{
  "abstract": "We present, to our knowledge, the first adaptation of Pauli Correlation Encoding (PCE) to quantum topological data analysis, reformulating Betti number estimation as a depth-efficient variational optimization over a compressed qubit register. From a Takens embedding and Vietoris-Rips filtration of S&P 500 returns, we extract combinatorial Laplacians and recast null-space counting as a continuous-PCE Rayleigh-quotient minimization with variational deflation, encoding $n_k$ simplex indices into $O(n_k^{1/κ})$ qubits with shallow, ancilla-free circuits. Because the resulting loss is rational rather than bilinear in the correlators, the barren-plateau bound of Sciorilli et al. does not transfer; empirically the gradient variance decays only polynomially, with no exponential barren plateau, over $n=4$-$12$ qubits. The classical stage matches ripser on all 190 sliding windows (2003-2010). On the real market Laplacians ($β_1=1$-$22$), PCE-VQE recovers no null vector from a random start, but warm-starting from a classical null-space surrogate recovers $β_1$ exactly on all seven windows tested ($n_k \\le 259$), placing the obstacle in the optimization landscape rather than the encoding. Chronologically split classification gives in-regime ROC AUC 0.818, but out-of-distribution evaluation on the 2020 COVID shock and 2022 rate cycle (AUC 0.009, 0.515) shows the calibration does not generalize across crisis regimes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.09906",
  "author_total": 2,
  "authors": [
    {
      "name": "Arul Rhik Mazumder"
    },
    {
      "name": "Shreyan Ronit Mazumder"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7dty718gm5tgw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.09906",
  "fulltext_url": null,
  "id": "7dty718gm5tgw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.09906",
  "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.LG"
    ],
    [
      "arxiv",
      "q-fin.ST"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7168259862",
  "pdf_url": "https://arxiv.org/pdf/2607.09906",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7dty718gm5tgw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:22Z",
      "native_id": "2607.09906",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.09906"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Depth-Efficient Quantum Topological Data Analysis for Regime-Specific Detection of Financial Stress",
  "title_text": "Depth-Efficient Quantum Topological Data Analysis for Regime-Specific Detection of Financial Stress",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:44Z",
  "url": "https://research.draconitic.com/paper/7dty718gm5tgw",
  "venue": "arXiv",
  "versions": []
}