{
  "abstract": "We propose a hybrid quantum state preparation method based on the Walsh--Hadamard transform within the dense-to-sparse quantum state preparation framework. The method approximately prepares structured classical data in a quantum circuit through an indirect approach. Instead of directly preparing the dense amplitude-encoded state, the method first transforms the classical data into the Walsh domain and prepares only the largest-magnitude coefficients using a sparse state-preparation algorithm. The original state can then be approximately recovered through a parallel layer of Hadamard gates. Since this reconstruction requires no CNOT gates and has circuit depth 1, the proposed method introduces no additional CNOT or circuit-depth overhead, and its quantum preparation cost is determined by the underlying sparse state-preparation algorithm. Numerical results on representative benchmark signals demonstrate that the proposed method enables accurate state preparation for signals admitting sparse or approximately sparse representations in the Walsh domain.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28760",
  "author_total": 1,
  "authors": [
    {
      "name": "Emad Rezaei Fard Boosari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b0r2wg67q14gf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28760",
  "fulltext_url": null,
  "id": "b0r2wg67q14gf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28760",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7214337371",
  "pdf_url": "https://arxiv.org/pdf/2609.28760",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b0r2wg67q14gf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.28760",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28760"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Walsh-Transform Realization of Dense-to-Sparse Quantum State Preparation",
  "title_text": "Walsh-Transform Realization of Dense-to-Sparse Quantum State Preparation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/b0r2wg67q14gf",
  "venue": "arXiv",
  "versions": []
}