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Related papers: Matrix product state renormalization

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We find an efficient approach to approximately convert matrix product states (MPSs) into restricted Boltzmann machine wave functions consisting of a multinomial hidden unit through a canonical polyadic (CP) decomposition of the MPSs. This…

Strongly Correlated Electrons · Physics 2025-10-29 Ryui Kaneko , Shimpei Goto

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

We propose a new method for low-rank approximation of Moore-Penrose pseudoinverses (MPPs) of large-scale matrices using tensor networks. The computed pseudoinverses can be useful for solving or preconditioning of large-scale overdetermined…

Numerical Analysis · Mathematics 2016-07-06 Namgil Lee , Andrzej Cichocki

We present matrix-product state (MPS) based band Lanczos method as solver for quantum cluster methods such as the variational cluster approximation. While a na\"ive implementation of MPS as cluster solver would barely improve its range of…

Strongly Correlated Electrons · Physics 2026-01-21 Sebastian Paeckel , Thomas Köhler , Salvatore R. Manmana , Benjamin Lenz

We solve the nonequilibrium dynamical mean-field theory (DMFT) using matrix product states (MPS). This allows us to treat much larger bath sizes and by that reach substantially longer times (factor $\sim$ 2 -- 3) than with exact…

Strongly Correlated Electrons · Physics 2014-12-22 F. Alexander Wolf , Ian P. McCulloch , Ulrich Schollwöck

We have implemented the sweep algorithm for the variational optimization of SU(2) x U(1) (spin and particle number) invariant matrix product states (MPS) for general spin and particle number invariant fermionic Hamiltonians. This class…

Strongly Correlated Electrons · Physics 2012-04-06 Sebastian Wouters , Peter A. Limacher , Dimitri Van Neck , Paul W. Ayers

Path integral techniques for the density matrix of a one-dimensional statistical system near a boundary previously employed in black-hole physics are applied to providing a new interpretation of the density matrix renormalization group: its…

Statistical Mechanics · Physics 2008-11-26 Jose Gaite

Tensor networks (TNs) are one of the best available tools to study many-body quantum systems. TNs are particularly suitable for one-dimensional local Hamiltonians, while their performance for generic geometries is mainly limited by two…

Quantum Physics · Physics 2026-04-08 Apimuk Sornsaeng , Itai Arad , Dario Poletti

In recent years, a close connection between the description of open quantum systems, the input-output formalism of quantum optics, and continuous matrix product states in quantum field theory has been established. So far, however, this…

Quantum Physics · Physics 2019-10-14 G. Haack , A. Steffens , J. Eisert , R. Hübener

We determine the local symmetries and local transformation properties of translationally invariant matrix product states (MPS). We focus on physical dimension $d=2$ and bond dimension $D=3$ and use the procedure introduced in D. Sauerwein…

Quantum Physics · Physics 2022-03-23 Martin Hebenstreit , David Sauerwein , Andras Molnar , J. Ignacio Cirac , Barbara Kraus

We present a variational matrix product state (vMPS) for the ground state of the spin-1/2 Heisenberg model. The MPS effectively organizes the various dimer configurations, in faithful reflection of the resonating valence bond (RVB) picture…

Strongly Correlated Electrons · Physics 2021-04-07 Jintae Kim , Minsoo Kim , Pramod Padmanabhan , Jung Hoon Han , Hyun-Yong Lee

In this work, we prove that any element in the tensor product of separable infinite-dimensional Hilbert spaces can be expressed as a matrix product state (MPS) of possibly infinite bond dimension. The proof is based on the singular value…

Mathematical Physics · Physics 2025-08-12 Niilo Heikkinen

We propose a way to construct a thermal pure quantum matrix product state (TPQ-MPS) that can simulate finite temperature quantum many-body systems with a minimal numerical cost comparable to the matrix product algorithm for the ground…

Strongly Correlated Electrons · Physics 2021-06-02 Atsushi Iwaki , Akira Shimizu , Chisa Hotta

This work explores the representation of univariate and multivariate functions as matrix product states (MPS), also known as quantized tensor-trains (QTT). It proposes an algorithm that employs iterative Chebyshev expansions and Clenshaw…

Recent contributions in the field of quantum state tomography have shown that, despite the exponential growth of Hilbert space with the number of subsystems, tomography of one-dimensional quantum systems may still be performed efficiently…

Quantum Physics · Physics 2013-07-19 Tillmann Baumgratz , David Gross , Marcus Cramer , Martin B. Plenio

We study phases of one-dimensional matrix-product states (MPS) when transformations are restricted to symmetric local circuits supplemented with symmetric measurements and feedforward (G-CMF). Building on the framework introduced in Gunn et…

Quantum Physics · Physics 2026-04-17 David Gunn , Georgios Styliaris , Barbara Kraus , Tristan Kraft

I revisit the infinite-size variant of the Density Matrix Renormalization Group (iDMRG) algorithm for obtaining a fixed-point translationally invariant matrix product wavefunction in the context of one-dimensional quantum systems. A crucial…

Strongly Correlated Electrons · Physics 2008-04-17 I. P. McCulloch

Permutation symmetries of multipartite quantum states are defined only when the constituent subsystems are of equal dimensions. In this work we extend this notion of permutation symmetry to heterogeneous systems, that is, systems composed…

Quantum Physics · Physics 2017-06-02 Gururaj Kadiri , S Sivakumar

This paper revisits the problem of decomposing a positive semidefinite matrix as a sum of a matrix with a given rank plus a sparse matrix. An immediate application can be found in portfolio optimization, when the matrix to be decomposed is…

Optimization and Control · Mathematics 2021-06-16 Michel Baes , Calypso Herrera , Ariel Neufeld , Pierre Ruyssen

In order to compute the Schmidt decomposition of $A\in M_k\otimes M_m$, we must consider an associated self-adjoint map. Here, we show that if $A$ is positive under partial transposition (PPT) or symmetric with positive coefficients (SPC)…

Mathematical Physics · Physics 2016-11-15 Daniel Cariello