{
  "abstract": "Unused encoding states offer opportunities to simplify quantum circuits. For algorithms restricted to reachable subspaces, unspecified diagonal-operator entries can be optimized without changing ideal computation. We investigate exact diagonal completion for the quantum approximate optimization algorithm (QAOA) applied to placement, using permutation-preserving register swaps. We construct exact Manhattan-distance operators through weighted-$\\ell_1$ optimization of Walsh coefficients and a sparse recurrence requiring $O(\\sqrt{m})$ terms on balanced rectangles, avoiding $O(m^4)$ dense constraint storage. Across 160 geometries, weighted-$\\ell_1$ completion reduces controlled-NOT (CX) counts relative to four alternative extensions in all 96 cases with unused binary codes under Gray-code synthesis. On an independently specified 60-case cohort, median reductions relative to virtual-coordinate extension are 28.0\\%, 53.9\\%, and 21.6\\% at six, nine, and twelve sites. Under generic diagonal synthesis, reductions decrease to 10.9\\%, 1.3\\%, and 0.7\\%, demonstrating compiler dependence. Additional ancillas reduce mixer serialization, but token circuits remain deeper than one-hot baselines. Ideal placement simulations show baseline-dependent solution quality, with classical search performing better. OpenROAD integration takes 72 QAOA and 216 classical placements across six RTL designs through clock-tree synthesis and global routing with zero overflow. Completion improves phase construction; no end-to-end advantage is established.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38734",
  "author_total": 3,
  "authors": [
    {
      "name": "Owen Friedewald"
    },
    {
      "name": "Ali Shiri Sichani"
    },
    {
      "name": "Chi-Ren Shyu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2xhds7tgf2mtc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38734",
  "fulltext_url": null,
  "id": "2xhds7tgf2mtc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38734",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.AR"
    ],
    [
      "arxiv",
      "cs.ET"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7215062105",
  "pdf_url": "https://arxiv.org/pdf/2609.38734",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2xhds7tgf2mtc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.38734",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38734"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Exact Diagonal Completion on Reachable Subspaces: Application to QAOA Placement",
  "title_text": "Exact Diagonal Completion on Reachable Subspaces: Application to QAOA Placement",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/2xhds7tgf2mtc",
  "venue": "arXiv",
  "versions": []
}