{
  "abstract": "Scalable parameterized quantum circuits for machine learning face three obstacles: barren plateaus, no guarantee the learned function class is classically hard, and prohibitive circuit evaluations per gradient step. We propose the unitary brick-wall: a $k$-particle fermionic architecture for nearest-neighbor hardware, combining Reconfigurable Beam Splitters with interleaved single-qubit phases and a non-Gaussian magic-state encoding, where $k$ trades classical hardness against training cost. Trainable. The brick-wall has dynamical Lie algebra $\\mathfrak{u}(n)$ and is surjective onto $U(n)$ via Givens rotations, enabling Haar initialization. Two-body correlator readouts achieve gradient variance $Θ(k^3/n^5)$, polynomial in $n$ throughout $n-2k=Ω(n)$. Expressive. Hardness is controlled by $k$: best-known classical sampling runs in time $2^{Θ(k)}$, worst-case #P-hardness holds from $k=n^ε$, and the average-case machinery of Fermion Sampling applies at $k=Θ(n)$. The sampler is input-dependent, so costs are paid per query: at our operating point $k=100$ one query needs $\\sim 10^{15}$ operations, beyond commercial query rates, and at $k=120$ an exascale machine sustains under one query per second. Efficient. A multi-layer parallel parameter-shift rule computes all $O(n^2)$ gradients from $4kn$ circuit evaluations per step, a factor $n/k$ reduction over the standard rule's $4n^2$, growing linearly with $n$ at fixed $k$. The unitary butterfly targets all-to-all hardware, with $2\\log n$ layers of parallel gates and $(3/2)n\\log n$ parameters, similar hardness guarantees, and $4k\\log n$ evaluations per step -- the same factor-$n/k$ reduction. Its trainability holds at two levels: absence of exponential barren plateaus is unconditional, while the sharp $Θ(k^3/n^5)$ rate needs a conjectured scalar comparison with the two-particle Haar second moment.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.24014",
  "author_total": 1,
  "authors": [
    {
      "name": "Iordanis Kerenidis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ct433ef298exk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.24014",
  "fulltext_url": null,
  "id": "ct433ef298exk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.24014",
  "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": "W7171560984",
  "pdf_url": "https://arxiv.org/pdf/2607.24014",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ct433ef298exk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2607.24014",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.24014"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Scalable Quantum Machine Learning: Trainability, Expressivity and Efficiency",
  "title_text": "Scalable Quantum Machine Learning: Trainability, Expressivity and Efficiency",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:50Z",
  "url": "https://research.draconitic.com/paper/ct433ef298exk",
  "venue": "arXiv",
  "versions": []
}