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Monte Carlo sampling in tensor-network representation

日程 : 2023年2月20日(月) 1:00 pm - 2:00 pm 場所 : オンライン (Zoom) 講師 : 藤堂 眞治 所属 : 東京大学 物理学専攻 世話人 : 川島 直輝
e-mail: kawashima@issp.u-tokyo.ac.jp
講演言語 : 英語

Many classical and quantum lattice models can be represented as tensor networks. However, the exact contraction of a tensor network is generally exponentially expensive, and some approximation is usually required. In numerical simulations based on the tensor networks, approximations with the singular value decomposition are widely used. On the other hand, various contraction methods based on randomized algorithms have also been proposed. Unfortunately, with a simple weighted sampling, it is difficult to control the accuracy because the expected value variance diverges rapidly as the network grows. In this talk, I propose a new tensor contraction method based on Monte Carlo sampling. The proposed method combines the stochastic basis transformation of tensors with the Markov chain Monte Carlo framework. It can entirely remove the systematic error due to a finite bond dimension in the approximate tensor-network contraction while controlling the variance of measurements.

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(公開日: 2023年02月07日)