Strongly interacting quantum systems described by non-stoquastic Hamiltonians
exhibit rich low-temperature physics. Yet, their study poses a formidable
challenge, even for state-of-the-art numerical techniques. Here, we investigate
systematically the performance of a class of universal variational
wave-functions based on artificial neural networks, by considering the
frustrated spin-$1/2$ $J_1-J_2$ Heisenberg model on the square lattice.
Focusing on neural network architectures without physics-informed input, we
argue in favor of using an ansatz consisting of two decoupled real-valued
networks, one for the amplitude and the other for the phase of the variational
wavefunction. By introducing concrete mitigation strategies against inherent
numerical instabilities in the stochastic reconfiguration algorithm we obtain a
variational energy comparable to that reported recently with neural networks
that incorporate knowledge about the physical system. Through a detailed
analysis of the individual components of the algorithm, we conclude that the
rugged nature of the energy landscape constitutes the major obstacle in finding
a satisfactory approximation to the ground state wavefunction, and prevents
learning the correct sign structure. In particular, we show that in the present
setup the neural network expressivity and Monte Carlo sampling are not primary
limiting factors.

研究了利用人工神经网络作为通用变分波函数描述强相互作用量子系统的表现，特别是对于方格上的自旋模型，提出了使用由两个解耦实值网络组成的近似形式，并采用具体的缓解策略克服了固有的数值不稳定性。