Maximum-Likelihood Amplitude Estimation for Quantum Monte Carlo Integration on Trapped-Ion Hardware: Convergence, Noise-Floor Saturation, Depth-Dependent Bias
Abstract
Quantum Amplitude Estimation promises to accelerate Monte Carlo integration by replacing the classical ε ∝ N−1/2 sampling law with the Heisenberg-limited ε ∝ 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-Ry rotational state preparation, Grover-based amplitude amplification and maximum-likelihood inference and is benchmarked against bmax−1 ∫0bmax sin2 x dx with bmax=π/5 ,given results emerge. First, the noiseless limit it attains ε ∝ 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≤ 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 ≥ 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.
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BibTeX
@misc{lal2026maximumlikelihood,
title = {{Maximum-Likelihood Amplitude Estimation for Quantum Monte Carlo Integration on Trapped-Ion Hardware: Convergence, Noise-Floor Saturation, Depth-Dependent Bias}},
author = {Aditi Lal and Alex Khan and Rut Lineswala and Abhishek Chopra},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25992},
eprint = {2609.25992},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25992},
}
RIS
TY - UNPB
TI - Maximum-Likelihood Amplitude Estimation for Quantum Monte Carlo Integration on Trapped-Ion Hardware: Convergence, Noise-Floor Saturation, Depth-Dependent Bias
AU - Aditi Lal
AU - Alex Khan
AU - Rut Lineswala
AU - Abhishek Chopra
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25992
UR - https://arxiv.org/abs/2609.25992
AB - Quantum Amplitude Estimation promises to accelerate Monte Carlo integration by replacing the classical ε ∝ N^−1/2 sampling law with the Heisenberg-limited ε ∝ 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 ∫_0^b_max sin^2 x dx with b_max=π/5 ,given results emerge. First, the noiseless limit it attains ε ∝ 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≤ 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 ≥ 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.
ER -