论文标题
关于张量网络和规范形式的稳定性
On Stability of Tensor Networks and Canonical Forms
论文作者
论文摘要
张量网络（例如矩阵产品状态状态（MP）和预测的纠缠对状态（PEP）通常用于近似量子系统。这些网络是在诸如DMRG或本地运营商进化的方法中优化的。我们提供有关张量网络表示的条件到站点扰动的界限。这些边界表征了张量网络张量位点中局部近似误差的程度，可以扩增到其表示的张量中的误差。在已知的张量网络方法中，张量网络的规范形式用于最大程度地减少这种错误扩增。但是，对于许多感兴趣的张量网络，很难获得规范形式。我们量化了在一般张量网络中可以放大误差的程度，从而估算了使用规范形式的好处。对于MPS和PEPS张量网络，我们为最坏情况的错误放大提供了简单的表单。除了理论误差边界之外，我们还通过实验研究了误差对扰动随机MPS张量网络网络大小的依赖性。
Tensor networks such as matrix product states (MPS) and projected entangled pair states (PEPS) are commonly used to approximate quantum systems. These networks are optimized in methods such as DMRG or evolved by local operators. We provide bounds on the conditioning of tensor network representations to sitewise perturbations. These bounds characterize the extent to which local approximation error in the tensor sites of a tensor network can be amplified to error in the tensor it represents. In known tensor network methods, canonical forms of tensor network are used to minimize such error amplification. However, canonical forms are difficult to obtain for many tensor networks of interest. We quantify the extent to which error can be amplified in general tensor networks, yielding estimates of the benefit of the use of canonical forms. For the MPS and PEPS tensor networks, we provide simple forms on the worst-case error amplification. Beyond theoretical error bounds, we experimentally study the dependence of the error on the size of the network for perturbed random MPS tensor networks.
