{
  "abstract": "Recursive state estimation often executes approximate numerical solutions inside a feedback loop, where highly accurate local steps do not guarantee better overall results. For a fixed linear Kalman model, we characterize when a correction within a prescribed subspace and norm budget can meet a local admissibility tolerance, and how the defects actually executed affect the finite-horizon covariance response. Centering each defect on the exact gain for the implemented covariance separates current solve error from inherited gain drift. Expanding the exact residual-drift identity reveals opposing quartic contributions beyond the quadratic response: innovation-covariance inflation enters positively, while local-gain reoptimization enters subtractively. Under matched initialization, an absolute sixth-order remainder bound, uniform over bounded defect sequences at fixed horizon, gives sufficient conditions for quadratic under- or overprediction. Machine learning proposes bounded corrections, while a learner-independent residual certificate and verified fallback govern execution of classical and quantum candidates without changing the reference estimator. In a power-grid tolerance study, learned correction lowers the minimum conjugate-gradient iteration count for deployment without fallback relative to uncorrected solves under the same residual certificate. Gains reconstructed from a variational quantum linear solver and from an annealing-based binary encoding, with small-scale terminal measurements on superconducting hardware and sampling on a quantum annealer, are executed through the same interface. By linking local repairability to nonlinear error propagation, the framework evaluates approximate solvers and learned corrections through independent certification and finite-horizon response, providing a practical basis for studying hybrid quantum--classical computation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28425",
  "author_total": 11,
  "authors": [
    {
      "name": "Yanjun Ji"
    },
    {
      "name": "Dennis Willsch"
    },
    {
      "name": "Orkun Şensebat"
    },
    {
      "name": "Priyanka Arkalgud Ganeshamurthy"
    },
    {
      "name": "Zhi Pei"
    },
    {
      "name": "M. Sahnawaz Alam"
    },
    {
      "name": "Ivelina Stoyanova"
    },
    {
      "name": "Frank K. Wilhelm"
    },
    {
      "name": "Bo Zhao"
    },
    {
      "name": "Chao Wang"
    },
    {
      "name": "Kristel Michielsen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3e5h9hgcqf17c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28425",
  "fulltext_url": null,
  "id": "3e5h9hgcqf17c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28425",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Target Tracking and Data Fusion in Sensor Networks"
    ]
  ],
  "openalex": "W7214212061",
  "pdf_url": "https://arxiv.org/pdf/2609.28425",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3e5h9hgcqf17c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.28425",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28425"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Repairability of Inexact Solvers in Recursive State Estimation with Machine Learning",
  "title_text": "Repairability of Inexact Solvers in Recursive State Estimation with Machine Learning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:56Z",
  "url": "https://research.draconitic.com/paper/3e5h9hgcqf17c",
  "venue": "arXiv",
  "versions": []
}