Learning of network embedding with vector-based node representation has attracted wide attention over the decade. It differs from the general setting of graph node embedding whereby the node attributes are also considered and yet may incur privacy issues. In this paper, we depart from the classic CPU/GPU architecture to consider the well-established network alignment problem based on network embedding, and develop a quantum machine learning approach with a low qubit cost for its near-future applicability on Noisy Intermediate-Scale Quantum (NISQ) devices. Specifically, our model adopts the discrete-time quantum walk (QW) and conducts the QW on the tailored merged network to extract structure information from the two aligning networks without the need for quantum state preparation which otherwise requires high quantum gate cost. Then the quantum states from QW are fed to a quantum embedding ansatz (i.e., parameterized circuit) to learn the latent representation of each node. The key part of our approach is to connect these two quantum modules to achieve a pure quantum paradigm without involving classical modules. To our best knowledge, there has not been any classic-quantum hybrid approach to network embedding, let alone a pure quantum paradigm being free from the bottleneck of communication between classic devices and quantum devices, which is still an open problem. Experimental results on two real-world datasets show the effectiveness of our quantum embedding approach in comparison with classical embedding approaches. Our model is readily and efficiently implemented in Python with a full-amplitude simulation of the QW and the quantum circuit. Therefore, our model can be readily deployed on an existing NISQ device with all the circuits provided, and only 13 qubits are needed in the experiments, which is rarely attained in existing quantum graph learning works.
Learning of network embedding with vector-based node representation has attracted wide attention over the decade. It differs from the general setting of graph node embedding whereby the node attributes are also considered and yet may incur privacy issues. In this paper, we depart from the classic CPU/GPU architecture to consider the well-established network alignment problem based on network embedding, and develop a quantum machine learning approach with a low qubit cost for its near-future applicability on Noisy Intermediate-Scale Quantum (NISQ) devices. Specifically, our model adopts the discrete-time quantum walk (QW) and conducts the QW on the tailored merged network to extract structure information from the two aligning networks without the need for quantum state preparation which otherwise requires high quantum gate cost. Then the quantum states from QW are fed to a quantum embedding ansatz (i.e., parameterized circuit) to learn the latent representation of each node. The key part of our approach is to connect these two quantum modules to achieve a pure quantum paradigm without involving classical modules. To our best knowledge, there has not been any classic-quantum hybrid approach to network embedding, let alone a pure quantum paradigm being free from the bottleneck of communication between classic devices and quantum devices, which is still an open problem. Experimental results on two real-world datasets show the effectiveness of our quantum embedding approach in comparison with classical embedding approaches. Our model is readily and efficiently implemented in Python with a full-amplitude simulation of the QW and the quantum circuit. Therefore, our model can be readily deployed on an existing NISQ device with all the circuits provided, and only 13 qubits are needed in the experiments, which is rarely attained in existing quantum graph learning works.
Graph representation learning has been extensively studied, and recent models can well incorporate both node features and graph structures. Despite these progress, the inherent scalability challenge for classical computers of processing graph data and solving the downstream tasks (many are NP-hard) is still a bottleneck for existing classical graph learning models. On the other hand, quantum computing is known a promising direction for its theoretically verified scalability as well as the increasing evidence for the access to physical quantum machine in near-term. Different from many existing classical-quantum hybrid machine learning models on graphs, in this paper we take a more aggressive initiative for developing a native quantum paradigm for (attributed) graph representation learning, which to our best knowledge, has not been fulfilled in literature yet. Specifically, our model adopts the well-established theory and technique in quantum computing e.g. quantum random walk, and adapt it to the attributed graph. Then the node attribute quantum state sequence is fed into a quantum recurrent network to obtain the final node embedding. Experimental results on three public datasets show the effectiveness of our quantum model which also outperforms a classical learning approach GraphRNA notably in terms of efficiency even on a classical computer. Though it is still restricted to the classical loss-based learning paradigm with gradient descent for model parameter training, while our computing scheme is compatible with quantum computing without involving classical computers. This is in fact largely in contrast to many hybrid quantum graph learning models which often involve many steps and modules having to be performed on classical computers.
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.
Quantum machine learning has made remarkable progress in many important tasks. However, the gate complexity of the initial state preparation is seldom considered in lots of quantum machine learning algorithms, making them non-end-to-end. Herein, we propose a quantum algorithm for the node embedding problem that maps a node graph’s topological structure to embedding vectors. The resulting quantum embedding state can be used as an input for other quantum machine learning algorithms. With O(log(N)) qubits to store the information of N nodes, our algorithm will not lose quantum advantage for the subsequent quantum information processing. Moreover, owing to the use of a parameterized quantum circuit with O(poly(log(N))) depth, the resulting state can serve as an efficient quantum database. In addition, we explored the measurement complexity of the quantum node embedding algorithm, which is the main issue in training parameters, and extended the algorithm to capture high-order neighborhood information between nodes. Finally, we experimentally demonstrated our algorithm on an nuclear magnetic resonance quantum processor to solve a graph model.
With the emergence of the research field of Quantum Machine Learning, interest in finding advantageous real-world applications is growing as well. However, challenges concerning the number of available qubits on Noisy Intermediate Scale Quantum (NISQ) devices and accuracy losses due to hardware imperfections still remain and limit the applicability of such approaches in real-world scenarios. Therefore, for simplification, most studies assume nearly noise-free conditions as they are expected with logical, i.e. error-corrected, qubits instead of real qubits provided by hardware. However, the number of logical qubits is expected to scale slowly as they require a high number of real qubits for error correction. This is our motivation to deal with noise as an unavoidable, non-negligible problem on NISQ devices. As an application, we use the example of particle decay tree reconstruction as a highly complex combinatoric problem in High Energy Physics. We investigate methods to reduce the noise impact of such devices and propose a hybrid architecture that extends a classical graph neural network by a parameterized quantum circuit. While we have shown that such a hybrid architecture enables a reduction of the amount of trainable parameters compared to the fully classical case, we are now specifically interested in the actual performance in more realistic, i.e. noise prone scenarios. Using simple synthetic Decay Trees, we train the network in classical simulations to allow for efficient optimization of the parameters. The trained parameters are validated in noisy simulations based on devices by "IBM Quantum" and are used in interpretability and significance studies, enabling improvements in the accuracy on real devices.
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.
The state-of-the-art machine learning approaches are based on classical von Neumann computing architectures and have been widely used in many industrial and academic domains. With the recent development of quantum computing, researchers and tech-giants have attempted new quantum circuits for machine learning tasks. However, the existing quantum computing platforms are hard to simulate classical deep learning models or problems because of the intractability of deep quantum circuits. Thus, it is necessary to design feasible quantum algorithms for quantum machine learning for noisy intermediate scale quantum (NISQ) devices. This work explores variational quantum circuits for deep reinforcement learning. Specifically, we reshape classical deep reinforcement learning algorithms like experience replay and target network into a representation of variational quantum circuits. Moreover, we use a quantum information encoding scheme to reduce the number of model parameters compared to classical neural networks. To the best of our knowledge, this work is the first proof-of-principle demonstration of variational quantum circuits to approximate the deep Q-value function for decision-making and policy-selection reinforcement learning with experience replay and target network. Besides, our variational quantum circuits can be deployed in many near-term NISQ machines.