{
  "abstract": "We construct a restricted Boltzmann machine (RBM) whose visible input is a quantum state rather than a classical configuration. Each hidden unit carries a trainable quantum template prepared by a parametrized circuit and converts its overlap with the input into a feature. Treating quantum states as high-dimensional continuous visible objects creates nontrivial normalization and scaling problems. We regularize the continuous likelihood and derive two controlled high-dimensional limits, yielding a Hopfield-type network with continuous Hilbert-space patterns and a data-augmented Gram likelihood. The resulting algorithms are compact and use trainable circuit-prepared templates as measurement intermediaries between quantum data and classical optimization. Numerical simulations across several many-body systems demonstrate effective quantum-phase recognition and multicomponent feature extraction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19619",
  "author_total": 4,
  "authors": [
    {
      "name": "Zhe-Hao Zhang"
    },
    {
      "name": "Yi-Cong Yu"
    },
    {
      "name": "Xiaoming Cai"
    },
    {
      "name": "Hai-Qing Lin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9xmp258gy7704.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19619",
  "fulltext_url": null,
  "id": "9xmp258gy7704",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19619",
  "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": "W7213610365",
  "pdf_url": "https://arxiv.org/pdf/2609.19619",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9xmp258gy7704.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.19619",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19619"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A Restricted Boltzmann Machine with Quantum-State Visible Units",
  "title_text": "A Restricted Boltzmann Machine with Quantum-State Visible Units",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:19Z",
  "url": "https://research.draconitic.com/paper/9xmp258gy7704",
  "venue": "arXiv",
  "versions": []
}