{
  "abstract": "Diagrammatic languages such as ZX-calculus provide compact and intuitive descriptions of quantum processes and have become established tools for circuit simplification, verification, and compilation. However, their potential as a framework for constructing many-body states and the Hamiltonians that host them remains largely unexplored. Here, we introduce families of fractal many-body states obtained from ZX-diagrams based on the Sierpiński triangle and Sierpiński carpet. By construction, the underlying graph connectivity imposes atypical subvolume-law minimum-cut upper bounds on entanglement: at most logarithmic scaling for the triangle family and sublinear power-law for the carpet family. By adjusting the free parameters of the ZX-diagram construction, we can tune the actual entanglement scaling: we demonstrate both area-law and logarithmic scaling for the triangle, and both log law and power-law for the carpet. Additionally, their local observables retain fractal-like spatial structure, identifying these states as natural candidates for atypical eigenstates in otherwise thermalizing systems. For the triangle family, we combine parent-Hamiltonian methods, insights from ZX-calculus, and local ZX identities that certify exact annihilation of the target state, producing frustration-free Hamiltonians whose terms admit simple representations in the same diagrammatic language as the states themselves. We then construct a local deformation that produces chaotic level statistics while embedding the fractal ZX state in the bulk of the energy spectrum as an exact quantum many-body scar. Our results demonstrate, through this explicit construction, that ZX-calculus can serve as a framework for Hamiltonian inverse design, in which quantum many-body scars, their local annihilators, and the chaotic Hamiltonians embedding them can be constructed and related through a set of graphical identities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.22495",
  "author_total": 1,
  "authors": [
    {
      "name": "Marcin Szyniszewski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ccjd35x6fk0j4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.22495",
  "fulltext_url": null,
  "id": "ccjd35x6fk0j4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.22495",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7171430143",
  "pdf_url": "https://arxiv.org/pdf/2607.22495",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ccjd35x6fk0j4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2607.22495",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.22495"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Quantum many-body scars with tunable entanglement and Hamiltonian inverse design from ZX-calculus",
  "title_text": "Quantum many-body scars with tunable entanglement and Hamiltonian inverse design from ZX-calculus",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/ccjd35x6fk0j4",
  "venue": "arXiv",
  "versions": []
}