{
  "abstract": "Quantum-walk algorithms can quadratically reduce the dependence of spatial search on the classical hitting time $\\mathrm{HT}$. Realising this speedup using standard quantum-walk algorithms, however, requires deep coherent circuits, limiting their applicability on near-term and early fault-tolerant quantum devices. We derive a parameterised family of hybrid quantum-classical spatial search algorithms that continuously interpolates between the classical and fully coherent quantum regimes, trading off circuit depth for total query complexity. For any $γ\\in[0,1]$, our algorithms use circuits of depth $\\widetilde{O}(\\mathrm{HT}^{γ/2})$ and find a marked vertex with constant success probability at total cost $\\widetilde{O}(\\mathrm{HT}^{1-γ}\\mathsf{S} + \\mathrm{HT}^{1-γ/2}(\\mathsf{U} + \\mathsf{C}))$, where $\\mathsf{S}$, $\\mathsf{U}$, and $\\mathsf{C}$ denote the setup, update, and checking costs, respectively. We also derive an optimal continuous depth-query trade-off for fixed-point amplitude amplification, providing a potential building block for other hybrid designs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19255",
  "author_total": 2,
  "authors": [
    {
      "name": "Diogo Ramos"
    },
    {
      "name": "Duarte Magano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6nzkfk01waan2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19255",
  "fulltext_url": null,
  "id": "6nzkfk01waan2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19255",
  "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": "W7221970859",
  "pdf_url": "https://arxiv.org/pdf/2610.19255",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6nzkfk01waan2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2610.19255",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19255"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum-classical algorithm interpolation for spatial search",
  "title_text": "Quantum-classical algorithm interpolation for spatial search",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:31Z",
  "url": "https://research.draconitic.com/paper/6nzkfk01waan2",
  "venue": "arXiv",
  "versions": []
}