{
  "abstract": "We establish proper agnostic learning of matrix product states and tree tensor networks. Given copies of an arbitrary quantum state $ρ$, our algorithms return a state $|ψ\\rangle$ of chosen bond dimension such that $\\langleψ| ρ|ψ\\rangle$ is within $\\varepsilon$ of the optimum over the model class, without assuming that $ρ$ itself belongs to or is well approximated by that class. The main idea is to use improper learning to compress the mixed-state objective, reducing proper agnostic learning to optimization against a finite collection of explicitly specified pure states. We then introduce a comparator-dual compression procedure that reduces the bond dimension of these targets while uniformly preserving their overlaps with all bounded-bond comparators, with an error independent of system size. For matrix product states, this gives polynomial copy complexity in the system size, local dimension, bond dimension, and $1/\\varepsilon$, together with polynomial runtime in the system size for fixed local dimension, bond dimension, and accuracy. The same framework yields proper agnostic learning of tree tensor networks on bounded-degree trees, with both copy complexity and runtime polynomial in the system size when the remaining parameters are fixed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30148",
  "author_total": 2,
  "authors": [
    {
      "name": "Constantin Cedillo Vayson de Pradenne"
    },
    {
      "name": "Jordan Cotler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f9x11hd6xc4g1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30148",
  "fulltext_url": null,
  "id": "f9x11hd6xc4g1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30148",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7214380019",
  "pdf_url": "https://arxiv.org/pdf/2609.30148",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f9x11hd6xc4g1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.30148",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30148"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Proper Agnostic Learning of Matrix Product States and Tree Tensor Networks",
  "title_text": "Proper Agnostic Learning of Matrix Product States and Tree Tensor Networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/f9x11hd6xc4g1",
  "venue": "arXiv",
  "versions": []
}