Computations in quantum tensor networks

DOI10.1016/j.laa.2011.12.019zbMath1259.81088arXiv1212.5005OpenAlexW2092332806MaRDI QIDQ1931766

Th. Schulte-Herbrüggen, K. Waldherr, Thomas Kilian Huckle

Publication date: 16 January 2013

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.5005

zbMATH Keywords

quantum many-body systemscanonical decomposition (CANDECOMP or PARAFAC)density matrix renormalization group (DMRG)matrix product states (MPS)projected entangled-pair statestensor trains

Mathematics Subject Classification ID

Related Items (11)

The geometry of algorithms using hierarchical tensors ⋮ Constrained Optimization with Low-Rank Tensors and Applications to Parametric Problems with PDEs ⋮ Optimization problems in contracted tensor networks ⋮ A neural tensor decomposition model for high-order sparse data recovery ⋮ On manifolds of tensors of fixed TT-rank ⋮ TR-STF: a fast and accurate tensor ring decomposition algorithm via defined scaled tri-factorization ⋮ Algorithm 941 ⋮ Tensor numerical methods for multidimensional PDES: theoretical analysis and initial applications ⋮ Numerical tensor calculus ⋮ A literature survey of low-rank tensor approximation techniques ⋮ On traces of tensor representations of diagrams

Cites Work

• Unnamed Item
• Unnamed Item
• Tensor Decompositions and Applications
• Tensor-Train Decomposition
• The density-matrix renormalization group in the age of matrix product states
• Linear algebra for tensor problems
• Recursive decomposition of multidimensional tensors
• Finitely correlated states on quantum spin chains
• Abundance of translation invariant pure states on quantum spin chains
• Density-matrix renormalization. A new numerical method in physics. Lectures of a seminar and workshop held at the Max-Planck-Institut für Physik komplexer Systeme, Dresden, Germany, August 24 - September 18, 1998
• Two soluble models of an antiferromagnetic chain
• Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of ``Eckart-Young decomposition
• Matrix product operator representations
• Approximation of $2^d\times2^d$ Matrices Using Tensor Decomposition
• Colloquium: Area laws for the entanglement entropy
• The density-matrix renormalization group
• Unifying Variational Methods for Simulating Quantum Many-Body Systems
• Area Laws in Quantum Systems: Mutual Information and Correlations
• Computational Complexity of Projected Entangled Pair States
• Criticality, the Area Law, and the Computational Power of Projected Entangled Pair States
• Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions
• Renormalization and tensor product states in spin chains and lattices
• Properties of the Eigenvectors of Persymmetric Matrices with Applications to Communication Theory
• On the Best Rank-1 and Rank-(R₁ ,R₂ ,. . .,R_N) Approximation of Higher-Order Tensors
• Any Circulant-Like Preconditioner for Multilevel Matrices Is Not Superlinear
• Exploiting matrix symmetries and physical symmetries in matrix product states and tensor trains
• An area law for one-dimensional quantum systems
• Enhanced Line Search: A Novel Method to Accelerate PARAFAC
• Quantum Computing

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