Graph Neural Networks for Quantum State Simulation

Abstract

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.