Changing the topology of Tensor Networks

A Multilinear Singular Value Decomposition

L. De Lathauwer, B. De Moor, and J. Vandewalle · 2000

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Efficient Classical Simulation of Slightly Entangled Quantum Computations

Guifré Vidal · 2003

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A New Scheme for the Tensor Representation

W. Hackbusch and S. Kühn · 2009

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Compact matrix form of the d d -dimensional tensor decomposition

I. V. Oseledets · 2009

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Exploring frustrated spin–systems using Projected Entangled Pair States (PEPS)

Original

V. Murg, F. Verstraete, and J. I. Cirac · 2009

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Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions

I. V. Oseledets and E. E. Tyrtyshnikov · 2009

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Simulating strongly correlated quantum systems with tree tensor networks

V. Murg, F. Verstraete, Ö. Legeza, and R. M. Noack · 2010

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The Alternating Linear Scheme for Tensor Optimisation in the TT Format

S. Holtz, T. Rohwedder, and R. Schneider · 2010

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𝒪 ⁡ ( d ​ log ⁡ N ) \mathcal{O}(d\log{N}) -Quantics Approximation of N − d {N}-d Tensors in High-Dimensional Numerical Modeling

B. N. Khoromskij · 2010

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Computations in Quantum Tensor Networks

T. Huckle, K. Waldherr, and T. Schulte-Herbrüggen · 2010

Cited alongside, same era.

Monte Carlo simulation with tensor network states

L. Wang, I. Pižorn, and F. Verstraete · 2011

Cited alongside, same era.

Tensor-Train Decomposition

I. V. Oseledets · 2011

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On the geometry of tensor network states

Original

J. M. Landsberg, Y. Qi, and K. Ye · 2011

Later among the works it cites.

Optimization Problems in Contracted Tensor Networks

M. Espig, W. Hackbusch, S. Handschuh, and R. Schneider · 2011

Later among the works it cites.

Tensor Spaces and Numerical Tensor Calculus

Wolfgang Hackbusch · 2012

Closest in time.

TensorCalculus library, 2008–2012

M. Espig, M. Schuster, A. Killaitis, N. Waldren, P. Wähnert, S. Handschuh, and H. Auer · 2012

Closest in time.