{
  "abstract": "Quantum read only memory (QROM) is a substantial source of non-Clifford cost in fault-tolerant quantum algorithms. Borrowing dirty qubits can reduce this cost, provided their unknown initial states are restored. We consider the practically relevant qubit-constrained regime, where limited workspace restricts the table-block size and table loading dominates the cost. For $N$ entries of $b$ bits and approximately $bλ$ dirty qubits, SelectSwap has leading Toffoli count $2N/λ$. Recent work using sequential bit packets reduces this to $(1+1/b)N/λ$. In this work we introduce a dense encoding construction of QROM, where two bits of classical information are stored in each dirty qubit instead of one by utilizing both the $Z$ and $X$ bases. On its own, dense encoding provides a $2\\times$ improvement over SelectSwap by reducing the leading Toffoli count to $N/λ$. Combining it with sequential bit packets gives $\\tfrac12(1+1/b)N/λ$, a further halving of the sequential construction's leading cost, and an approximately $4\\times$ improvement over SelectSwap in the large-$N$ limit for practical values of $b$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02321",
  "author_total": 1,
  "authors": [
    {
      "name": "Danial Motlagh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/azrx377f3fhxt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02321",
  "fulltext_url": null,
  "id": "azrx377f3fhxt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02321",
  "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": "W7220399796",
  "pdf_url": "https://arxiv.org/pdf/2610.02321",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/azrx377f3fhxt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.02321",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02321"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Halving the cost of QROM again via dense encoding",
  "title_text": "Halving the cost of QROM again via dense encoding",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:45Z",
  "url": "https://research.draconitic.com/paper/azrx377f3fhxt",
  "venue": "arXiv",
  "versions": []
}