17 sources. Every identifier below was resolved against arXiv or Crossref on 2026-07-29, and the title, authors, and year shown are the ones those records returned.
That is identifier verification, not a re-reading of each full text. A reviewer auditing this atlas should check the mapping from a claim to a specific result in a specific paper — that is the step where a source trail most often goes wrong, and it is the step an identifier check cannot cover.
primary paper · identifier verified
Steven R. White · 1992
DOI:10.1103/PhysRevLett.69.2863
Primary source for DMRG, the variational method later understood as optimization over matrix product states.
Source record →primary paper · identifier verified
Guifré Vidal · 2003
arXiv:quant-ph/0301063
Ties classical simulation cost to the entanglement carried across a cut, which is the quantity a bond dimension budgets.
Source record →primary paper · identifier verified
F. Verstraete, J. I. Cirac · 2004
arXiv:cond-mat/0407066
Primary source for the projected entangled pair state (PEPS) generalization of MPS beyond one dimension.
Source record →primary paper · identifier verified
Guifré Vidal · 2005
arXiv:cond-mat/0512165
Introduces entanglement renormalization and the disentangler that distinguishes MERA from a plain tree network.
Source record →primary paper · identifier verified
G. Vidal · 2006
arXiv:quant-ph/0610099
Primary source for the MERA ansatz and its efficient contraction, including the scale-invariant construction.
Source record →primary paper · identifier verified
Norbert Schuch, Michael M. Wolf, Frank Verstraete, J. Ignacio Cirac · 2006
arXiv:quant-ph/0611050
Establishes hardness results for contracting PEPS — the reason higher-dimensional tensor networks are approximated, not contracted exactly.
Source record →primary paper · identifier verified
Igor L. Markov, Yaoyun Shi · 2005
arXiv:quant-ph/0511069
Connects the cost of contracting a tensor network to the treewidth of its graph, which is the structural quantity behind contraction-order search.
Source record →primary paper · identifier verified
M. B. Hastings · 2007
arXiv:0705.2024
Proves the one-dimensional area law that explains why a bounded bond dimension suffices for gapped 1D ground states — and, by implication, when it does not.
Source record →review article · identifier verified
F. Verstraete, J. I. Cirac, V. Murg · 2008
arXiv:0907.2796
Review tying MPS, PEPS, and variational renormalization group methods into one framework.
Source record →primary paper · identifier verified
Brian Swingle · 2009
arXiv:0905.1317
The paper that proposed reading the MERA network as a discretized holographic geometry. It is the origin of the AdS/MERA conjecture, not a proof of it.
Source record →review article · identifier verified
Ulrich Schollwöck · 2010
arXiv:1008.3477
Standard reference for MPS canonical forms, SVD truncation, and the reformulation of DMRG in tensor-network language.
Source record →review article · identifier verified
Román Orús · 2013
arXiv:1306.2164
Review covering tensor-network structure, entanglement scaling, and contraction strategy; the general reference for this atlas.
Source record →primary paper · identifier verified
Andrew Lucas · 2013
arXiv:1302.5843
Catalogues explicit Ising encodings for NP-hard problems — the step that turns a combinatorial problem into a spin model a tensor network can act on.
Source record →primary paper · identifier verified
Edward Farhi, Jeffrey Goldstone, Sam Gutmann · 2014
arXiv:1411.4028
Primary source for QAOA, the quantum method against which quantum-inspired classical optimizers are usually compared.
Source record →primary paper · identifier verified
Ning Bao, ChunJun Cao, Sean M. Carroll, Aidan Chatwin-Davies, Nicholas Hunter-Jones, Jason Pollack, Grant N. Remmen · 2015
arXiv:1504.06632
States conditions an AdS/MERA correspondence would have to satisfy and argues they are in tension. It is why tn-005 is labelled a conjecture rather than a result.
Source record →primary paper · identifier verified
Samuel Mugel, Carlos Kuchkovsky, Escolástico Sánchez, Samuel Fernández-Lorenzo, Jorge Luis-Hita, Enrique Lizaso, Román Orús · 2020
arXiv:2007.00017
A reported application of tensor-network optimization to portfolio construction alongside quantum processors — the closest thing in this source set to the commercial framing, and narrower than that framing suggests.
Source record →primary paper · identifier verified
Feng Pan, Keyang Chen, Pan Zhang · 2021
arXiv:2111.03011
Classical tensor-network contraction applied to the Sycamore sampling task. The strongest evidence here that a specific claimed quantum advantage narrowed — for one benchmark task, not for an application.
Source record →