论文标题
具有近端优化的神经网络量子状态：基于变异蒙特卡洛的地面搜索方案
Neural network quantum state with proximal optimization: a ground-state searching scheme based on variational Monte Carlo
论文作者
论文摘要
神经网络量子状态（NQS）与变异蒙特卡洛（VMC）方法结合在一起，被证明是研究量子多体物理学的一种有前途的方法。香草VMC方法每个样本执行一个梯度更新，但我们引入了一个新的目标函数，具有近端优化（PO），该功能可以通过重复使用不匹配的样本来实现多个更新。我们的VMC-PO方法保持了先前重要性采样梯度优化算法的优势[L.杨，{\ it等人}，物理。 Rev. Research {\ bf 2}，012039（r）（2020）]有效地使用采样状态。 PO可以减轻网络更新过程中的数值不稳定性，这类似于随机重新配置（SR）方法，但具有较低的计算复杂性，实现了一种替代和更简单的实现。我们研究了我们的VMC-PO算法在平方晶格上使用一维横向场ISING模型和2维Heisenberg Antermagnet进行地下态搜索的性能，并证明达到的地面能量与较为省心的结果可比性。
Neural network quantum states (NQS), incorporating with variational Monte Carlo (VMC) method, are shown to be a promising way to investigate quantum many-body physics. Whereas vanilla VMC methods perform one gradient update per sample, we introduce a novel objective function with proximal optimization (PO) that enables multiple updates via reusing the mismatched samples. Our VMC-PO method keeps the advantage of the previous importance sampling gradient optimization algorithm [L. Yang, {\it et al}, Phys. Rev. Research {\bf 2}, 012039(R)(2020)] that efficiently uses sampled states. PO mitigates the numerical instabilities during network updates, which is similar to stochastic reconfiguration (SR) methods, but achieves an alternative and simpler implement with lower computational complexity. We investigate the performance of our VMC-PO algorithm for ground-state searching with a 1-dimensional transverse-field Ising model and 2-dimensional Heisenberg antiferromagnet on a square lattice, and demonstrate that the reached ground-state energies are comparable to state-of-the-art results.
