibility due to graph-specific quantum circuit designs, limiting their applicability to diverse real-world problems. To address this, we propose a versatile QGNN framework inspired by GraphSAGE, using quantum models as aggregators to generate quantum-native node embeddings. We integrate inductive representation learning techniques with parameterized quantum convolutional and pooling layers, bridging classical and quantum paradigms. The convolutional layer is flexible, allowing tailored designs for specific tasks. Benchmarked on a node regression task with the QM9 dataset, our framework, using a single minimal circuit for all aggregation steps, handles molecules with varying numbers of atoms without changing qubits or circuit architecture. While classical GNNs achieve higher training performance, our quantum approach remains competitive and often shows enhanced generalization as molecular complexity increases. We also observe faster learning in early training epochs. To mitigate trainability limitations of a single-circuit setup, we extend the framework with multiple quantum aggregators on QM9. Assigning distinct circuits to each hop substantially improves training performance across all cases. Additionally, we numerically demonstrate the absence of barren plateaus as qubit numbers increase, suggesting that the proposed model remains trainable to larger, more complex graph-based problems.
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.