{
  "abstract": "We study both the classical and the quantum complexity of the problem of estimating disorder-averaged quench dynamics for all-to-all spin Hamiltonians such as quantum Hopfield, Sherrington--Kirkpatrick (SK) or Dicke-type models. Disorder averaging restores permutation invariance in this setting, so states of $N$ spins can be stored in $\\mathcal O(\\log N)$ qubits. While logarithmic-space quantum computations are known to be simulatable classically in polynomial time or in polylogarithmic space, whether a single algorithm can achieve both is open, raising the possibility of simultaneous quantum advantage. To this end, we give a quantum algorithm for permutation-invariant $k$-local dynamics without disorder using polynomial time and $\\mathcal O(\\log N)$ quantum and classical space. We show that any classical algorithm matching these resources would imply $\\mathsf{BQL}\\subseteq \\mathsf{SC}$. For short times, however, we provide such algorithms, including for SK models. For Hopfield models, we discuss how dilating the disorder to ancilla qubits reduces the problem to the disorder-free case on an enlarged system, thus extending both classical and quantum results to them. We give some evidence that their long-time dynamics are non-trivial. They thus emerge as a candidate for a simultaneous time--space advantage in quantum simulation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40162",
  "author_total": 3,
  "authors": [
    {
      "name": "Maximilian Lutz"
    },
    {
      "name": "Rahul Trivedi"
    },
    {
      "name": "J. Ignacio Cirac"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aqmd8f28e21eb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40162",
  "fulltext_url": null,
  "id": "aqmd8f28e21eb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40162",
  "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": "W7215049481",
  "pdf_url": "https://arxiv.org/pdf/2609.40162",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aqmd8f28e21eb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.40162",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40162"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Classical and Quantum Simulation of All-to-All Quantum Dynamics in Logarithmic Space",
  "title_text": "Classical and Quantum Simulation of All-to-All Quantum Dynamics in Logarithmic Space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/aqmd8f28e21eb",
  "venue": "arXiv",
  "versions": []
}