论文标题
在坚固的神经网络景观中学习非杂音量子哈密顿量的基态
Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape
论文作者
论文摘要
非杂志的哈密顿人描述的强烈相互作用的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，他们的研究也构成了巨大的挑战。在这里，我们通过考虑沮丧的旋转$ 1/2 $ $ $ J_1-J_2 $ HEISENBERG模型，系统地研究了基于人工神经网络的一类通用变分波功能的性能。我们专注于没有物理信息输入的神经网络体系结构，我们主张使用由两个脱钩的实价网络组成的ANSATZ，一个用于幅度，另一个用于变异波函数的阶段。通过在随机重新配置算法中引入固有数值不稳定性的具体缓解策略，我们获得了一种与最近与神经网络报道的可比的变异能量，这些神经网络结合了有关物理系统的知识。通过对算法的各个组件的详细分析，我们得出结论，能量景观的坚固性构成了找到对基态波函数令人满意的近似值的主要障碍，并防止学习正确的符号结构。特别是，我们表明在当前设置中，神经网络表达和蒙特卡洛采样不是主要因素。
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.
