Neural-network quantum states (NQSs), variationally optimized by combining
traditional methods and deep learning techniques, is a new way to find quantum
many-body ground states and gradually becomes a competitor of traditional
variational methods. However, there are still some difficulties in the
optimization of NQSs, such as local minima, slow convergence, and sign
structure optimization. Here, we split a quantum many-body variational wave
function into a multiplication of a real-valued amplitude neural network and a
sign structure, and focus on the optimization of the amplitude network while
keeping the sign structure fixed. The amplitude network is a convolutional
neural network (CNN) with residual blocks, namely a ResNet. Our method is
tested on three typical quantum many-body systems. The obtained ground state
energies are lower than or comparable to those from traditional variational
Monte Carlo (VMC) methods and density matrix renormalization group (DMRG).
Surprisingly, for the frustrated Heisenberg $J_1$-$J_2$ model, our results are
better than those of the complex-valued CNN in the literature, implying that
the sign structure of the complex-valued NQS is difficult to be optimized. We
will study the optimization of the sign structure of NQSs in the future.

神经网络量子态（NQSs）是通过结合传统方法和深度学习技术进行变分优化的一种新方法，用于找到量子多体基态，并逐渐成为传统变分方法的竞争对手。本文将量子多体变分波函数拆分为实值振幅神经网络和符号结构的乘积，专注于振幅网络的优化，同时保持符号结构固定。我们的方法在三个典型的量子多体系统上进行了测试，所得到的基态能量低于或与传统变分蒙特卡罗（VMC）方法和密度矩阵重整化群（DMRG）相当。令人惊讶的是，在受挫型海森堡 $J_1$-$J_2$ 模型中，我们的结果优于文献中复值卷积神经网络，这意味着复值 NQS 的符号结构很难被优化。我们将来将研究 NQS 的符号结构优化。