Tensor networks provide an efficient classical representation of certain strongly correlated quantum many-body systems. We present a general lifting method to ascribe quantum states to the network structure itself that reveals important new physical features. To illustrate, we focus on the multiscale entanglement renormalization ansatz (MERA) tensor network for 1D critical ground states on a lattice. The MERA representation of the said state can be lifted to a 2D quantum dual in a way that is suggestive of a lattice version of the holographic correspondence from string theory. The bulk 2D state has an efficient quantum circuit construction and exhibits several features of holography, including the appearance of horizon-like holographic screens, short-ranged correlations described via a strange correlator and bulk gauging of global on-site symmetries at the boundary. Notably, the lifting provides a way to calculate a quantum-corrected Ryu–Takayanagi formula, and map bulk operators to boundary operators and vice versa.

张量网络提供了某些强相关的量子多体系统的有效经典表示。我们提出了一种通用的提升方法，将量子态归因于网络结构本身，从而揭示了重要的新物理特征。为了说明这一点，我们重点关注晶格上一维临界基态的多尺度纠缠重归一化安萨兹（MERA）张量网络。所述状态的MERA表示可以以暗示来自弦理论的全息对应的晶格形式的方式被提升为2D量子对偶。体二维状态具有高效的量子电路构造，并展现出全息术的一些特征，包括类似地平线的全息屏幕的外观，通过奇异的相关器和边界处的全局现场对称性的整体测量来描述短距离相关。值得注意的是，提升提供了一种计算经过量子校正的Ryu–Takayanagi公式，并将体算子映射到边界算子的方法，反之亦然。