計算物性物理メーリングリストのみなさま
東京大学の大久保です。
12/8に下記の内容で統計力学セミナーを開催します。
対面とオンラインのハイブリッドで、学外の方も、オンラインで参加できます。
参加をご希望の方は大久保
t-okubo@phys.s.u-tokyo.ac.jp
までご連絡ください。
折り返し、Zoomの接続情報を送ります。
大久保 毅
——
統計力学セミナー StatPhys Seminar @ UTokyo Hongo
sites.google.com/view/statphys-seminar
Room: 理学部1号館287教室 (Room No. 287, Science 1st Bldg.) and Online(Zoom)
Speaker: 藤堂眞治（東大）, Synge Todo (University of Tokyo)
Title: Tensor network and Markov chain Monte Carlo
Abstract:
Many classical and quantum lattice models can be represented as tensor networks [1]. 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 (e.g., [2,3,4]). Unfortunately, with naive weighted sampling, controlling the variance is impossible because it diverges exponentially as the network grows.
Here, we propose a new Monte Carlo scheme that combines the stochastic basis transformation of tensors with the Markov-chain Monte Carlo. It can entirely remove the systematic error due to a finite bond dimension of the low-rank approximation in tensor-network contraction while keeping the high accuracy of the tensor-network method. In this talk, we will demonstrate how the proposed method solves the severe sign problems for systems with negative (or complex) weights, such as the unitary evolution in quantum circuits.
[1] J. C. Bridgeman, and C. T. Chubb, J. Phys. A: Math. Theor. 50, 223001 (2017).
[2] A. Sandvik and G. Vidal, Phys. Rev. Lett. 99, 220602 (2007).
[3] L. Wang, I. Pizorn, and F. Verstraete, Phys. Rev. B 83, 134421 (2011).
[4] A. J. Ferris, arXiv:1507.00767.
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大久保 毅
東京大学大学院理学系研究科 量子ソフトウェア寄付講座
特任准教授
〒113-0033 東京都文京区本郷7-3-1
東京大学大学院理学系研究科知の物理学研究センター
理学部1号館9階 950
e-mail: t-okubo@phys.s.u-tokyo.ac.jp
Tel: 03-5841-8890
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