Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an approximate, fast, and simple algorithm to optimize disentangling unitary tensors. Our algorithm is asymptotically faster than previous iterative algorithms and often results in a residual entanglement entropy that is within 10 to 40% of the minimum. For certain input tensors, our algorithm returns an optimal solution. When disentangling order-4 tensors with equal bond dimensions, our algorithm achieves an entanglement spectrum where nearly half of the singular values are zero. We further validate our algorithm by showing that it can efficiently disentangle random 1D states of qubits.

中文翻译：

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快速张量解缠算法

许多最近的张量网络算法将幺正算子应用于张量网络的各个部分，以减少纠缠。然而，许多以前使用的迭代算法来最小化纠缠可能会很慢。我们引入了一种近似、快速且简单的算法来优化解缠酉张量。我们的算法比以前的迭代算法渐进快，并且经常导致残留纠缠熵在最小值的 10% 到 40% 之内。对于某些输入张量，我们的算法会返回一个最优解。当解开具有相同键维数的 4 阶张量时，我们的算法实现了纠缠谱，其中近一半的奇异值为零。我们通过证明它可以有效地解开量子位的随机一维状态来进一步验证我们的算法。