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.

中文翻译：

---

在崎岖的神经网络环境中学习非随机量子哈密顿量的基态

由非随机哈密顿量描述的强相互作用量子系统表现出丰富的低温物理学。然而，即使对于最先进的数值技术，他们的研究也提出了艰巨的挑战。在这里，我们通过考虑方形格子上的受挫自旋-$1/2$$J_1-J_2$ 海森堡模型，系统地研究了一类基于人工神经网络的通用变分波函数的性能。专注于没有物理信息输入的神经网络架构，我们主张使用由两个解耦实值网络组成的 ansatz，一个用于振幅，另一个用于变分波函数的相位。通过在随机重构算法中引入针对固有数值不稳定性的具体缓解策略，我们获得了与最近报告的包含物理系统知识的神经网络相当的变分能量。通过对算法各个组成部分的详细分析，我们得出结论，能量景观的崎岖性质构成了找到令人满意的基态波函数近似的主要障碍，并阻止学习正确的符号结构。特别是，我们表明在当前设置中，神经网络表达能力和蒙特卡罗采样不是主要的限制因素。通过对算法各个组成部分的详细分析，我们得出结论，能量景观的崎岖性质构成了找到令人满意的基态波函数近似的主要障碍，并阻止学习正确的符号结构。特别是，我们表明在当前设置中，神经网络表达能力和蒙特卡罗采样不是主要的限制因素。通过对算法各个组成部分的详细分析，我们得出结论，能量景观的崎岖性质构成了找到令人满意的基态波函数近似的主要障碍，并阻止学习正确的符号结构。特别是，我们表明在当前设置中，神经网络表达能力和蒙特卡罗采样不是主要的限制因素。