论文标题
特征空间预测和维度诅咒的张量网络等级
Ranks of Tensor Networks for Eigenspace Projections and the Curse of Dimensionality
论文作者
论文摘要
订单的层次结构（多线性）等级 - $ d $张量是确定表示张量为（（树）张量网络（TN）的成本的关键。通常，众所周知，对于固定的准确性，不希望具有随机条目的张量，如果没有维度的诅咒，即具有$ d $的复杂性，可以有效地近似。在这项工作中，我们表明，一类无界汉密尔顿人的基态预测（GSP）可以大约表示为低有效维度的操作员，该操作员独立于GSP的（高）$ d $。这允许无需维度的诅咒即可近似GSP。
The hierarchical (multi-linear) rank of an order-$d$ tensor is key in determining the cost of representing a tensor as a (tree) Tensor Network (TN). In general, it is known that, for a fixed accuracy, a tensor with random entries cannot be expected to be efficiently approximable without the curse of dimensionality, i.e., a complexity growing exponentially with $d$. In this work, we show that the ground state projection (GSP) of a class of unbounded Hamiltonians can be approximately represented as an operator of low effective dimensionality that is independent of the (high) dimension $d$ of the GSP. This allows to approximate the GSP without the curse of dimensionality.
