{
  "abstract": "We determine the non-Clifford $T$-gate cost of constructing block encodings of structured fermionic and spin Hamiltonians in a unitary Clifford$+T$ model, when arbitrarily many clean ancillas and unrestricted block-encoding subnormalization are allowed, but without mid-circuit measurements or classical feed-forward. Our main technical tool is an ancilla-compression theorem: any block encoding of an $n$-qubit operator with $a$ clean ancillas and at most $s$ $T$ gates can be compressed to use at most $\\min\\{a,n+2s\\}$ ancillas, without increasing the absolute error or $T$-count. For general second-quantized Hamiltonians with bounded one- and two-body coefficients, at operator-norm block-encoding error $ε$, a volume-covering argument combined with circuit counting gives the worst-case lower bound $Ω(n^2\\sqrt{\\log(n^4/ε)})$, matching the existing upper bound at fixed precision. For the bond-dependent Kitaev honeycomb family on $n$ spins, we obtain independent lower bounds $Ω(n)$ from stabilizer nullity and $Ω(\\log(1/ε))$ from one-qubit state preparation, established using different Hamiltonian instances. Together with an explicit LCU construction, they give the tight worst-case scaling $Θ(n+\\log(1/ε))$. As an application, we evaluate the $T$-count of a Hamiltonian simulation circuit based on quantum singular value transformation, with each block-encoding query compiled separately. When phase synthesis and controlled queries add at most constant-factor overhead, the simulation $T$-count scales as the query count times the optimal $T$-count per query.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11153",
  "author_total": 3,
  "authors": [
    {
      "name": "Jiaxin Ma"
    },
    {
      "name": "Kevin J. Joven"
    },
    {
      "name": "Yuan Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8nr4bkjkndj9r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11153",
  "fulltext_url": null,
  "id": "8nr4bkjkndj9r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11153",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7212247362",
  "pdf_url": "https://arxiv.org/pdf/2609.11153",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8nr4bkjkndj9r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:26Z",
      "native_id": "2609.11153",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11153"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Optimal T-Count for Block Encodings of Fermionic and Spin Hamiltonians",
  "title_text": "Optimal T-Count for Block Encodings of Fermionic and Spin Hamiltonians",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:26Z",
  "url": "https://research.draconitic.com/paper/8nr4bkjkndj9r",
  "venue": "arXiv",
  "versions": []
}