{
  "abstract": "On the span of the first $N$ oscillator modes, Gauss--Hermite quadrature gives an exact change of basis between mode coefficients and $N$ weighted position space samples. We implement this transform with $O(N\\operatorname{polylog}(N,1/\\varepsilon))$ logical gates and polylogarithmic quantum width. The operator-error bound $\\varepsilon$ holds on arbitrary superpositions and includes all auxiliary registers. The construction uses signed averages on adaptive windows to convert uniform-grid samples into weighted Hermite-root samples. Their varying widths control the amplification cost, giving the near-linear bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20739",
  "author_total": 2,
  "authors": [
    {
      "name": "Nitay Mayo"
    },
    {
      "name": "Aryeh Lev Zabokritskiy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ac4fcs9qvdjg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20739",
  "fulltext_url": null,
  "id": "2ac4fcs9qvdjg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20739",
  "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",
      "cs.DC"
    ],
    [
      "arxiv",
      "cs.ET"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7213587301",
  "pdf_url": "https://arxiv.org/pdf/2609.20739",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ac4fcs9qvdjg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2609.20739",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20739"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Efficient Non-Uniform Quantum Hermite Transform through Adaptive Sampling",
  "title_text": "Efficient Non-Uniform Quantum Hermite Transform through Adaptive Sampling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/2ac4fcs9qvdjg",
  "venue": "arXiv",
  "versions": []
}