In the NISQ era, implementing practical quantum ma002 chine learning faces challenges due to limited resources. A recent advancement involves a novel single-qubit methodology, allowing for the execution of numerous operations on a single qubit. However, its applicability to complex neural network architectures remains uncertain. This study focuses on graph data, known for its intricate structure and inherent challenges for machine learning. Utilizing the quantum walk, we introduce a graph embedding approach to reduce network parameters, resulting in the design of a novel architecture called the single-qubit Quantum Graph Neural Network (sQGNN). Experimental assessments, including simulations, demonstrate the adaptability of sQGNNs to graphs of varying dimensions and compositions. The resource-efficient nature of sQGNNs is showcased through practical executions on quantum computers, using only one qubit. This capability highlights the efficient utilization of limited qubit resources, paving the way for expansive quantum graph neural networks on resource-constrained Variational Quantum Circuits (VQCs). This breakthrough opens up new possibilities for practical applications within the current NISQ regime.
In the NISQ era, implementing practical quantum ma002 chine learning faces challenges due to limited resources. A recent advancement involves a novel single-qubit methodology, allowing for the execution of numerous operations on a single qubit. However, its applicability to complex neural network architectures remains uncertain. This study focuses on graph data, known for its intricate structure and inherent challenges for machine learning. Utilizing the quantum walk, we introduce a graph embedding approach to reduce network parameters, resulting in the design of a novel architecture called the single-qubit Quantum Graph Neural Network (sQGNN). Experimental assessments, including simulations, demonstrate the adaptability of sQGNNs to graphs of varying dimensions and compositions. The resource-efficient nature of sQGNNs is showcased through practical executions on quantum computers, using only one qubit. This capability highlights the efficient utilization of limited qubit resources, paving the way for expansive quantum graph neural networks on resource-constrained Variational Quantum Circuits (VQCs). This breakthrough opens up new possibilities for practical applications within the current NISQ regime.
Quantum computing holds significant potential for advancing machine learning, particularly in handling complex graph-structured data. This paper introduces Single-Qubit Quantum Graph Neural Networks (sQGNNs), a novel model that integrates quantum networks with quantum walk operations to improve generalization in graph learning tasks. By leveraging quantum walks, we demonstrated sQGNNs capture complex relational patterns and enhance network expressiveness beyond classical methods. Our results proved that quantum encoding efficiently represents high-dimensional graph data, preserving dependencies and optimizing memory use. Across benchmark datasets, sQGNNs demonstrate superior generalization and robustness against overfitting, achieving higher accuracy with reduced computational cost. Our results underscore sQGNNs’ promise for scalable, quantum-enhanced graph learning, establishing a foundation for future quantum-assisted machine learning applications.
The convergence of quantum computing and machine learning offers significant potential for processing complex data distributions. However, the realization of this potential in the Noisy Intermediate-Scale Quantum (NISQ) era is constrained by physical hardware limitations, particularly restricted qubit counts and system noise. This thesis addresses the challenge of the ”Representation Bottleneck” by establishing a framework for resource-efficient quantum representation learning. The research demonstrates that effective learning on near-term devices can be achieved by optimizing circuit architectures and objective functions to align with hardware constraints. First, to address resource limitations in high-dimensional visual recognition, we propose the Multi-Gate Quantum Convolutional Neural Network (MG-QNN). By employing a Multi-Gate strategy, this architecture optimizes the utilization of quan tum resources within the circuit design. Empirical evaluations on face recognition benchmarks indicate that this approach maintains competitive recognition accuracy while reducing the qubit requirement compared to standard quantum convolutional methods. Second, extending the framework to non-Euclidean data, we introduce the Single-Qubit Graph Neural Network (sQGNN). Utilizing Discrete-Time Quantum Walks, this method encodes graph topologies and relational patterns onto a single qubit. This approach circumvents the need for multi-qubit entangling gates, thereby reducing the computational overhead and noise sensitivity typically associated with processing graph-structured data. Third, in the domain of generative modeling, we present the Single-Qubit Quan tum Convolutional Variational Autoencoder (QCVAE). Addressing the difficulty of generative tasks on constrained devices, this model integrates the Information Bottleneck principle with efficient data re-uploading techniques. The study demonstrates that a single qubit possesses sufficient expressivity to model and reconstruct image distributions effectively when guided by appropriate information theoretic constraints. Finally, to resolve the fundamental limitations of classical loss functions in quantum learning, we establish the Hilbert-Schmidt Information Bottleneck (HSIB). We identify that standard Euclidean metrics often fail to respect the geometric structure of the Hilbert space. The HSIB framework employs the Hilbert Schmidt distance as a tractable geometric measure, providing a learning objective that maximizes information retention while adhering to the intrinsic geometry of quantum states. Collectively, these contributions illustrate that practical quantum machine learning advantage in the NISQ era does not rely solely on scaling hardware, but on the strategic design of resource-efficient architectures and geometrically valid metrics.
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.
Graph neural networks (GNNs) are a powerful framework for learning representations from graph-structured data, but their direct implementation on near-term quantum hardware remains challenging due to circuit depth, multi-qubit interactions, and qubit scalability constraints. In this work, we introduce a hybrid quantum graph learning architecture designed explicitly for unsupervised learning in the noisy intermediate-scale quantum (NISQ) regime. Our approach combines a variational quantum feature extraction layer with an edge-local and qubit-efficient quantum message-passing mechanism inspired by the Quantum Alternating Operator Ansatz (QAOA) framework. The message-passing operation is decomposed into pairwise interactions along graph edges using standard single- and two-qubit gates. For a graph with N nodes and n-qubit feature registers, this reduces the number of qubits required at one time from Nn to at most 2n. We train the model using the Deep Graph Infomax objective to perform unsupervised node representation learning. The external class labels are not used during graph construction or training and are used only to evaluate the learned embeddings. Experiments on the Cora citation network and the Phase 3 release of the 1000 Genomes Project show that the quantum edge interaction contributes to the quality of the learned node representations.
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.
Graph Neural Networks (GNNs) are powerful machine learning models that excel at analyzing structured data represented as graphs, demonstrating remarkable performance in applications like social network analysis and recommendation systems. However, classical GNNs face scalability challenges when dealing with large-scale graphs. This paper proposes frameworks for implementing GNNs on quantum computers to potentially address the challenges. We devise quantum algorithms corresponding to the three fundamental types of classical GNNs: Graph Convolutional Networks, Graph Attention Networks, and Message-Passing GNNs. A complexity analysis of our quantum implementation of the Simplified Graph Convolutional (SGC) Network shows potential quantum advantages over its classical counterpart, with significant improvements in time and space complexities. Our complexities can have trade-offs between the two: when optimizing for minimal circuit depth, our quantum SGC achieves logarithmic time complexity in the input sizes (albeit at the cost of linear space complexity). When optimizing for minimal qubit usage, the quantum SGC exhibits space complexity logarithmic in the input sizes, offering an exponential reduction compared to classical SGCs, while still maintaining better time complexity. These results suggest our Quantum GNN frameworks could efficiently process large-scale graphs. This work paves the way for implementing more advanced Graph Neural Network models on quantum computers, opening new possibilities in quantum machine learning for analyzing graph-structured data.