{
  "abstract": "Implicit discretizations of transient heat conduction repeatedly generate sparse linear systems, making diffusion problems a natural test bed for quantum linear solvers. This study evaluates how accurately a variational quantum linear solver (VQLS) recovers the temperature field produced by one backward-Euler step of one-dimensional conduction on IBM quantum hardware. A pre-specified confirmatory experiment compares N=4 interior temperatures encoded on two qubits with N=8 temperatures encoded on three qubits using ten paired hardware blocks; a separately defined N=16, four-qubit extension is evaluated in five independently scheduled exploratory blocks. Local VQLS optimization reduces relative temperature-field error to approximately 10^{-8} for all three cases, establishing an essentially exact ideal reference at this scale. On hardware, mean relative L2 temperature-field error is 8.07% for N=4 and 20.14% for N=8, a paired increase of 12.06 percentage points (95% CI, 10.71-13.42; exact paired sign-flip p=0.001953). The exploratory N=16 mean is 24.75+/-1.84%. A pre-specified N=16 shot-count follow-up then evaluates the same locked circuit at 2,048, 8,192, and 32,768 shots in six independently scheduled blocks. Mean field error remains 23.64%, 24.57%, and 24.37%, respectively; the 32,768-minus-2,048-shot contrast is +0.74 percentage points (95% CI, -0.65 to 2.12; p=0.281). In contrast, ideal multinomial sampling predicts a reduction from 2.68% to 0.75%. Higher shot counts reduce block-to-block variability but do not recover the mean cold-side temperature field. The results show that full-field readout of a strongly nonuniform thermal state is limited by more than ordinary finite-shot sampling under the tested hardware conditions, motivating observable-focused quantum formulations for heat flux, stored energy, and selected temperatures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24004",
  "author_total": 2,
  "authors": [
    {
      "name": "Yijin Mao"
    },
    {
      "name": "Yuwen Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2x4pc7hrr0r36.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24004",
  "fulltext_url": null,
  "id": "2x4pc7hrr0r36",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24004",
  "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",
      "physics.comp-ph"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7223068497",
  "pdf_url": "https://arxiv.org/pdf/2610.24004",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2x4pc7hrr0r36.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.24004",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24004"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Transient Heat Conduction on Quantum Hardware: Replicated Temperature-Field Reconstruction and Shot-Count Sensitivity with a Variational Quantum Linear Solver",
  "title_text": "Transient Heat Conduction on Quantum Hardware: Replicated Temperature-Field Reconstruction and Shot-Count Sensitivity with a Variational Quantum Linear Solver",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:41Z",
  "url": "https://research.draconitic.com/paper/2x4pc7hrr0r36",
  "venue": "arXiv",
  "versions": []
}