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.

In dealing with post-sale warranties, considering only operating time may not be sufficient because products often deteriorate through usage and over time, which both influence product reliability. A two-dimensional warranty is thus more reasonable in practice for both manufacturers and customers. Periodic preventive maintenance within the warranty term seems more prevalent in practice due to its convenience and operability for manufacturers and consumers. However, increases in product deterioration may cause breakdowns to occur more often, even after periodic preventive maintenance has just been performed. In this study, a two-dimensional warranty policy is examined with consideration of non-periodic preventive maintenance to determine the optimal two-dimensional warranty term with a constraint that the product reliability should be above a certain threshold. A numerical application is provided to demonstrate the effectiveness of the proposed approach, with sensitivity analyses being conducted to investigate the robustness of the derived optimal warranty policy.