Pan Feng, Zhou Pengfei, Li Sujie, Zhang Pan
CAS Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.
School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China.
Phys Rev Lett. 2020 Aug 7;125(6):060503. doi: 10.1103/PhysRevLett.125.060503.
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.
我们提出了一种用于近似收缩具有任意连通性的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，以便在定义于一般图上的推理和学习问题中广泛应用。我们展示了我们算法在图形模型中的应用，具体是在估计定义于各种图上的自旋玻璃的自由能方面，在该应用中我们的方法在很大程度上优于现有算法，包括平均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模拟，并证明，在截断误差可忽略不计的权衡下，我们的方法能够模拟现有最先进模拟方法无法企及的大型量子电路。
