Quantum many-body physics simulation has important impacts on understanding fundamental science and has applications to quantum materials design and quantum technology. However, due to the exponentially growing size of the Hilbert space with respect to the particle number, a direct simulation is intractable. While representing quantum states with tensor networks and neural networks are the two state-of-the-art methods for approximate simulations, each has its own limitations in terms of expressivity and optimization. To address these challenges, we develop a novel architecture, Autoregressive Neural TensorNet (ANTN), which bridges tensor networks and autoregressive neural networks. We show that Autoregressive Neural TensorNet parameterizes normalized wavefunctions with exact sampling, generalizes the expressivity of tensor networks and autoregressive neural networks, and inherits a variety of symmetries from autoregressive neural networks. We demonstrate our approach on the 2D $J_1$-$J_2$ Heisenberg model with different systems sizes and coupling parameters, outperforming both tensor networks and autoregressive neural networks. Our work opens up new opportunities for both scientific simulations and machine learning applications.

翻译：量子多体物理模拟对理解基础科学具有重要意义，并在量子材料设计与量子技术中具有应用价值。然而，由于希尔伯特空间随粒子数呈指数级增长，直接模拟在计算上难以实现。尽管利用张量网络和神经网络表示量子态是当前两种最先进的近似模拟方法，但它们在表达能力和优化方面各有局限性。为解决这些挑战，我们开发了一种新颖架构——自回归神经张量网络（ANTN），该架构桥接了张量网络与自回归神经网络。我们证明，自回归神经张量网络能够通过精确采样参数化归一化波函数，泛化张量网络与自回归神经网络的表达能力，并继承自回归神经网络的多种对称性。我们在不同系统尺寸和耦合参数的二维 $J_1$-$J_2$ 海森堡模型上验证了该方法，其性能优于纯张量网络和自回归神经网络。我们的工作为科学模拟和机器学习应用开辟了新机遇。