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Quantum computing is finding promising applications in optimization, machine learning and physics, leading to the development of various models for representing quantum information. Because these representations are often studied in…

Quantum Physics · Physics 2024-01-03 Lieuwe Vinkhuijzen , Tim Coopmans , Alfons Laarman

A deep neural network is a parametrization of a multilayer mapping of signals in terms of many alternatively arranged linear and nonlinear transformations. The linear transformations, which are generally used in the fully connected as well…

Machine Learning · Computer Science 2020-07-01 Ze-Feng Gao , Song Cheng , Rong-Qiang He , Z. Y. Xie , Hui-Hai Zhao , Zhong-Yi Lu , Tao Xiang

We derive a criterion to determine when a translationally invariant matrix product state (MPS) has long-range localizable entanglement, where that quantity remains finite in the thermodynamic limit. We give examples fulfilling this…

Quantum Physics · Physics 2013-08-30 Thorsten B. Wahl , David Perez-Garcia , J. Ignacio Cirac

We introduce an efficient algorithm for the systematic design of shallow-depth quantum circuits capable of preparing many-body quantum states represented as Matrix Product States (MPS). The proposed method leverages Schmidt spectrum…

Quantum Physics · Physics 2025-12-24 Josh Green , Joshua Snow , Jingbo B Wang

By taking inspiration from the backflow transformation for correlated systems, we introduce a novel tensor network ansatz which extend the well-established Matrix Product State representation of a quantum-many body wave function. This new…

Strongly Correlated Electrons · Physics 2022-08-31 Guglielmo Lami , Giuseppe Carleo , Mario Collura

In this work, we present a novel representation of matrix product states (MPS) within the framework of quasi-local algebras. By introducing an enhanced compatibility condition, we enable the extension of finite MPS to an infinite-volume…

Quantum Physics · Physics 2024-11-08 Abdessatar Souissi , Amenallah Andolsi

Models whose ground states can be written as an exact matrix product state (MPS) provide valuable insights into phases of matter. While MPS-solvable models are typically studied as isolated points in a phase diagram, they can belong to a…

Strongly Correlated Electrons · Physics 2021-11-01 Nick G. Jones , Julian Bibo , Bernhard Jobst , Frank Pollmann , Adam Smith , Ruben Verresen

We study low-rank parameterizations of weight matrices with embedded spectral properties in the Deep Learning context. The low-rank property leads to parameter efficiency and permits taking computational shortcuts when computing mappings.…

Machine Learning · Computer Science 2021-07-15 Anton Obukhov , Maxim Rakhuba , Alexander Liniger , Zhiwu Huang , Stamatios Georgoulis , Dengxin Dai , Luc Van Gool

Matrix-product state (MPS) skeletons are connected networks of Hamiltonians with exact MPS ground states that underlie a phase diagram. Such skeletons have previously been found in classes of free-fermion models. For the…

Quantum Physics · Physics 2025-11-11 Imogen Camp , Nick G. Jones

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

Relativistic continuous matrix product states (RCMPS) are a powerful variational ansatz for quantum field theories of a single field. However, they inherit a property of their non-relativistic counterpart that makes them divergent for…

Quantum Physics · Physics 2025-11-27 Karan Tiwana , Antoine Tilloy

Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks such as Projected Entangled Pair States…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-09-04 Yuchen Pang , Tianyi Hao , Annika Dugad , Yiqing Zhou , Edgar Solomonik

We show the feasibility of tensor network solutions for lattice gauge theories in Hamiltonian formulation by applying matrix product states algorithms to the Schwinger model with zero and non-vanishing fermion mass. We introduce new…

High Energy Physics - Lattice · Physics 2013-12-10 M. C. Bañuls , K. Cichy , K. Jansen , J. I. Cirac

Tensor networks provide an efficient approximation of operations involving high dimensional tensors and have been extensively used in modelling quantum many-body systems. More recently, supervised learning has been attempted with tensor…

Computer Vision and Pattern Recognition · Computer Science 2021-07-02 Raghavendra Selvan , Erik B Dam , Jens Petersen

For the past twenty years, Matrix Product States (MPS) have been widely used in solid state physics to approximate the ground state of one-dimensional spin chains. In this paper, we study homogeneous MPS (hMPS), or MPS constructed via…

Quantum Physics · Physics 2018-02-01 Miguel Navascues , Tamas Vertesi

We introduce a matrix product state (MPS) with an incommensurate periodicity by applying the spin-rotation operator of each site to a uniform MPS in the thermodynamic limit. The spin rotations decrease the variational energy with…

Strongly Correlated Electrons · Physics 2012-09-04 Hiroshi Ueda , Isao Maruyama

We explore various ways to group orbitals into clusters in a matrix product state (MPS). We explain how a generic cluster MPS can often lead to an increase in computational cost and instead propose a special cluster structure, involving…

Chemical Physics · Physics 2022-10-03 Henrik R. Larsson , Huanchen Zhai , Klaas Gunst , Garnet Kin-Lic Chan

A systematic and compact treatment of arbitrary $su(2)$ invariant spin-$s$ quantum chains with nearest-neighbour interactions is presented. The ground-state is derived in terms of matrix product states (MPS). The fundamental MPS…

Strongly Correlated Electrons · Physics 2016-08-24 Rubina Zadourian , Andreas Fledderjohann , Andreas Klümper

The exact treatment of Markovian models of complex systems requires knowledge of probability distributions exponentially large in the number of components $n$. Mean-field approximations provide an effective reduction in complexity of the…

Statistical Mechanics · Physics 2025-03-12 Wout Merbis , Madelon Geurts , Clélia de Mulatier , Philippe Corboz

We obtain an exact matrix-product-state (MPS) representation of a large series of fractional quantum Hall (FQH) states in various geometries of genus 0. The states in question include all paired k=2 Jack polynomials, such as the Moore-Read…

Strongly Correlated Electrons · Physics 2013-06-03 B. Estienne , Z. Papic , N. Regnault , B. A. Bernevig