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Existing tensor network models of holography are limited to representing the geometry of constant time slices of static spacetimes. We study the possibility of describing the geometry of a dynamic spacetime using tensor networks. We find it…

High Energy Physics - Theory · Physics 2019-10-24 Alex May

We introduce complex-valued tensor network models for sequence processing motivated by correspondence to probabilistic graphical models, interpretability and resource compression. Inductive bias is introduced to our models via network…

Quantum Physics · Physics 2023-08-16 Carys Harvey , Richie Yeung , Konstantinos Meichanetzidis

The success of tensor network approaches in simulating strongly correlated quantum systems crucially depends on whether the many body states that are relevant for the problem can be encoded in a local tensor network. Despite numerous…

Strongly Correlated Electrons · Physics 2011-04-14 B. Béri , N. R. Cooper

Tensor network states constitute an important variational set of quantum states for numerical studies of strongly correlated systems in condensed-matter physics, as well as in mathematical physics. This is specifically true for finitely…

Quantum Physics · Physics 2014-11-27 M. Kliesch , D. Gross , J. Eisert

When studying interacting systems, computing their statistical properties is a fundamental problem in various fields such as physics, applied mathematics, and machine learning. However, this task can be quite challenging due to the…

Statistical Mechanics · Physics 2023-05-04 Yijia Wang , Yuwen Ebony Zhang , Feng Pan , Pan Zhang

Tensor networks are a powerful tool for many-body ground states with limited entanglement. These methods can nonetheless fail for certain time-dependent processes - such as quantum transport or quenches - where entanglement growth is linear…

Strongly Correlated Electrons · Physics 2020-05-20 Gabriela Wojtowicz , Justin E. Elenewski , Marek M. Rams , Michael Zwolak

Compared to sequential learning models, graph-based neural networks exhibit some excellent properties, such as ability capturing global information. In this paper, we investigate graph-based neural networks for text classification problem.…

Computation and Language · Computer Science 2020-02-27 Xien Liu , Xinxin You , Xiao Zhang , Ji Wu , Ping Lv

We discuss how to formulate lattice gauge theories in the Tensor Network language. In this way we obtain both a consistent truncation scheme of the Kogut-Susskind lattice gauge theories and a Tensor Network variational ansatz for gauge…

Strongly Correlated Electrons · Physics 2014-12-22 Luca Tagliacozzo , Alessio Celi , Maciej Lewenstein

We describe the use of tensor networks to numerically determine wave functions of interacting two-dimensional fermionic models in the continuum limit. We use two different tensor network states: one based on the numerical continuum limit of…

Strongly Correlated Electrons · Physics 2021-04-28 Reza Haghshenas , Zhi-Hao Cui , Garnet Kin-Lic Chan

The constantly increasing dimensionality of artificial quantum systems demands for highly efficient methods for their characterization and benchmarking. Conventional quantum tomography fails for larger systems due to the exponential growth…

Quantum Physics · Physics 2023-09-04 Sergei S. Kuzmin , Varvara I. Mikhailova , Ivan V. Dyakonov , Stanislav S. Straupe

Tensor network states and parton wave functions are two pivotal methods for studying quantum many-body systems. This work connects these two subjects as we demonstrate that a variety of parton wave functions, such as projected Fermi sea and…

Strongly Correlated Electrons · Physics 2020-06-22 Ying-Hai Wu , Lei Wang , Hong-Hao Tu

We study tensor network varieties associated with the triangular graph, with a focus on the case where one of the physical dimensions is 2. This allows us to interpret the tensors as pencils of matrices. We provide a complete…

Algebraic Geometry · Mathematics 2026-02-18 Alessandra Bernardi , Fulvio Gesmundo

The groundbreaking performance of deep neural networks (NNs) promoted a surge of interest in providing a mathematical basis to deep learning theory. Low-rank tensor decompositions are specially befitting for this task due to their close…

Machine Learning · Computer Science 2025-12-18 Ricardo Borsoi , Konstantin Usevich , Marianne Clausel

TensorNetwork is an open source library for implementing tensor network algorithms. Tensor networks are sparse data structures originally designed for simulating quantum many-body physics, but are currently also applied in a number of other…

It is a critical challenge to simultaneously gain high interpretability and efficiency with the current schemes of deep machine learning (ML). Tensor network (TN), which is a well-established mathematical tool originating from quantum…

Quantum Physics · Physics 2023-11-21 Shi-Ju Ran , Gang Su

Tensor networks, originally designed to address computational problems in quantum many-body physics, have recently been applied to machine learning tasks. However, compared to quantum physics, where the reasons for the success of tensor…

Quantum Physics · Physics 2020-07-14 John Martyn , Guifre Vidal , Chase Roberts , Stefan Leichenauer

We present applications of the renormalization algorithm with graph enhancement (RAGE). This analysis extends the algorithms and applications given for approaches based on matrix product states introduced in [Phys. Rev. A 79, 022317 (2009)]…

Quantum Physics · Physics 2015-03-17 R. Hübener , C. Kruszynska , L. Hartmann , W. Dür , M. B. Plenio , J. Eisert

Tensor networks are a class of algorithms aimed at reducing the computational complexity of high-dimensional problems. They are used in an increasing number of applications, from quantum simulations to machine learning. Exploiting data…

Numerical Analysis · Mathematics 2024-10-25 Melven Röhrig-Zöllner , Manuel Joey Becklas , Jonas Thies , Achim Basermann

Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…

Numerical Analysis · Mathematics 2020-03-02 A. Goeßmann , M. Götte , I. Roth , R. Sweke , G. Kutyniok , J. Eisert

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