{
  "abstract": "Quantum signal processing (QSP) realizes operator functions through polynomial transformations of a finite degree. In addition to function approximation errors, realistic implementations incur algorithmic errors also when encoding the input operator and in synthesizing gates into a discrete fault-tolerant gate set. We provide an end-to-end analysis of these errors and show that the input error propagation is governed by the operator-Lipschitz constant $L_\\star$ of the implemented function. We then derive an efficient classical algorithm to compute tight lower and upper bounds on $L_\\star$, and we show that these bounds induce in turn lower and upper bounds on the total quantum-resource cost (for instance, $T$-gate count) needed for QSP implementations compatible with a target total error. We further devise a procedure to search for a polynomial with minimum cost based solely on its coefficients, yielding a resource-aware polynomial-design procedure for QSP. We illustrate the resulting method for ground state energy estimation via eigenvalue thresholding for the H$_6$ molecular Hamiltonian. In the tested hardware profiles, the resource-aware family improves the total-error budget and reduces the modeled $T$-gate count by $51.9\\%$--$56.7\\%$ relative to the standard analytical polynomial obtained from an error-function approximation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03885",
  "author_total": 6,
  "authors": [
    {
      "name": "Thiago O. Maciel"
    },
    {
      "name": "Giancarlo Camilo"
    },
    {
      "name": "Allan Tosta"
    },
    {
      "name": "Daniel Stilck-França"
    },
    {
      "name": "Leandro Aolita"
    },
    {
      "name": "Thais de Lima Silva"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/50zvmqz11khnw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03885",
  "fulltext_url": null,
  "id": "50zvmqz11khnw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03885",
  "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": "W7220685382",
  "pdf_url": "https://arxiv.org/pdf/2610.03885",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/50zvmqz11khnw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.03885",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03885"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Robustness of Quantum Signal Processing and Resource-aware Polynomial Design",
  "title_text": "Robustness of Quantum Signal Processing and Resource-aware Polynomial Design",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/50zvmqz11khnw",
  "venue": "arXiv",
  "versions": []
}