Improving the efficiency of variational tensor network algorithms
Improving the efficiency of variational tensor network algorithms
复制标题
提高变分张量网络算法的效率
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
R. N. C. Pfeifer
中科院分区：
文献类型：
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作者：
G. Evenbly;R. N. C. Pfeifer
我们提出了几个结果有关的通用张量网络的收缩，并讨论了它们的应用程序的量子多体系统的模拟使用变分方法的基础上张量网络状态。给定一个封闭的张量网络T，我们证明了如果网络中单个张量的环境可以用计算成本κ来计算，那么T中任何其他张量的环境都可以用相同的成本κ来计算。此外，我们描述了如何从T的所有单张量环境的集合可以同时评估固定成本3κ。这些结果，这是适用于各种张量网络方法的有用性，被证明为优化的多尺度纠缠重整化Annomalization的基态的一维量子系统，在那里他们被证明大大减少了计算时间。
We present several results relating to the contraction of generic tensor networks and discuss their application to the simulation of quantum many-body systems using variational approaches based upon tensor network states. Given a closed tensor network T, we prove that if the environment of a single tensor from the network can be evaluated with computational cost κ, then the environment of any other tensor from T can be evaluated with identical cost κ. Moreover, we describe how the set of all single tensor environments from T can be simultaneously evaluated with fixed cost 3κ. The usefulness of these results, which are applicable to a variety of tensor network methods, is demonstrated for the optimization of a multiscale entanglement renormalization Ansatz for the ground state of a one-dimensional quantum system, where they are shown to substantially reduce the computation time.