Representations of Graph States with Neural Networks

Peng Yan, Linjing Li, Miaotianzi Jin +1 more

Yu Lei, Gaoxiang Chen, Hongyang Chen +2 more

Ying Yang, Huaixin Cao

With the rapid development of machine learning, artificial neural networks provide a powerful tool to represent or approximate many-body quantum states. It was proved that every graph state can be generated by a neural network. Here, we introduce digraph states and explore their neural network representations (NNRs). Based on some discussions about digraph states and neural network quantum states (NNQSs), we construct explicitly an NNR for any digraph state, implying every digraph state is an NNQS. The obtained results will provide a theoretical foundation for solving the quantum many-body problem with machine learning method whenever the wave-function is known as an unknown digraph state or it can be approximated by digraph states.

Martin J. A. Schuetz, John Kyle Brubaker, Helmut G. Katzgraber

Wenxuan Wang, Jinjing Shi, Nan Guan +2 more

Representing and learning from graphs is essential for developing effective machine learning models tailored to non-Euclidean data. While Graph Neural Networks (GNNs) strive to address the challenges posed by complex, high-dimensional graph data, Quantum Neural Networks (QNNs) present a compelling alternative due to their potential for quantum parallelism. However, much of the current QNN research tends to overlook the vital connection between quantum state encoding and graph structures, which limits the full exploitation of quantum computational advantages. To address these challenges, this paper introduces a quantum graph Hamiltonian neural network (QGHNN) to enhance graph representation and learning on noisy intermediate-scale quantum computers. Concretely, a quantum graph Hamiltonian learning method (QGHL) is first created by mapping graphs to the Hamiltonian of the topological quantum system. Then, QGHNN based on QGHL is presented, which trains parameters by minimizing the loss function and uses the gradient descent method to learn the graph. Experiments on the PennyLane quantum platform reveal that QGHNN outperforms all assessment metrics, achieving the lowest mean squared error of0.004and the maximum cosine similarity of99.8%, which shows that QGHNN not only excels in representing and learning graph information, but it also has high robustness ability. QGHNN can reduce the impact of quantum channel noise and has significant potential application in future research of quantum knowledge graphs and recommendation systems.

Wenbo Qiao, Peng Zhang, Jiaming Zhao +1 more

Graphons are continuous functions hidden behind large-scale graphs. Traditional approaches to graphon learning either suffer from the resolution limitations of piecewise-constant functions or struggle to capture the high-frequency structures intrinsic to graphons. In this paper, we propose quantum graphon neural representation (QGNR), a quantum-enhanced machine learning method that enables arbitrarily high-resolution and high-frequency graphon modeling through Fourier series expressivity of data re-uploading quantum circuits. We further extend QGNR to conditional graphon learning, thereby allowing the handling of complex graph-related tasks. Numerical results demonstrate that QGNR outperforms classical state-of-the-art methods in graphon learning and excels in graph classification tasks across domains like molecular property prediction and social network analysis. Notably, QGNR attains superior performance while requiring up to 81.65% fewer variational parameters than the most advanced neural network-based baselines. This work pioneers the application of quantum machine learning to graphons, demonstrating promising quantum advantages in representational power and learning efficiency.