Tensor-network states (TNS) are a promising but numerically challenging tool for simulating two-dimensional (2D) quantum many-body problems. We introduce an isometric restriction of the TNS ansatz that allows for highly efficient contraction of the network. We consider two concrete applications using this ansatz. First, we show that a matrix-product state representation of a 2D quantum state can be iteratively transformed into an isometric 2D TNS. Second, we introduce a 2D version of the time-evolving block decimation algorithm for approximating of the ground state of a Hamiltonian as an isometric TNS-which we demonstrate for the 2D transverse field Ising model.

中文翻译：

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二维等距张量网络状态。

张量网络状态（TNS）是用于模拟二维（2D）量子多体问题的有前途但在数值上具有挑战性的工具。我们引入了TNS ansatz的等距限制，以实现网络的高效收缩。我们考虑使用此ansatz的两个具体应用。首先，我们表明可以将2D量子状态的矩阵乘积状态表示迭代地转换为等距2D TNS。其次，我们介绍了一种时变块抽取算法的2D版本，用于近似作为等距TNS的哈密顿量的基态-我们在2D横向场Ising模型中进行了演示。