论文标题
通过采样
Entanglement estimation in tensor network states via sampling
论文作者
论文摘要
我们介绍了一种在一般维度中提取张量网络状态的有意义的纠缠度量的方法。当前的方法需要对密度矩阵的明确重建，该密度矩阵高度要求或复制品的收缩，这需要在复制品数量中的努力指数，并且在内存方面是昂贵的。相反，我们的方法要求相对于从构成框架的简单产品概率测量的随机状态相对于经典表示的降低状态的矩阵元素的随机采样。即使与物理操作相对应，此类矩阵元素对于张量的网络状态而言很简单，并且它们的矩提供了rényi的熵和负面性及其对称分辨的组件。我们在棋盘几何形状中的一维临界XX链和二维复曲面代码上测试我们的方法。尽管成本在子系统规模中是指数级的，但它足够适度，因此与其他方法相比，可以在个人计算机上获得相对较大的子系统尺寸的准确结果。
We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction of replicas, which requires an effort exponential in the number of replicas and which is costly in terms of memory. In contrast, our method requires the stochastic sampling of matrix elements of the classically represented reduced states with respect to random states drawn from simple product probability measures constituting frames. Even though not corresponding to physical operations, such matrix elements are straightforward to calculate for tensor network states, and their moments provide the Rényi entropies and negativities as well as their symmetry-resolved components. We test our method on the one-dimensional critical XX chain and the two-dimensional toric code in a checkerboard geometry. Although the cost is exponential in the subsystem size, it is sufficiently moderate so that - in contrast with other approaches - accurate results can be obtained on a personal computer for relatively large subsystem sizes.
