English
Related papers

Related papers: Optimization at the boundary of the tensor network…

200 papers

Tensor network states (TNS) are a promising but numerically challenging tool for simulating two-dimensional (2D) quantum many-body problems. We introduce an isometric restriction of the TNS ansatz that allows for highly efficient…

Strongly Correlated Electrons · Physics 2020-02-10 Michael P. Zaletel , Frank Pollmann

We study the conditions under which Matrix Product States (MPS) or Matrix Product Operators are exact eigenvectors of an extensive local operator, such as a Hamiltonian. By suitably choosing the local operator, this covers a wide range of…

Quantum Physics · Physics 2026-03-31 José Garre Rubio , András Molnár , Norbert Schuch , Frank Verstraete

We describe a numerical many-body technique that is based on both tensor networks and quantum Monte Carlo. The variational ansatz is a tensor network that can harvest volume-law entanglement. It is constructed from a tensor train to which…

Strongly Correlated Electrons · Physics 2026-04-27 Miha Srdinsek , Gabriel Gouraud , Xavier Waintal

Efficient quantum circuit optimization schemes are central to quantum simulation of strongly interacting quantum many body systems. Here, we present an optimization algorithm which combines machine learning techniques and tensor network…

Quantum Physics · Physics 2024-08-23 David Rogerson , Ananda Roy

We present a general graph-based Projected Entangled-Pair State (gPEPS) algorithm to approximate ground states of nearest-neighbor local Hamiltonians on any lattice or graph of infinite size. By introducing the structural-matrix which…

Strongly Correlated Electrons · Physics 2019-05-08 Saeed S. Jahromi , Roman Orus

Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular class of TNS and are used for the simulation of…

High Energy Physics - Lattice · Physics 2016-06-27 Boye Buyens , Jutho Haegeman , Frank Verstraete , Karel Van Acoleyen

Projected entangled-pair states (PEPS) have become a powerful tool for studying quantum many-body systems in the condensed matter and quantum materials context, particularly with advances in variational energy optimization methods. A key…

Strongly Correlated Electrons · Physics 2025-06-10 Jan Naumann , Erik Lennart Weerda , Jens Eisert , Matteo Rizzi , Philipp Schmoll

Quantum variational algorithms are one of the most promising applications of near-term quantum computers; however, recent studies have demonstrated that unless the variational quantum circuits are configured in a problem-specific manner,…

We introduce a variational algorithm to simulate quantum many-body states based on a tree tensor network ansatz which releases the isometry constraint usually imposed by the real-space renormalization coarse-graining: This additional…

Statistical Mechanics · Physics 2014-10-08 Matthias Gerster , Pietro Silvi , Matteo Rizzi , Rosario Fazio , Tommaso Calarco , Simone Montangero

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

While highly entangled ground states of gapless local Hamiltonians have been known to exist in one dimension, their two-dimensional counterparts were only recently found, with rather sophisticated interactions involving at least four…

Quantum Physics · Physics 2025-12-16 Zhao Zhang , Olai B. Mykland

Suppose we would like to approximate all local properties of a quantum many-body state to accuracy $\delta$. In one dimension, we prove that an area law for the Renyi entanglement entropy $R_\alpha$ with index $\alpha<1$ implies a matrix…

Quantum Physics · Physics 2019-03-26 Yichen Huang

Matrix product states (MPS), a tensor network designed for one-dimensional quantum systems, has been recently proposed for generative modeling of natural data (such as images) in terms of `Born machine'. However, the exponential decay of…

Machine Learning · Statistics 2019-05-13 Song Cheng , Lei Wang , Tao Xiang , Pan Zhang

Progress in the application of machine learning techniques to the prediction of solid-state and molecular materials properties has been greatly facilitated by the development state-of-the-art feature representations and novel deep learning…

Materials Science · Physics 2022-03-21 David E. Sommer , Scott T. Dunham

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

Tensor networks are factorisations of high rank tensors into networks of lower rank tensors and have primarily been used to analyse quantum many-body problems. Tensor networks have seen a recent surge of interest in relation to supervised…

Computer Vision and Pattern Recognition · Computer Science 2021-03-26 Raghavendra Selvan , Silas Ørting , Erik B Dam

We introduce a method that generates ground-state ansatzes for quantum many-body systems which are both analytically tractable and accurate over wide parameter regimes. Our approach leverages a custom symbolic language to construct tensor…

Quantum Physics · Physics 2025-12-01 Matt Lourens , Ilya Sinayskiy , Johannes N. Kriel , Francesco Petruccione

It was recently proposed to leverage the representational power of artificial neural networks, in particular Restricted Boltzmann Machines, in order to model complex quantum states of many-body systems [Science, 355(6325), 2017]. States…

Quantum Physics · Physics 2019-07-04 Nahuel Freitas , Giovanna Morigi , Vedran Dunjko

We present a general computational framework to investigate ground state properties of quantum spin models on infinite two-dimensional lattices using automatic differentiation-based gradient optimization of infinite projected entangled-pair…

Computational Physics · Physics 2023-08-08 Xing-Yu Zhang , Shuang Liang , Hai-Jun Liao , Wei Li , Lei Wang

We present an approach to identify topological order based on unbiased infinite projected entangled-pair states (iPEPS) simulations, i.e. where we do not impose a virtual symmetry on the tensors during the optimization of the tensor network…

Strongly Correlated Electrons · Physics 2020-09-04 S. P. G. Crone , P. Corboz