{
  "abstract": "We construct Clifford+$T$ circuits implementing arbitrary $n$-qubit unitaries with worst-case $T$-count $\\widetilde{O}(N^{8/7})$ at constant operator-norm error, where $N=2^n$, improving the previous exponent $5/4$. The construction uses $\\widetilde{O}(N^{6/7})$ clean ancillas. The main idea is to reduce the data addressed by each query to the block-encoding circuit for a sparse piece while controlling the additional simulation work needed to combine the pieces. We simulate a Hermitian logarithm of the target by flattening its traceless part with a two-layer random similarity transformation, randomly partitioning the transformed generator into block-sparse Hermitian pieces, and combining their evolutions using qDRIFT. For a target operator-norm error $ε\\in(0,1/2)$, let $L=\\log_2(N/ε)$, the qubit count plus the requested bits of accuracy. By successively correcting the approximation error, we obtain a circuit using $\\widetilde{O}(N^{8/7}L^{3/7}+NL)$ $T$ gates and $\\widetilde{O}(N)$ clean ancillas whenever $L\\le N$. We also prove that, at constant precision, the exponent $8/7$ is optimal within a sequential block-SELECT model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18589",
  "author_total": 6,
  "authors": [
    {
      "name": "Diyi Liu"
    },
    {
      "name": "Shuchen Zhu"
    },
    {
      "name": "Wibe Albert de Jong"
    },
    {
      "name": "Di Fang"
    },
    {
      "name": "David Williams-Young"
    },
    {
      "name": "Chao Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fyvybmapma4d9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18589",
  "fulltext_url": null,
  "id": "fyvybmapma4d9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18589",
  "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",
      "cs.CC"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7221786425",
  "pdf_url": "https://arxiv.org/pdf/2610.18589",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fyvybmapma4d9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2610.18589",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18589"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "$T$-efficient unitary synthesis via block-sparse Hamiltonian simulation",
  "title_text": "T-efficient unitary synthesis via block-sparse Hamiltonian simulation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:11Z",
  "url": "https://research.draconitic.com/paper/fyvybmapma4d9",
  "venue": "arXiv",
  "versions": []
}