{
  "abstract": "Quantum oracles play a fundamental role in many quantum algorithms, such as Grover's search and quantum counting. In oracle synthesis, reducing the circuit depth under a limited number of ancilla qubits is essential, given the constraints of current quantum devices. However, for satisfiability oracles (SAT-oracles) under a limited ancilla budget, existing synthesis methods fail to fully exploit clause-level parallelism, leading to deep circuits. In practice, evaluating clauses in parallel can quickly exhaust the ancilla budget. To address this issue, we introduce the Clustered Synthesis Tree (CST), a depth-oriented SAT-oracle synthesis framework that exploits clause-level parallelism while respecting the ancilla budget. CST leverages a recursive synthesis tree as the backbone for scheduling clause evaluations and groups its clause leaves into clusters, whose clauses are evaluated in parallel by a reversible oracle called ClausePack. To form the clusters, CST introduces a polynomial-time heuristic called SeedGrow for the NP-hard clause-grouping problem, and the resulting tree is compiled into an executable circuit by CST-Map. Compared with the depth-oriented pAND baseline, CST can reduce the circuit depth by an average of 10.2x and 8.8x-11.0x on SATLIB and random 4-CNF benchmarks, respectively, under the same ancilla budgets, while also outperforming the width-oriented pAND, clause-storing, and qSAT baselines.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.11401",
  "author_total": 10,
  "authors": [
    {
      "name": "Zhihang Li"
    },
    {
      "name": "Wei Zi"
    },
    {
      "name": "Shuai Yang"
    },
    {
      "name": "Bei Zhou"
    },
    {
      "name": "Zongjiang Yi"
    },
    {
      "name": "Woji He"
    },
    {
      "name": "Yingjie Lin"
    },
    {
      "name": "Kaixiang Ji"
    },
    {
      "name": "Heru Du"
    },
    {
      "name": "Jinchen Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fd40aj3r5cs17.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.11401",
  "fulltext_url": null,
  "id": "fd40aj3r5cs17",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.11401",
  "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": "W7168250856",
  "pdf_url": "https://arxiv.org/pdf/2607.11401",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fd40aj3r5cs17.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2607.11401",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.11401"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "From Leaves to Clusters: Depth-Efficient SAT-Oracle Synthesis Based on the FORM Model",
  "title_text": "From Leaves to Clusters: Depth-Efficient SAT-Oracle Synthesis Based on the FORM Model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:50Z",
  "url": "https://research.draconitic.com/paper/fd40aj3r5cs17",
  "venue": "arXiv",
  "versions": []
}