{
  "abstract": "We present an efficient quantum algorithm for the non-uniform Chebyshev transform. It is defined as the projection of a function onto Chebyshev polynomials sampled at given nodes that are uniform in $x\\in[-1,1]$, and hence non-uniform in the angle $θ=\\arccos x$, a setting that QFT-based quantum Chebyshev transforms cannot handle. Our construction is based on an improvement of an existing Non-uniform Quantum Fourier Transform (NUQFT) whereby we remove the conditioning from non-uniform node sampling. Hence, error bounds are independent of the geometry-dependent parameter $κ$ of prior work. We use the fact that Chebyshev transform matrix is the average of two Type-II non-uniform DFTs, which we implement with a single controlled NUQFT circuit. We provide explicit oracle constructions, including the row-access oracle previously left as an assumption. The resulting $\\varepsilon$-accurate block encoding has $O(1)$ normalization and uses $O(L)$ qubits and $\\widetilde O(L^2)$ gates, where $L=\\log N+\\log(1/\\varepsilon)$. We give an end-to-end implementation with complexity analysis, including the success probability and output-state error.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40277",
  "author_total": 2,
  "authors": [
    {
      "name": "Chaowen Guan"
    },
    {
      "name": "Akshit Katiyar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/870w7mhswpef9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40277",
  "fulltext_url": null,
  "id": "870w7mhswpef9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40277",
  "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.DS"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7215095377",
  "pdf_url": "https://arxiv.org/pdf/2609.40277",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/870w7mhswpef9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2609.40277",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40277"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Conditioning-Free Non-Uniform Quantum Fourier and Chebyshev Transforms",
  "title_text": "Conditioning-Free Non-Uniform Quantum Fourier and Chebyshev Transforms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:22Z",
  "url": "https://research.draconitic.com/paper/870w7mhswpef9",
  "venue": "arXiv",
  "versions": []
}