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Simulating quantum many-body systems (QMBS) is one of the long-standing, highly non-trivial challenges in condensed matter physics and quantum information due to the exponentially growing size of the system's Hilbert space. To date, tensor…

Quantum Physics · Physics 2026-02-06 Belal Abouraya , Jirawat Saiphet , Fedor Jelezko , Ressa S. Said

One of the challenging problems in the condensed matter physics is to understand the quantum many-body systems, especially, their physical mechanisms behind. Since there are only a few complete analytical solutions of these systems, several…

Statistical Mechanics · Physics 2020-03-27 Jozef Genzor , Tomotoshi Nishino , Andrej Gendiar

Tensor networks (TNs) have been gaining interest as multiway data analysis tools owing to their ability to tackle the curse of dimensionality and to represent tensors as smaller-scale interconnections of their intrinsic features. However,…

Signal Processing · Electrical Eng. & Systems 2017-11-03 Giuseppe G. Calvi , Ilia Kisil , Danilo P. Mandic

We present a 2D bosonization duality using the language of tensor networks. Specifically, we construct a tensor network operator (TNO) that implements an exact 2D bosonization duality. The primary benefit of the TNO is that it allows for…

Strongly Correlated Electrons · Physics 2020-04-15 Sujeet K. Shukla , Tyler D. Ellison , Lukasz Fidkowski

Symmetry-resolved entanglement is a useful tool for characterizing symmetry-protected topological states. In two dimensions, their entanglement spectra are described by conformal field theories but the symmetry resolution is largely…

Strongly Correlated Electrons · Physics 2023-03-13 Daniel Azses , David F. Mross , Eran Sela

We propose an efficient algorithm for simulating quantum many-body systems in two spatial dimensions using projected entangled pair states. This is done by approximating the environment, arising in the context of updating tensors in the…

Quantum Physics · Physics 2011-05-26 Iztok Pizorn , Ling Wang , Frank Verstraete

Hybrid tensor networks offer a promising route to enhance the expressivity of classical tensor network methods by incorporating quantum states prepared on a quantum computer. Existing approaches are limited by the variational optimization…

Quantum Physics · Physics 2026-05-21 Julian Schuhmacher , Alberto Baiardi , Francesco Tacchino , Ivano Tavernelli

Low-rank tensor approximation approaches have become an important tool in the scientific computing community. The aim is to enable the simulation and analysis of high-dimensional problems which cannot be solved using conventional methods…

Numerical Analysis · Mathematics 2019-02-26 Patrick Gelß , Stefan Klus , Sebastian Matera , Christof Schütte

Tensor networks are often used to accurately represent ground states of quantum spin chains. Two popular choices of such tensor network representations can be seen to implement linear maps that correspond, respectively, to euclidean time…

Strongly Correlated Electrons · Physics 2018-06-01 Ashley Milsted , Guifre Vidal

We revisit the application of neural networks techniques to quantum state tomography. We confirm that the positivity constraint can be successfully implemented with trained networks that convert outputs from standard feed-forward neural…

Quantum Physics · Physics 2022-07-20 D. Koutny , L. Motka , Z. Hradil , J. Rehacek , L. L. Sanchez-Soto

We introduce a change of perspective on tensor network states that is defined by the computational graph of the contraction of an amplitude. The resulting class of states, which we refer to as tensor network functions, inherit the…

Quantum Physics · Physics 2025-01-06 Wen-Yuan Liu , Si-Jing Du , Ruojing Peng , Johnnie Gray , Garnet Kin-Lic Chan

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

Tensor network (TN) representation is a powerful technique for computer vision and machine learning. TN structure search (TN-SS) aims to search for a customized structure to achieve a compact representation, which is a challenging NP-hard…

Machine Learning · Computer Science 2024-04-15 Yu-Bang Zheng , Xi-Le Zhao , Junhua Zeng , Chao Li , Qibin Zhao , Heng-Chao Li , Ting-Zhu Huang

The experimental realization of increasingly complex synthetic quantum systems calls for the development of general theoretical methods, to validate and fully exploit quantum resources. Quantum-state tomography (QST) aims at reconstructing…

Disordered Systems and Neural Networks · Physics 2018-05-17 Giacomo Torlai , Guglielmo Mazzola , Juan Carrasquilla , Matthias Troyer , Roger Melko , Giuseppe Carleo

This work is concerned with tree tensor network operators (TTNOs) for representing quantum Hamiltonians. We first establish a mathematical framework connecting tree topologies with state diagrams. Based on these, we devise an algorithm for…

Quantum Physics · Physics 2024-07-09 Richard M. Milbradt , Qunsheng Huang , Christian B. Mendl

Optimization problems pose challenges across various fields. In recent years, quantum annealers have emerged as a promising platform for tackling such challenges. To provide a new perspective, we develop a heuristic tensor network (TN)…

Disordered Systems and Neural Networks · Physics 2025-06-17 Anna Maria Dziubyna , Tomasz Śmierzchalski , Bartłomiej Gardas , Marek M. Rams , Masoud Mohseni

Quantum state tomography is a fundamental task in quantum information science, enabling detailed characterization of correlations, entanglement, and electronic structure in quantum systems. However, its exponential measurement and…

Inspired by the advancements in large language models based on transformers, we introduce the transformer quantum state (TQS): a versatile machine learning model for quantum many-body problems. In sharp contrast to Hamiltonian/task specific…

Quantum Physics · Physics 2023-03-08 Yuan-Hang Zhang , Massimiliano Di Ventra

An augmented tree tensor network (aTTN) is a tensor network ansatz constructed by applying a layer of unitary disentanglers to a tree tensor network. The disentanglers absorb a part of the system's entanglement. This makes aTTNs suitable…

Quantum Physics · Physics 2025-07-30 Nora Reinić , Luka Pavešić , Daniel Jaschke , Simone Montangero

Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…

Machine Learning · Statistics 2017-08-03 Masaaki Imaizumi , Takanori Maehara , Kohei Hayashi