{
  "abstract": "Sampling from discrete Markov random fields (MRFs) is a hard problem. We study amplitude-encoded i.i.d. sampling for small MRFs where $2^n$ target probabilities are precomputed classically. This removes quantum exponential speedup but allows a clean comparison against classical MCMC based on independent circuit samples ($τ\\approx 1$). Across 60 instances spanning five graph families (1k-step burn-in, 3k retained samples), the mean ESS ratios of Quantum to Single-Site Gibbs, Block Gibbs, Tuned-Block, and Parallel Tempering are $16.35$, $7.29$, $1.82$, and $1.79$, showing modern classical samplers substantially close this gap. Amortizing $O(2^n)$ preprocessing into wall-clock time, exact inverse-CDF sampling yields $17.7$M ESS/s versus $488$K ESS/s for the quantum sampler ($36\\times$ mean rate, $153\\times$ per-instance), confirming no wall-clock advantage. We characterize MCMC autocorrelation costs and benchmark amplitude-encoded state preparation at $n \\in \\{8,10,12\\}$. An MPS scaling study ($n \\le 40$) shows bond dimension $χ=32$ achieves $F=0.721\\pm0.059$ at $n=40$. Finally, a matched-budget VQC vs. MPS comparison at $n \\in \\{8,10,12\\}$ shows VQC fidelities fall far below MPS: $(F_{\\mathrm{VQC}}, F_{\\mathrm{MPS}}) = (0.31, 0.99), (0.21, 0.96), (0.17, 0.88)$ at compressions $10.7\\times$, $34.1\\times$, and $113.8\\times$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.09893",
  "author_total": 2,
  "authors": [
    {
      "name": "Arul Rhik Mazumder"
    },
    {
      "name": "Elias Towe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f3wp3k4vsmtdk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.09893",
  "fulltext_url": null,
  "id": "f3wp3k4vsmtdk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.09893",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7168257623",
  "pdf_url": "https://arxiv.org/pdf/2607.09893",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f3wp3k4vsmtdk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2607.09893",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.09893"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "An End-to-End Hybrid Quantum-Classical Sampling Workflow for Discrete Markov Random Fields: A Reproducible Case Study",
  "title_text": "An End-to-End Hybrid Quantum-Classical Sampling Workflow for Discrete Markov Random Fields: A Reproducible Case Study",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:50Z",
  "url": "https://research.draconitic.com/paper/f3wp3k4vsmtdk",
  "venue": "arXiv",
  "versions": []
}