Contracting Arbitrary Tensor Networks: General Approximate Algorithm and Applications in Graphical Models and Quantum Circuit Simulations.,Physical Review Letters

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Contracting Arbitrary Tensor Networks: General Approximate Algorithm and Applications in Graphical Models and Quantum Circuit Simulations.
Physical Review Letters ( IF 8.1 ) Pub Date : 2020-08-07 , DOI: 10.1103/physrevlett.125.060503
Feng Pan _{1,

2} , Pengfei Zhou _{1,

2} , Sujie Li _{1,

2} , Pan Zhang _{1,

3,

4}

Affiliation

We present a general method for approximately contracting tensor networks with an arbitrary connectivity. This enables us to release the computational power of tensor networks to wide use in inference and learning problems defined on general graphs. We show applications of our algorithm in graphical models, specifically on estimating free energy of spin glasses defined on various of graphs, where our method largely outperforms existing algorithms, including the mean-field methods and the recently proposed neural-network-based methods. We further apply our method to the simulation of random quantum circuits and demonstrate that, with a trade-off of negligible truncation errors, our method is able to simulate large quantum circuits that are out of reach of the state-of-the-art simulation methods.

中文翻译：

收缩任意张量网络：通用近似算法及其在图形模型和量子电路仿真中的应用。

我们提出了一种具有任意连通性的近似收缩张量网络的通用方法。这使我们能够释放张量网络的计算能力，以广泛用于一般图上定义的推理和学习问题。我们展示了我们的算法在图形模型中的应用，特别是在估计在各种图形上定义的旋转玻璃的自由能方面，其中我们的方法大大优于现有的算法，包括均值场方法和最近提出的基于神经网络的方法。我们进一步将我们的方法应用于随机量子电路的仿真，并证明，通过权衡可忽略的截断误差，我们的方法能够仿真大型量子电路，而这是最新技术无法实现的方法。

更新日期：2020-08-08

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