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Differentiable programming is a new programming paradigm which enables large scale optimization through automatic calculation of gradients also known as auto-differentiation. This concept emerges from deep learning, and has also been…

Quantum Physics · Physics 2022-02-01 Chenhua Geng , Hong-Ye Hu , Yijian Zou

In this paper we explore the practical use of the corner transfer matrix and its higher-dimensional generalization, the corner tensor, to develop tensor network algorithms for the classical simulation of quantum lattice systems of infinite…

Strongly Correlated Electrons · Physics 2012-05-11 Roman Orus

Tensor networks (TNs) have become one of the most essential building blocks for various fields of theoretical physics such as condensed matter theory, statistical mechanics, quantum information, and quantum gravity. This review provides a…

Statistical Mechanics · Physics 2022-05-10 Kouichi Okunishi , Tomotoshi Nishino , Hiroshi Ueda

Based on the scheme of variational Monte Carlo sampling, we develop an accurate and efficient two-dimensional tensor-network algorithm to simulate quantum lattice models. We find that Monte Carlo sampling shows huge advantages in dealing…

Strongly Correlated Electrons · Physics 2021-06-28 Wen-Yuan Liu , Yi-Zhen Huang , Shou-Shu Gong , Zheng-Cheng Gu

We investigate the phase transition of the four-dimensional Ising model with two types of tensor network scheme, one is the higher-order tensor renormalization group and the other is the anisotropic tensor renormalization group. The results…

High Energy Physics - Lattice · Physics 2020-09-28 Shinichiro Akiyama , Yoshinobu Kuramashi , Takumi Yamashita , Yusuke Yoshimura

We show that the formalism of tensor-network states, such as the matrix product states (MPS), can be used as a basis for variational quantum Monte Carlo simulations. Using a stochastic optimization method, we demonstrate the potential of…

Strongly Correlated Electrons · Physics 2009-11-13 A. W. Sandvik , G. Vidal

We propose a second renormalization group (SRG) in the triad representation of tensor networks. The SRG method improves two parts of the triad tensor renormalization group, which are the decomposition of intermediate tensors and the…

Strongly Correlated Electrons · Physics 2022-05-11 Daisuke Kadoh , Hideaki Oba , Shinji Takeda

Tensor Network methods have been established as a powerful technique for simulating low dimensional strongly-correlated systems for over two decades. Employing the formalism of Matrix Product States, we investigate the phase diagram of the…

High Energy Physics - Lattice · Physics 2017-10-30 Mari Carmen Bañuls , Krzysztof Cichy , Ying-Jer Kao , C. -J. David Lin , Yu-Ping Lin , David Tao-Lin Tan

We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density matrix renormalization group…

Strongly Correlated Electrons · Physics 2010-11-08 Valentin Murg , Örs Legeza , Reinhard M. Noack , Frank Verstraete

The multi-scale entanglement renormalization ansatz (MERA) is a hierarchical class of tensor network states motivated by the real-space renormalization group. It is used to simulate strongly correlated quantum many-body systems. For…

Strongly Correlated Electrons · Physics 2025-01-07 Thomas Barthel , Qiang Miao

Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be…

Numerical Analysis · Mathematics 2023-03-30 Yajie Yu , Hanyu Li , Jingchun Zhou

The number of triangles is a computationally expensive graph statistic which is frequently used in complex network analysis (e.g., transitivity ratio), in various random graph models (e.g., exponential random graph model) and in important…

Data Structures and Algorithms · Computer Science 2015-05-20 Mihail N. Kolountzakis , Gary L. Miller , Richard Peng , Charalampos E. Tsourakakis

A promising new algebraic approach to weighted model counting makes use of tensor networks, following a reduction from weighted model counting to tensor-network contraction. Prior work has focused on analyzing the single-core performance of…

Data Structures and Algorithms · Computer Science 2021-06-16 Jeffrey M. Dudek , Moshe Y. Vardi

Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…

Disordered Systems and Neural Networks · Physics 2024-12-24 Yixiong Ren , Jianhui Zhou

The real-world effectiveness of deep neural networks often depends on their latency, thereby necessitating optimization techniques that can reduce a model's inference time while preserving its performance. One popular approach is to…

Machine Learning · Computer Science 2024-10-10 Jakob Hartmann , Guoliang He , Eiko Yoneki

Monte Carlo sampling techniques have been proposed as a strategy to reduce the computational cost of contractions in tensor network approaches to solving many-body systems. Here we put forward a variational Monte Carlo approach for the…

Strongly Correlated Electrons · Physics 2012-05-01 Andrew J. Ferris , Guifre Vidal

We introduce a new coarse-graining algorithm, tensor network skeletonization, for the numerical computation of tensor networks. This approach utilizes a structure-preserving skeletonization procedure to remove short-range correlations…

Numerical Analysis · Mathematics 2016-07-05 Lexing Ying

We investigate the multi-particle states of the (1+1)-dimensional Ising model using a spectroscopy scheme based on the tensor renormalization group method. We start by computing the finite-volume energy spectrum of the model from the…

High Energy Physics - Lattice · Physics 2026-02-17 Fathiyya Izzatun Az-zahra , Shinji Takeda , Takeshi Yamazaki

Tensor networks have emerged as promising tools for machine learning, inspired by their widespread use as variational ansatze in quantum many-body physics. It is well known that the success of a given tensor network ansatz depends in part…

Quantum Physics · Physics 2022-03-02 Ian Convy , William Huggins , Haoran Liao , K. Birgitta Whaley

We consider the problem of the estimation of a high-dimensional probability distribution from i.i.d. samples of the distribution using model classes of functions in tree-based tensor formats, a particular case of tensor networks associated…

Machine Learning · Statistics 2021-05-21 Erwan Grelier , Anthony Nouy , Régis Lebrun