We design quantum compression algorithms for parametric families of tensor network states. We first establish an upper bound on the amount of memory needed to store an arbitrary state from a given state family. The bound is determined by the minimum cut of a suitable flow network, and is related to the flow of information from the manifold of parameters that specify the states to the physical systems in which the states are embodied. For given network topology and given edge dimensions, our upper bound is tight when all edge dimensions are powers of the same integer. When this condition is not met, the bound is optimal up to a multiplicative factor smaller than 1.585. We then provide a compression algorithm for general state families, and show that the algorithm runs in polynomial time for matrix product states.

中文翻译：

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张量网络状态的量子压缩

我们为张量网络状态的参数族设计量子压缩算法。我们首先建立存储来自给定状态族的任意状态所需的内存量的上限。边界由合适的流网络的最小割确定，并且与从指定状态的参数流形到包含状态的物理系统的信息流有关。对于给定的网络拓扑和给定的边尺寸，当所有边尺寸都是相同整数的幂时，我们的上限是严格的。当不满足此条件时，该界限在乘法因子小于 1.585 时是最佳的。然后我们为一般状态族提供了一种压缩算法，并表明该算法在矩阵乘积状态的多项式时间内运行。