论文标题
复杂价值的限制性玻尔兹曼机器的表达力，用于解决非争议的哈密顿量
Expressive power of complex-valued restricted Boltzmann machines for solving non-stoquastic Hamiltonians
论文作者
论文摘要
事实证明，具有神经网络量子状态的变异蒙特卡洛是评估自旋汉密尔顿人的基态能量的有前途的途径。然而，尽管持续努力，这种方法对沮丧的汉密尔顿人的表现仍然比没有迹象的哈密顿人的汉密尔顿人差得多。我们提出了基于限制的玻尔兹曼机器（RBM）的详细而系统的研究，用于量子旋转链，以解决这种情况下的相关性。我们表明，在大多数情况下，当哈密顿量与静止点相连时，复杂的RBM状态可以忠实地表示基态，并且可以通过抽样有效地评估局部数量。另一方面，我们确定了对RBM Ansatz充满挑战的几个新阶段，包括非稳定的非拼写阶段以及采样效率低下的拼写阶段。此外，我们发现，在非拼写阶段的基础状态的准确神经网络表示不仅受符号结构的限制，而且还受到其振幅的阻碍。
Variational Monte Carlo with neural network quantum states has proven to be a promising avenue for evaluating the ground state energy of spin Hamiltonians. However, despite continuous efforts the performance of the method on frustrated Hamiltonians remains significantly worse than those on stoquastic Hamiltonians that are sign-free. We present a detailed and systematic study of restricted Boltzmann machine (RBM) based variational Monte Carlo for quantum spin chains, resolving how relevant stoquasticity is in this setting. We show that in most cases, when the Hamiltonian is phase connected with a stoquastic point, the complex RBM state can faithfully represent the ground state, and local quantities can be evaluated efficiently by sampling. On the other hand, we identify several new phases that are challenging for the RBM Ansatz, including non-topological robust non-stoquastic phases as well as stoquastic phases where sampling is nevertheless inefficient. Furthermore, we find that an accurate neural network representation of ground states in non-stoquastic phases is hindered not only by the sign structure but also by their amplitudes.
