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Neural-network quantum states (NQSs), variationally optimized by combiningtraditional methods and deep learning techniques, is a new way to find quantummany-body ground states and gradually becomes a competitor of traditionalvariational methods. However, there are still some difficulties in theoptimization of NQSs, such as local minima, slow convergence, and signstructure optimization. Here, we split a quantum many-body variational wavefunction into a multiplication of a real-valued amplitude neural network and asign structure, and focus on the optimization of the amplitude network whilekeeping the sign structure fixed. The amplitude network is a convolutionalneural network (CNN) with residual blocks, namely a ResNet. Our method istested on three typical quantum many-body systems. The obtained ground stateenergies are lower than or comparable to those from traditional variationalMonte Carlo (VMC) methods and density matrix renormalization group (DMRG).Surprisingly, for the frustrated Heisenberg $J_1$-$J_2$ model, our results arebetter than those of the complex-valued CNN in the literature, implying thatthe sign structure of the complex-valued NQS is difficult to be optimized. Wewill study the optimization of the sign structure of NQSs in the future.

Variational optimization of the amplitude of neural-network quantum many-body ground states