{
  "abstract": "Random unitary operations are a fundamental resource for quantum information processing, yet provably generating them with experimentally available controls remains challenging. Existing approaches often require calculating higher-order operator expectation values, relying on statistical assumptions about the experimental Hamiltonian's spectrum to make these calculations tractable. We show how to implement random unitaries by a sequence of evolutions generated by a fixed Hamiltonian conjugated by a global control operator. We give a geometric argument that establishes exponential convergence to the uniform random (Haar) measure on the accessible unitary group under uniform parameter sampling, beyond a finite sequence-length threshold that we bound. We show this holds when the connected Lie subgroup generated by the conjugated Hamiltonians is closed. Native dynamics and global control thus provide a constructive route to uniform randomness, with applications to many experimental platforms including Rydberg atoms, bosons and fermions in optical lattices, transmons, and trapped ions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38738",
  "author_total": 3,
  "authors": [
    {
      "name": "Oscar Scholin"
    },
    {
      "name": "Apollonas S. Matsoukas-Roubeas"
    },
    {
      "name": "Sathyawageeswar Subramanian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6csce42stbfrk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38738",
  "fulltext_url": null,
  "id": "6csce42stbfrk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38738",
  "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": "W7215060814",
  "pdf_url": "https://arxiv.org/pdf/2609.38738",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6csce42stbfrk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.38738",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38738"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Generating random unitaries by products of conjugated Hamiltonian evolutions",
  "title_text": "Generating random unitaries by products of conjugated Hamiltonian evolutions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/6csce42stbfrk",
  "venue": "arXiv",
  "versions": []
}