Variational optimization of the amplitude of neural-network quantum
  many-body ground states
Jia-Qi Wang Rong-Qiang He Zhong-Yi Lu
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.