{
  "abstract": "Quantum amplitude estimation offers a theoretical quadratic speedup over classical Monte Carlo methods for financial derivative pricing. However, extending gate-based algorithms to path-dependent barrier options has historically been hampered by sequential path discretization, where tracking price paths across $d$ monitoring dates incurs a linear escalation in qubit footprint and gate depth ($\\mathcal{O}(d)$), posing severe coherence challenges for near-term quantum processors. In this work, we present a constant-depth quantum pricing framework that fundamentally eliminates the temporal dependency of barrier monitoring. Leveraging the Brownian reflection principle and Girsanov theorem, we project the continuous supremum dynamics onto a static bivariate joint distribution of the terminal price $S_T$ and running supremum $M_T$. This allows decoupling dynamic boundary checks into a static bivariate oracle comprising two parallel comparators and a dual-controlled rotation gate. We prove this architecture reduces circuit depth and comparator complexity from $\\mathcal{O}(d)$ to an invariant $\\mathcal{O}(1)$, while supporting discrete monitoring via zero-quantum-cost boundary corrections. Transpilation benchmarks for daily monitoring ($d = 252$) show our framework slashes physical CNOT count by 98.59% (from 2262 to 32) and compresses two-qubit depth by 98.02% (from 1514 to 30 layers). Under a realistic 127-qubit IBM Eagle noise model, the shallow circuit achieves a 7.84% relative valuation error with M3 readout mitigation. Finally, the framework seamlessly extends to nonlinear exotic payoffs lacking analytical solutions, establishing a noise-resilient pathway toward practical quantum advantage in computational finance.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27929",
  "author_total": 2,
  "authors": [
    {
      "name": "Ji-Hui Mo"
    },
    {
      "name": "Yuan-Hong Tao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5eyd3hcha3nee.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27929",
  "fulltext_url": null,
  "id": "5eyd3hcha3nee",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27929",
  "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": "W7223141874",
  "pdf_url": "https://arxiv.org/pdf/2610.27929",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5eyd3hcha3nee.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.27929",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27929"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Constant-Depth Quantum Barrier Option Pricing via a Static Bivariate Oracle Framework",
  "title_text": "Constant-Depth Quantum Barrier Option Pricing via a Static Bivariate Oracle Framework",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:04Z",
  "url": "https://research.draconitic.com/paper/5eyd3hcha3nee",
  "venue": "arXiv",
  "versions": []
}