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 $\varepsilon \propto N^{-1/2}$ 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 $b_{\max}=\pi/5$ ,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 $\alpha \le\!0$ 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.

arXiv:2609.25992 [quant-ph]

(or arXiv:2609.25992v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.25992 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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