{
  "abstract": "For every odd prime power $q$ and $D=q+1$, we construct an infinite family of Ramanujan quantum expanders of degree $D$. The construction transfers Morgenstern's Ramanujan Cayley graphs on $\\operatorname{PSL}_2(\\mathbb{F}_{p})$ for $p$ which is an even power of $q$, through the odd irreducible subrepresentation of the Weil representation of $\\operatorname{SL}_2(\\mathbb{F}_{p})$. For a quantum expander of dimension $N$, our implementation uses $O(\\log^2 N)$ elementary gates, and $O(\\log N)$ ancilla qudits, using a fixed finite gate set depending on $q$. An advantage compared to the previous work of Iyer, Jain, Jordan, and Somma (FOCS 2026) is that assuming the quantum circuit is implemented exactly, we satisfy the $2\\sqrt{D-1}/D$ singular value bound exactly without any additive error.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38075",
  "author_total": 1,
  "authors": [
    {
      "name": "Siddhartha Jain"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/agmpbs3abr1e9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38075",
  "fulltext_url": null,
  "id": "agmpbs3abr1e9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38075",
  "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.CC"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7214988857",
  "pdf_url": "https://arxiv.org/pdf/2609.38075",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/agmpbs3abr1e9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.38075",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38075"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Ramanujan quantum expanders from the Weil representation",
  "title_text": "Ramanujan quantum expanders from the Weil representation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/agmpbs3abr1e9",
  "venue": "arXiv",
  "versions": []
}