{
  "abstract": "Hamiltonian engineering (HE) simulates quantum dynamics under a target Hamiltonian using a native entangling system Hamiltonian and restricted control, with applications from quantum gate design to analog quantum simulation. Observing that, for many systems, formulating HE as a linear program only requires specific commutation relations between the control pulses and the system Hamiltonian, we provide a unified framework for broad classes of $2$-local qubit, qudit, and fermionic systems. We reformulate time-optimal HE as a complex $k$-cut polytope problem, with $k$ the number of distinct phases in these commutation relations, and prove it NP-complete for every finite $k$. We therefore relax the polytope to the elliptope and apply a Krivine-type rounding, yielding pulses informed by the system and target Hamiltonians, which we then use in a linear program. We derive how many informed pulses are necessary and sufficient for the linear program to be reliably feasible. Additionally mixing in uniformly sampled pulses guarantees a solution close to the relaxation value from $\\mathrm{O}(m)$ pulses, with $m$ the number of interaction terms. Together with upper and lower bounds on the optimal quantum run time, this yields an $\\mathrm{O}(\\sqrt{m})$ approximation ratio. In benchmarks on a fully connected Ising model, a chiral clock model for qudits, and the fermionic Harper-Hofstadter model, our approach attains near-optimal quantum run times wherever the optimum is computable, reaches run times that saturate with the lattice size in the fermionic case, and outperforms state-of-the-art methods with $\\mathrm{O}(m)$ pulses. This establishes a unified approach with provable guarantees to the automatic programming of analog quantum simulators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36006",
  "author_total": 4,
  "authors": [
    {
      "name": "Thomas Joachim Friese"
    },
    {
      "name": "Özgün Kum"
    },
    {
      "name": "Aram W. Harrow"
    },
    {
      "name": "Martin Kliesch"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dwa8xt4c60ghv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36006",
  "fulltext_url": null,
  "id": "dwa8xt4c60ghv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36006",
  "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",
      "cond-mat.quant-gas"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.36006",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dwa8xt4c60ghv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.36006",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36006"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.quant-gas",
      "subfield": "amo"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.quant-gas",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Fast Hamiltonian engineering from cut polytope geometry",
  "title_text": "Fast Hamiltonian engineering from cut polytope geometry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/dwa8xt4c60ghv",
  "venue": "arXiv",
  "versions": []
}