{"@context":"https://schema.org","@type":"DataCatalog","name":"Tensor Network Optimization Atlas — source trail","url":"https://research.mahastrategies.com/atlas/tensor-networks/sources.json","isPartOf":"https://research.mahastrategies.com/atlas/tensor-networks#atlas","version":"0.1.0","dateModified":"2026-07-29","license":"CC BY 4.0","verificationNote":"Every identifier was resolved against the arXiv API or Crossref on its verifiedOn date, and the title, authors, and year here are what that record returned. This is identifier verification: it establishes that the identifier denotes the named paper, not that the full text was re-read.","sources":[{"@type":"ScholarlyArticle","@id":"https://research.mahastrategies.com/atlas/tensor-networks/sources/white-1992#source","id":"white-1992","title":"Density matrix formulation for quantum renormalization groups","authors":"Steven R. White","year":1992,"identifier":"DOI:10.1103/PhysRevLett.69.2863","url":"https://doi.org/10.1103/PhysRevLett.69.2863","sourceType":"primary-paper","verification":"identifier-verified","verifiedOn":"2026-07-29","whyHere":"Primary source for DMRG, the variational method later understood as optimization over matrix product states.","canonicalUrl":"https://research.mahastrategies.com/atlas/tensor-networks/sources/white-1992"},{"@type":"ScholarlyArticle","@id":"https://research.mahastrategies.com/atlas/tensor-networks/sources/vidal-2003#source","id":"vidal-2003","title":"Efficient classical simulation of slightly entangled quantum computations","authors":"Guifré Vidal","year":2003,"identifier":"arXiv:quant-ph/0301063","url":"https://arxiv.org/abs/quant-ph/0301063","sourceType":"primary-paper","verification":"identifier-verified","verifiedOn":"2026-07-29","whyHere":"Ties classical simulation cost to the entanglement carried across a cut, which is the quantity a bond dimension budgets.","canonicalUrl":"https://research.mahastrategies.com/atlas/tensor-networks/sources/vidal-2003"},{"@type":"ScholarlyArticle","@id":"https://research.mahastrategies.com/atlas/tensor-networks/sources/verstraete-cirac-2004#source","id":"verstraete-cirac-2004","title":"Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions","authors":"F. 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Cirac","year":2004,"identifier":"arXiv:cond-mat/0407066","url":"https://arxiv.org/abs/cond-mat/0407066","sourceType":"primary-paper","verification":"identifier-verified","verifiedOn":"2026-07-29","whyHere":"Primary source for the projected entangled pair state (PEPS) generalization of MPS beyond one dimension.","canonicalUrl":"https://research.mahastrategies.com/atlas/tensor-networks/sources/verstraete-cirac-2004"},{"@type":"ScholarlyArticle","@id":"https://research.mahastrategies.com/atlas/tensor-networks/sources/vidal-2005#source","id":"vidal-2005","title":"Entanglement renormalization","authors":"Guifré Vidal","year":2005,"identifier":"arXiv:cond-mat/0512165","url":"https://arxiv.org/abs/cond-mat/0512165","sourceType":"primary-paper","verification":"identifier-verified","verifiedOn":"2026-07-29","whyHere":"Introduces entanglement renormalization and the disentangler that distinguishes MERA from a plain tree network.","canonicalUrl":"https://research.mahastrategies.com/atlas/tensor-networks/sources/vidal-2005"},{"@type":"ScholarlyArticle","@id":"https://research.mahastrategies.com/atlas/tensor-networks/sources/vidal-2006#source","id":"vidal-2006","title":"A class of quantum many-body states that can be efficiently simulated","authors":"G. Vidal","year":2006,"identifier":"arXiv:quant-ph/0610099","url":"https://arxiv.org/abs/quant-ph/0610099","sourceType":"primary-paper","verification":"identifier-verified","verifiedOn":"2026-07-29","whyHere":"Primary source for the MERA ansatz and its efficient contraction, including the scale-invariant construction.","canonicalUrl":"https://research.mahastrategies.com/atlas/tensor-networks/sources/vidal-2006"},{"@type":"ScholarlyArticle","@id":"https://research.mahastrategies.com/atlas/tensor-networks/sources/schuch-2006#source","id":"schuch-2006","title":"The computational complexity of PEPS","authors":"Norbert Schuch, Michael M. Wolf, Frank Verstraete, J. Ignacio Cirac","year":2006,"identifier":"arXiv:quant-ph/0611050","url":"https://arxiv.org/abs/quant-ph/0611050","sourceType":"primary-paper","verification":"identifier-verified","verifiedOn":"2026-07-29","whyHere":"Establishes hardness results for contracting PEPS — the reason higher-dimensional tensor networks are approximated, not contracted exactly.","canonicalUrl":"https://research.mahastrategies.com/atlas/tensor-networks/sources/schuch-2006"},{"@type":"ScholarlyArticle","@id":"https://research.mahastrategies.com/atlas/tensor-networks/sources/markov-shi-2005#source","id":"markov-shi-2005","title":"Simulating quantum computation by contracting tensor networks","authors":"Igor L. Markov, Yaoyun Shi","year":2005,"identifier":"arXiv:quant-ph/0511069","url":"https://arxiv.org/abs/quant-ph/0511069","sourceType":"primary-paper","verification":"identifier-verified","verifiedOn":"2026-07-29","whyHere":"Connects the cost of contracting a tensor network to the treewidth of its graph, which is the structural quantity behind contraction-order search.","canonicalUrl":"https://research.mahastrategies.com/atlas/tensor-networks/sources/markov-shi-2005"},{"@type":"ScholarlyArticle","@id":"https://research.mahastrategies.com/atlas/tensor-networks/sources/hastings-2007#source","id":"hastings-2007","title":"An Area Law for One Dimensional Quantum Systems","authors":"M. B. Hastings","year":2007,"identifier":"arXiv:0705.2024","url":"https://arxiv.org/abs/0705.2024","sourceType":"primary-paper","verification":"identifier-verified","verifiedOn":"2026-07-29","whyHere":"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.","canonicalUrl":"https://research.mahastrategies.com/atlas/tensor-networks/sources/hastings-2007"},{"@type":"ScholarlyArticle","@id":"https://research.mahastrategies.com/atlas/tensor-networks/sources/verstraete-2008#source","id":"verstraete-2008","title":"Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems","authors":"F. Verstraete, J. I. Cirac, V. Murg","year":2008,"identifier":"arXiv:0907.2796","url":"https://arxiv.org/abs/0907.2796","sourceType":"review-article","verification":"identifier-verified","verifiedOn":"2026-07-29","whyHere":"Review tying MPS, PEPS, and variational renormalization group methods into one framework.","canonicalUrl":"https://research.mahastrategies.com/atlas/tensor-networks/sources/verstraete-2008"},{"@type":"ScholarlyArticle","@id":"https://research.mahastrategies.com/atlas/tensor-networks/sources/swingle-2009#source","id":"swingle-2009","title":"Entanglement Renormalization and Holography","authors":"Brian Swingle","year":2009,"identifier":"arXiv:0905.1317","url":"https://arxiv.org/abs/0905.1317","sourceType":"primary-paper","verification":"identifier-verified","verifiedOn":"2026-07-29","whyHere":"The paper that proposed reading the MERA network as a discretized holographic geometry. 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Carroll, Aidan Chatwin-Davies, Nicholas Hunter-Jones, Jason Pollack, Grant N. Remmen","year":2015,"identifier":"arXiv:1504.06632","url":"https://arxiv.org/abs/1504.06632","sourceType":"primary-paper","verification":"identifier-verified","verifiedOn":"2026-07-29","whyHere":"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.","canonicalUrl":"https://research.mahastrategies.com/atlas/tensor-networks/sources/bao-2015"},{"@type":"ScholarlyArticle","@id":"https://research.mahastrategies.com/atlas/tensor-networks/sources/mugel-2020#source","id":"mugel-2020","title":"Dynamic Portfolio Optimization with Real Datasets Using Quantum Processors and Quantum-Inspired Tensor Networks","authors":"Samuel Mugel, Carlos Kuchkovsky, Escolástico Sánchez, Samuel Fernández-Lorenzo, Jorge Luis-Hita, Enrique Lizaso, Román Orús","year":2020,"identifier":"arXiv:2007.00017","url":"https://arxiv.org/abs/2007.00017","sourceType":"primary-paper","verification":"identifier-verified","verifiedOn":"2026-07-29","whyHere":"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.","canonicalUrl":"https://research.mahastrategies.com/atlas/tensor-networks/sources/mugel-2020"},{"@type":"ScholarlyArticle","@id":"https://research.mahastrategies.com/atlas/tensor-networks/sources/pan-2021#source","id":"pan-2021","title":"Solving the sampling problem of the Sycamore quantum circuits","authors":"Feng Pan, Keyang Chen, Pan Zhang","year":2021,"identifier":"arXiv:2111.03011","url":"https://arxiv.org/abs/2111.03011","sourceType":"primary-paper","verification":"identifier-verified","verifiedOn":"2026-07-29","whyHere":"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.","canonicalUrl":"https://research.mahastrategies.com/atlas/tensor-networks/sources/pan-2021"}]}