Maximum-Likelihood Amplitude Estimation for Quantum Monte Carlo Integration on Trapped-Ion Hardware: Convergence, Noise-Floor Saturation, Depth-Dependent Bias

arXiv:2609.25992 · quant-ph · Submitted 2026-09-22 · Read on arXiv

quant-ph

Submitted: 2026-09-22

Updated: 2026-09-22

Comments: 7 pages 3 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Accuracy — 9× in this paper · explained in 1 episode
• Benchmark — 5× in this paper · explained in 2 episodes
• Maximum-Likelihood Amplitude Estimation — 5× in this paper
• Quantum Amplitude Estimation — 3× in this paper
• Uncertainty Quantification — 3× in this paper · explained in 8 episodes
• All-to-All Connectivity — 1× in this paper · explained in 1 episode
• Approximate Counting — 1× in this paper · explained in 1 episode
• Benchmarking — 1× in this paper · explained in 3 episodes
• Calibration — 1× in this paper · explained in 7 episodes
• Fisher Information — 1× in this paper · explained in 3 episodes
• Heisenberg Scaling — 1× in this paper · explained in 4 episodes
• Systematic Bias — 1× in this paper · explained in 3 episodes

Sources

• Quantum Amplitude Amplification and Estimation
• Quantum speedup of Monte Carlo methods
• Amplitude estimation without phase estimation
• Iterative Quantum Amplitude Estimation
• Quantum Approximate Counting, Simplified
• Amplitude estimation via maximum likelihood on noisy quantum computer
• The Problem with Grover-Rudolph State Preparation for Quantum Monte-Carlo
• Creating superpositions that correspond to efficiently integrable probability distributions
• Quantum Risk Analysis
• Option Pricing using Quantum Computers
• Quantum computational finance: Monte Carlo pricing of financial derivatives
• Benchmarking an 11-qubit quantum computer

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• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians