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.

提出了一种新的 Autoregressive Neural TensorNet (ANTN) 架构， 该架构能够准确模拟具有规范化波函数的量子状态的样本，拥有更广泛的表现力和对称性， 并能够应用于科学模拟和机器学习等领域。