论文标题
用神经自回旋量子状态计算Renyi熵
Calculating Renyi Entropies with Neural Autoregressive Quantum States
论文作者
论文摘要
纠缠熵是表征量子多体系统的必不可少的指标，但是迄今为止，其对量子状态的神经网络表示的数值评估效率低下，仅针对受限的玻尔兹曼机器架构而言。在这里，我们估计使用量子蒙特卡洛方法的自回归神经量子状态的概括性肾脏熵。幼稚的“直接采样”方法对于低阶Renyi熵表现良好，但在1D海森贝格模型上进行基准测试时，较大订单失败。因此，我们提出了一种改进的“条件抽样”方法，利用网络ANSATZ的自回旋结构，该方法的表现优于直接采样，并促进了在1D和2D Heisenberg模型中高阶Renyi熵的计算。访问高阶Renyi熵可以近似von Neumann熵以及单副本纠缠的提取。两种方法都阐明了在多体系统的纠缠熵的量子卡洛研究中，神经网络量子状态的潜力。
Entanglement entropy is an essential metric for characterizing quantum many-body systems, but its numerical evaluation for neural network representations of quantum states has so far been inefficient and demonstrated only for the restricted Boltzmann machine architecture. Here, we estimate generalized Renyi entropies of autoregressive neural quantum states with up to N=256 spins using quantum Monte Carlo methods. A naive "direct sampling" approach performs well for low-order Renyi entropies but fails for larger orders when benchmarked on a 1D Heisenberg model. We therefore propose an improved "conditional sampling" method exploiting the autoregressive structure of the network ansatz, which outperforms direct sampling and facilitates calculations of higher-order Renyi entropies in both 1D and 2D Heisenberg models. Access to higher-order Renyi entropies allows for an approximation of the von Neumann entropy as well as extraction of the single copy entanglement. Both methods elucidate the potential of neural network quantum states in quantum Monte Carlo studies of entanglement entropy for many-body systems.
