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We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based…

Strongly Correlated Electrons · Physics 2015-11-04 Glen Evenbly , Guifre Vidal

We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017)]. By encoding the truth table of each vertex…

Statistical Mechanics · Physics 2018-03-09 Zhi-Cheng Yang , Stefanos Kourtis , Claudio Chamon , Eduardo R. Mucciolo , Andrei E. Ruckenstein

Efficient preparation of many-body ground states is key to harnessing the power of quantum computers in studying quantum many-body systems. In this work, we propose a simple method to design exact linear-depth parameterized quantum circuits…

Quantum Physics · Physics 2024-12-12 Yu-Jie Liu , Kirill Shtengel , Frank Pollmann

Topological order in a 2d quantum matter can be determined by the topological contribution to the entanglement R\'enyi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. Here we show how…

Strongly Correlated Electrons · Physics 2014-12-24 Roman Orus , Tzu-Chieh Wei , Oliver Buerschaper , Artur Garcia-Saez

Based on the tensor network state representation, we develop a nonlinear dynamic theory coined as network contractor dynamics (NCD) to explore the thermodynamic properties of two-dimensional quantum lattice models. By invoking the rank-$1$…

Strongly Correlated Electrons · Physics 2013-08-20 Shi-Ju Ran , Bin Xi , Tao Liu , Gang Su

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

This paper introduces matrix product state (MPS) decomposition as a new and systematic method to compress multidimensional data represented by higher-order tensors. It solves two major bottlenecks in tensor compression: computation and…

Machine Learning · Statistics 2017-08-02 Johann A. Bengua , Ho N. Phien , Hoang D. Tuan , Minh N. Do

In the tensor-network framework, the expectation values of two-dimensional quantum states are evaluated by contracting a double-layer tensor network constructed from initial and final tensor-network states. The computational cost of…

Strongly Correlated Electrons · Physics 2017-07-24 Z. Y. Xie , H. J. Liao , R. Z. Huang , H. D. Xie , J. Chen , Z. Y. Liu , T. Xiang

Network science provides very powerful tools for extracting information from interacting data. Although recently the unsupervised detection of phases of matter using machine learning has raised significant interest, the full prediction…

Disordered Systems and Neural Networks · Physics 2024-10-08 Hanlin Sun , Rajat Kumar Panda , Roberto Verdel , Alex Rodriguez , Marcello Dalmonte , Ginestra Bianconi

Modern approaches to generative modeling of continuous data using tensor networks incorporate compression layers to capture the most meaningful features of high-dimensional inputs. These methods, however, rely on traditional Matrix Product…

Machine Learning · Computer Science 2024-12-11 Danylo Kolesnyk , Yelyzaveta Vodovozova

This work studies the problem of high-dimensional data (referred to as tensors) completion from partially observed samplings. We consider that a tensor is a superposition of multiple low-rank components. In particular, each component can be…

Computer Vision and Pattern Recognition · Computer Science 2021-09-22 Chang Nie , Huan Wang , Zhihui Lai

We simulate the Shastry-Sutherland model in two dimensions by means of infinite projected entangled-pair states (iPEPS) - a variational tensor network method where the accuracy can be systematically controlled by the so-called bond…

Strongly Correlated Electrons · Physics 2015-06-12 Philippe Corboz , Frederic Mila

We propose the entanglement bipartitioning approach to design an optimal network structure of the tree-tensor-network (TTN) for quantum many-body systems. Given an exact ground-state wavefunction, we perform sequential bipartitioning of…

Quantum Physics · Physics 2023-03-02 Kouichi Okunishi , Hiroshi Ueda , Tomotoshi Nishino

Tensor networks are a powerful modeling framework developed for computational many-body physics, which have only recently been applied within machine learning. In this work we utilize a uniform matrix product state (u-MPS) model for…

Machine Learning · Computer Science 2021-04-26 Jacob Miller , Guillaume Rabusseau , John Terilla

We present an asymptotically faster algorithm for solving linear systems in well-structured 3-dimensional truss stiffness matrices. These linear systems arise from linear elasticity problems, and can be viewed as extensions of graph…

Data Structures and Algorithms · Computer Science 2018-05-25 Rasmus Kyng , Richard Peng , Robert Schwieterman , Peng Zhang

We study the two-dimensional square lattice Ising ferromagnet and antiferromagnet with a magnetic field by using tensor network method. Focusing on the role of guage fixing, we present the partition function in terms of a tensor network.…

Statistical Mechanics · Physics 2025-01-03 Myung-Hoon Chung

We present a new method for online prediction and learning of tensors ($N$-way arrays, $N >2$) from sequential measurements. We focus on the specific case of 3-D tensors and exploit a recently developed framework of structured tensor…

Machine Learning · Statistics 2015-07-30 John Pothier , Josh Girson , Shuchin Aeron

We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction…

Strongly Correlated Electrons · Physics 2022-07-28 Noa Feldman , Augustine Kshetrimayum , Jens Eisert , Moshe Goldstein

Matrix product states (MPS) have proven to be a very successful tool to study lattice systems with local degrees of freedom such as spins or bosons. Topologically ordered systems can support anyonic particles which are labeled by conserved…

Strongly Correlated Electrons · Physics 2014-04-03 Sukhwinder Singh , Robert N. C. Pfeifer , Guifre Vidal , Gavin K. Brennen

Tensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum…

Computational Physics · Physics 2020-01-31 Shi-Ju Ran , Emanuele Tirrito , Cheng Peng , Xi Chen , Luca Tagliacozzo , Gang Su , Maciej Lewenstein