{
  "abstract": "We consider spin-coupled Grover walks on hypercubes within the framework of quantum Bernoulli noises (QBN). We identify parity-dependent harmonic subspaces generated by the central Hamming layers: in even dimension they give a fixed-point subspace, whereas in odd dimension the walk reduces on the harmonic subspace to an explicit eight-dimensional reduced dynamics. Using symmetric-group representation theory, we characterize the corresponding isotypic structure and determine the reduced spectrum. The harmonic reduction also yields explicit long-time probability behavior and shows that the resulting states may occupy an asymptotically vanishing fraction of the hypercube while still spanning its full Hamming diameter.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14467",
  "author_total": 1,
  "authors": [
    {
      "name": "Ce Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6fft2by48m5nx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14467",
  "fulltext_url": null,
  "id": "6fft2by48m5nx",
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  "landing_url": "https://arxiv.org/abs/2610.14467",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
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      "arxiv",
      "math.CO"
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      "math.RT"
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      "arxiv",
      "quant-ph"
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    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
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  "openalex": "W7221762463",
  "pdf_url": "https://arxiv.org/pdf/2610.14467",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6fft2by48m5nx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2610.14467",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14467"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Harmonic Reduction of Spin-Coupled Grover Walks on Hypercubes via Quantum Bernoulli Noises",
  "title_text": "Harmonic Reduction of Spin-Coupled Grover Walks on Hypercubes via Quantum Bernoulli Noises",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/6fft2by48m5nx",
  "venue": "arXiv",
  "versions": []
}