{
  "abstract": "We investigate Nielsen's geometric approach to quantum complexity in the presence of multiple cost factors, extending the standard framework where a single penalty distinguishes easy from hard directions of the group manifold. By introducing a hierarchy of penalties associated with different degrees of non-locality, we develop a generalized right-invariant complexity geometry and analyze its implications for geodesic evolution. We derive the modified Euler-Arnold and Jacobi equations and study how multiple cost factors reshape the structure and scaling of conjugate points, where geodesic optimality breaks down. The formalism is illustrated in two settings: a single-qubit system with two cost factors, where we develop a semi-analytic approach to investigate complexity growth and its dependence on penalty hierarchies, and SYK-type models, where we analyze both free and chaotic regimes. In these many-body systems, we show that distinct non-local sectors generate multiple families of conjugate points whose occurrence depends on both the cost hierarchy and the system size. Our results highlight how refining the penalty structure provides a richer and more realistic description of quantum complexity and its dynamical behavior.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Physical Review D 114, 085018 (2026)",
  "arxiv": "2606.02817",
  "author_total": 2,
  "authors": [
    {
      "name": "Marcos Rios Ribeiro"
    },
    {
      "name": "Diego Trancanelli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d0sq3jt4pjdbn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.02817",
  "fulltext_url": null,
  "id": "d0sq3jt4pjdbn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.02817",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.02817",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d0sq3jt4pjdbn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2606.02817",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.02817"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Nielsen complexity with multiple cost factors",
  "title_text": "Nielsen complexity with multiple cost factors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:04Z",
  "url": "https://research.draconitic.com/paper/d0sq3jt4pjdbn",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/bf4j-b7sm",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}