{
  "abstract": "Provable guarantees for preparing quantum Gibbs states, such as rapid mixing or gapped coherent preparation paths, are known only for restricted Hamiltonian families and usually must be re-derived for each new family. Building on homomorphic polynomial transduction, a generalization of decoded quantum interferometry (DQI) and Hamiltonian DQI (HDQI), we show how relative decoding transfers such a guarantee from a source Hamiltonian $H_A$ to a target $H_B$. Writing each Hamiltonian as a sum of $m$ Pauli terms, the subsets of terms whose product is proportional to the identity, its relations, form a binary linear code, $K_A$ for the source and $K_B$ for the target, with the Pauli-label matrix as parity-check matrix as in DQI. Starting from the canonical thermofield double (TFD) of $H_A$, a Bell transform, a reversible label map, and a coherent decoder for the quotient code $K_B/K_A$ prepare an approximate TFD of $H_B$, and hence its Gibbs state. Because this decoder only resolves target relations absent from the source, the reachable inverse temperature is set by the relative distance $d_{\\rm rel}$, the fewest terms in any such relation. It can far exceed the ordinary distance $d_{\\rm ord}$, the fewest terms in any target relation, which bounds the uniform exact decoding radius of DQI and HDQI. We show that linear $d_{\\rm rel}$ with efficient decoding at linear radius certifies a constant inverse temperature. As an example, starting from a nearest-neighbor spin chain whose TFD is known to be preparable at every finite temperature, a sparse classical parity-check matrix yields bounded-degree, geometrically nonlocal, noncommuting targets with $d_{\\rm ord}=3$ and $d_{\\rm rel}=Θ(m)$. To our knowledge, this gives a new class of efficiently preparable TFDs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06667",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhong-Xia Shang"
    },
    {
      "name": "Yufei Wang"
    },
    {
      "name": "Daniel Stilck França"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1971w7k311xjy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06667",
  "fulltext_url": null,
  "id": "1971w7k311xjy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06667",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7220649511",
  "pdf_url": "https://arxiv.org/pdf/2610.06667",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1971w7k311xjy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2610.06667",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06667"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Gibbs State Preparation via Relative Decoding: From Fast-Mixing Sources to Broader Target Classes",
  "title_text": "Quantum Gibbs State Preparation via Relative Decoding: From Fast-Mixing Sources to Broader Target Classes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:22Z",
  "url": "https://research.draconitic.com/paper/1971w7k311xjy",
  "venue": "arXiv",
  "versions": []
}