{
  "abstract": "Pauli decomposition of an $n$-qubit operator is expensive if each of the $4^n$ Pauli strings is treated as an unstructured object. Labeling those strings by the configuration space $(\\mathbb{Z}_2)^n$ makes them displacement operators $X^{\\otimes x}Z^{\\otimes z}$ on the computational space: shifts by~$x$ and multiplications by characters $Z^{\\otimes z}$ in the computational basis. That labeling organizes the operator into $2^n$ fibers of length $2^n$, one per shift~$x$, each collecting the computational-basis amplitudes that hop by~$x$. Expanding each fiber function in the character basis of $(\\mathbb{Z}_2)^n$ --- a length-$2^n$ Walsh--Hadamard transform --- recovers the Pauli coefficients at total cost $O(n\\cdot4^n)$. The same fiber / shift--character picture extends to $(\\mathbb{Z}_p)^n$ (Heisenberg--Weyl qudits). \\texttt{paulikit} is a memory-bounded realization for qubits: for matrix-sparse inputs, peak memory need not densify to a full $2^n\\times2^n$ operator. Performance is checked on a stated low-end GNU/Linux platform for a coupled-oscillator sweep beyond a billion Pauli terms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08299",
  "author_total": 4,
  "authors": [
    {
      "name": "Mohammadreza Khellat"
    },
    {
      "name": "Mohammad Masoumi"
    },
    {
      "name": "Saman Nasoori"
    },
    {
      "name": "Soroush Nasoori"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/23h8420v1z7z8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08299",
  "fulltext_url": null,
  "id": "23h8420v1z7z8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08299",
  "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.MS"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7221021398",
  "pdf_url": "https://arxiv.org/pdf/2610.08299",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/23h8420v1z7z8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:18Z",
      "native_id": "2610.08299",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08299"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Pauli Decomposition by Character Theory: A Memory-Bounded Algorithm for Qubits and Qudits",
  "title_text": "Pauli Decomposition by Character Theory: A Memory-Bounded Algorithm for Qubits and Qudits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:18Z",
  "url": "https://research.draconitic.com/paper/23h8420v1z7z8",
  "venue": "arXiv",
  "versions": []
}