  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 inductive bias. 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, allows for 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
quantum state learning as well as finding the ground state of the challenging
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 quantum many-body physics
simulation, quantum technology design, and generative modeling in artificial
intelligence.
