{
  "abstract": "The SU$(N)$ matrix-model potential $V=-\\tfrac{g^2}{4}\\sum_{I,J}Tr[X_I,X_J]^2$, the interaction of the BFSS/BMN family, whose thermal large-$N$ states are dual to black holes, is diagonal in the coordinate basis and is compiled in the literature as a phase polynomial with $O(d^2N^4Q^4)$ rotations per Trotter step. That cost is close to optimal for its gate class: we show that for a generic Trotter step the Walsh support $m_{\\min}$ lower-bounds both the rotation count and the two-qubit count of every circuit over $\\{CNOT,CZ,CPhase,R_{ZZ},SWAP,X,R_z\\}$, ancillas included, and we build a parity network attaining $1.01$--$1.10\\,m_{\\min}$. Improvement therefore requires a gate outside that class, and the exact factorisation of $V$ into a sum of squared commutator entries supplies one in each era. For NISQ, Hadamard: each squared entry is added into a Fourier register and squared there, $Θ(d^2N^3Q^3)$ two-qubit gates. For fault tolerance, $T$: reversible arithmetic with one phase-gradient injection per squared entry, $Θ(d^2N^3Q^2)$ T gates and no arbitrary-angle rotation. Both are built and verified. With a native $R_{ZZ}$ the NISQ circuit uses fewer two-qubit gates than every parity network from $Q=6$ at SU(2) and $Q=2$ at SU(5); the oracle beats a precision-matched Hamming-weight-phasing incumbent at every point built except the smallest, by up to $11.9\\times$ in T count and, at equal width, $25.5\\times$ in surface-code spacetime. An ablation with the same arithmetic but no factorisation costs up to $21\\times$ more and loses to that incumbent at $15$ of $17$ points, so the factorisation, not the arithmetic, produces the win. Both constructions survive the supersymmetric deformation to mini-BMN with fermions, and complete Trotter evolutions on a statevector simulator reproduce the exact product formula to $2\\times10^{-12}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04731",
  "author_total": 2,
  "authors": [
    {
      "name": "Ayanendu Dutta"
    },
    {
      "name": "Nabanita Sarkar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bmh3kd4kszh2c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04731",
  "fulltext_url": null,
  "id": "bmh3kd4kszh2c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04731",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7220685471",
  "pdf_url": "https://arxiv.org/pdf/2610.04731",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bmh3kd4kszh2c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.04731",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04731"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Sum-of-squares compilation of matrix-model dynamics for NISQ and fault-tolerant hardware",
  "title_text": "Sum-of-squares compilation of matrix-model dynamics for NISQ and fault-tolerant hardware",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/bmh3kd4kszh2c",
  "venue": "arXiv",
  "versions": []
}