Over the past decades, various neural networks have been proposed with the rapid development of the machine learning field. In particular, graph neural networks using feature-vectors assigned to nodes and edges have been attracting attention in various fields. The usefulness of graph neural networks also affected the field of quantum computing, which led to the birth of quantum graph neural networks composed of parameterized quantum circuits. The quantum graph neural networks have many possibilities as applications from the simulation perspective of quantum dynamics. Among the application models of various quantum graph neural networks, the quantum graph recurrent neural network (QGRNN) is proven to be effective in training the Ising model Hamiltonian. Thus, this paper introduces the concepts of the Ising model, variational quantum eigensolver (VQE) for preparing quantum data, and QGRNN from a software engineer's point of view.
Over the past decades, various neural networks have been proposed with the rapid development of the machine learning field. In particular, graph neural networks using feature-vectors assigned to nodes and edges have been attracting attention in various fields. The usefulness of graph neural networks also affected the field of quantum computing, which led to the birth of quantum graph neural networks composed of parameterized quantum circuits. The quantum graph neural networks have many possibilities as applications from the simulation perspective of quantum dynamics. Among the application models of various quantum graph neural networks, the quantum graph recurrent neural network (QGRNN) is proven to be effective in training the Ising model Hamiltonian. Thus, this paper introduces the concepts of the Ising model, variational quantum eigensolver (VQE) for preparing quantum data, and QGRNN from a software engineer's point of view.
We introduce Quantum Graph Neural Networks (QGNN), a new class of quantum neural network ansatze which are tailored to represent quantum processes which have a graph structure, and are particularly suitable to be executed on distributed quantum systems over a quantum network. Along with this general class of ansatze, we introduce further specialized architectures, namely, Quantum Graph Recurrent Neural Networks (QGRNN) and Quantum Graph Convolutional Neural Networks (QGCNN). We provide four example applications of QGNNs: learning Hamiltonian dynamics of quantum systems, learning how to create multipartite entanglement in a quantum network, unsupervised learning for spectral clustering, and supervised learning for graph isomorphism classification.
Machine learning that combines the power of graph neural networks has its own significance in developing quick report analysis for various dynamic data which traditional statistical models may not be able to accomplish. Alongside the use of Quantum Computing in Neural Networks have become increasingly important over the years due to their ability to learn and process complex patterns. The Importance of QNN lies in the approaches it follows like entanglement, interference multiple super positional states, parallel computing, and backpropagation trainings which cannot be possible for Classical Neural Networks to work with. Also, the QNN, GNN integrates with the Quantum Machine Learning techniques like PennyLane that acts as an OpenShift framework to execute the optimized, trained algorithms for quick computational outcomes. This paper contains the use of Quantum Neural Networking, Quantum Machine Learning.
Abstract Graphs are fundamental structures for representing complex, nonlinear structured data across various domains, including social networks and quantum systems. Quantum graph recurrent neural networks (QGRNNs) have been proposed to model quantum dynamics in graph-based quantum systems, but their applicability to classical data remains an open problem. In this paper, we leverage QGRNNs to process classical graph-structured data. In particular, we demonstrate how QGRNN can reconstruct node features in classical datasets. Our results show that QGRNN achieves high feature reconstruction accuracy, resulting in near-perfect classification. Furthermore, we propose an information hiding technique based on our QGRNN, where messages are embedded into a graph and then retrieved under certain conditions. We assess retrieval accuracy for different dictionary sizes and message lengths, showing that QGRNN maintains high retrieval accuracy, with minor degradation as complexity increases. These findings demonstrate the scalability and robustness of QGRNNs for both classical data processing and secure information hiding, paving the way toward quantum-enhanced feature extraction, privacy-preserving computations, and quantum steganography.
Quantum state simulation is a cornerstone of quantum computing, aiming to accurately represent and manipulate the behavior of quantum systems. However, traditional methods of quantum state simulation, such as the Density Matrix Renormalization Group (DMRG) method and the Variational Quantum Eigensolver (VQE), often suffer from significant computational challenges, particularly as the size of the quantum system increases. This paper proposes a novel approach to quantum state simulation leveraging the power of Graph Neural Networks (GNNs). We represent a quantum state as a graph, where nodes correspond to individual quantum states and edges represent the correlations between them. A GNN is then trained to learn the complex relationships within the quantum state, enabling efficient and scalable simulation. Our method significantly reduces the computational burden associated with traditional techniques, offering a promising path towards practical quantum state simulation. The core claim is the utilization of graph neural networks' structural information for efficient quantum state simulation. The core mechanism involves representing quantum states as nodes in a graph and employing GNNs to learn relationships between them, facilitating efficient quantum state simulation.
Machine learning has achieved dramatic success over the past decade, with applications ranging from face recognition to natural language processing. Meanwhile, rapid progress has been made in the field of quantum computation including developing both powerful quantum algorithms and advanced quantum devices. The interplay between machine learning and quantum physics holds the intriguing potential for bringing practical applications to the modern society. Here, we focus on quantum neural networks in the form of parameterized quantum circuits. We will mainly discuss different structures and encoding strategies of quantum neural networks for supervised learning tasks, and benchmark their performance utilizing Yao.jl, a quantum simulation package written in Julia Language. The codes are efficient, aiming to provide convenience for beginners in scientific works such as developing powerful variational quantum learning models and assisting the corresponding experimental demonstrations.
The output prediction of quantum circuits is a formidably challenging task imperative in developing quantum devices. Motivated by the natural graph representation of quantum circuits, this paper proposes a Graph Neural Networks (GNNs)-based framework to predict the output expectation values of quantum circuits under noisy and noiseless conditions and compare the performance of different parameterized quantum circuits (PQCs). We construct datasets under noisy and noiseless conditions using a non-parameterized quantum gate set to predict circuit expectation values. The node feature vectors for GNNs are specifically designed to include noise information. In our simulations, we compare the prediction performance of GNNs in both noisy and noiseless conditions against Convolutional Neural Networks (CNNs) on the same dataset and their qubit scalability. GNNs demonstrate superior prediction accuracy across diverse conditions. Subsequently, we utilize the parameterized quantum gate set to construct noisy PQCs and compute the ground state energy of hydrogen molecules using the Variational Quantum Eigensolver (VQE). We propose two schemes: the Indirect Comparison scheme, which involves directly predicting the ground state energy and subsequently comparing circuit performances, and the Direct Comparison scheme, which directly predicts the relative performance of the two circuits. Simulation results indicate that the Direct Comparison scheme significantly outperforms the Indirect Comparison scheme by an average of 36.2% on the same dataset, providing a new and effective perspective for using GNNs to predict the overall properties of PQCs, specifically by focusing on their performance differences.