{
  "abstract": "Quantum Amplitude Estimation promises to accelerate Monte Carlo integration by replacing the classical $\\varepsilon \\propto N^{-1/2}$ sampling law with the Heisenberg-limited $\\varepsilon \\propto N^{-1}$ scaling, but whether any part of that advantage survives on present-day hardware is an empirical question. We report a systematic experimental benchmark of a Maximum-Likelihood Amplitude Estimation QMC pipeline on IonQ trapped-ion processors, comprising 60 hardware trials on IonQ Forte-1 across five settings(5 & 9 qubits, 100-200 shots per depth, linear & exponential amplification schedules, ~113 device-hours), together with 100 trials on IonQ Aria-1 & Forte-1 noise models at 5, 9 & 19 qubits. The pipeline combines controlled-$R_y$ rotational state preparation, Grover-based amplitude amplification and maximum-likelihood inference and is benchmarked against $b_{\\max}^{-1}\\!\\int_0^{b_{\\max}}\\!\\sin^2\\!x\\,\\mathrm{d}x$ with $b_{\\max}=π/5$ ,given results emerge. First, the noiseless limit it attains $\\varepsilon \\propto N^{-0.88}$, close to the Heisenberg-scaling reference, reducing the error 54-74x over a 133x increase in oracle calls. Second, scaling does not survive on hardware. Every noisy backend saturates at an error floor of (2-5)x 10^{-2}, with fitted exponents of 0.04-0.15 on Forte-1 linear schedules and $α\\le\\!0$ on the vendor noise models: beyond the optimal shallow depth, however, deeper amplification provides no sustained accuracy gain and instead returns to the noise floor. Forte-1 hardware also outperformed IonQ's own Aria-1 noise model at every depth $m \\ge 2$, indicating that vendor noise models are bad predictors of MLAE accuracy. The practical implication for UQ is that on current devices the useful operating point is a shallow, schedule-tuned amplification depth chosen so that the deepest circuit lands near p~1/2 not the deepest schedule the coherence budget allows.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25992",
  "author_total": 4,
  "authors": [
    {
      "name": "Aditi Lal"
    },
    {
      "name": "Alex Khan"
    },
    {
      "name": "Rut Lineswala"
    },
    {
      "name": "Abhishek Chopra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bq2h38nxws4kh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25992",
  "fulltext_url": null,
  "id": "bq2h38nxws4kh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25992",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7214094770",
  "pdf_url": "https://arxiv.org/pdf/2609.25992",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bq2h38nxws4kh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:39Z",
      "native_id": "2609.25992",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25992"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Maximum-Likelihood Amplitude Estimation for Quantum Monte Carlo Integration on Trapped-Ion Hardware: Convergence, Noise-Floor Saturation, Depth-Dependent Bias",
  "title_text": "Maximum-Likelihood Amplitude Estimation for Quantum Monte Carlo Integration on Trapped-Ion Hardware: Convergence, Noise-Floor Saturation, Depth-Dependent Bias",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:39Z",
  "url": "https://research.draconitic.com/paper/bq2h38nxws4kh",
  "venue": "arXiv",
  "versions": []
}