Bayesian Sequential Quantum Amplitude Estimation for Rare-Event Structural Failure Probability

2026-07-21

AI Summary

This work addresses the inefficiency of estimating rare failure events in structural reliability analysis by proposing a novel method that integrates quantum amplitude estimation with Bayesian sequential inference. The failure probability is encoded as a quantum amplitude, and amplitude amplification is achieved via Grover iterations employing a lookup-table-based oracle. Leveraging measurement outcomes from varying iteration depths, the method performs sequential Bayesian updating to infer the posterior distribution of the amplitude angle. To the best of our knowledge, this is the first approach to incorporate Bayesian sequential inference into iterative quantum amplitude estimation. Under a fixed oracle query budget, the proposed method significantly outperforms classical Monte Carlo simulation in efficiency, achieves point estimation accuracy comparable to maximum-likelihood-based iterative quantum amplitude estimation, and further provides full uncertainty quantification, credible intervals, and convergence diagnostics—thereby enhancing the statistical interpretability of the results.

Abstract

Structural reliability analysis often requires estimating small failure probabilities under uncertainty, a task for which direct Monte Carlo simulation becomes inefficient because failure observations are scarce. Quantum amplitude estimation offers a potential quadratic improvement in query complexity for bounded expectation estimation, but practical iterative formulations require reliable inference from finite, amplified measurement data. This paper develops a Bayesian sequential formulation of iterative quantum amplitude estimation for rare-event structural failure probability estimation. Structural failure is represented as a binary indicator over a finite stochastic ensemble and encoded through a lookup-table oracle, allowing the failure probability to be treated as a quantum amplitude. Measurement outcomes collected at different Grover depths are assimilated through Bayesian updating over the amplitude angle, yielding posterior estimates, credible intervals, and uncertainty-aware convergence diagnostics. The framework is evaluated on stochastic finite-element benchmark problems, including a one-dimensional bar and an L-bracket with stress concentration. The results show that amplitude amplification converts rare failure events into measurable success probabilities, enabling substantially lower estimation errors than direct Monte Carlo simulation under the same idealized oracle-query budget. The Bayesian formulation achieves point-estimation accuracy comparable to maximum-likelihood IQAE while additionally providing posterior uncertainty quantification, credible intervals, and transparent convergence assessment. The study demonstrates Bayesian IQAE as a statistically interpretable proof-of-concept for quantum-assisted rare-event reliability analysis, while relying on idealized oracle access.

Problem

• rare-event
• structural failure probability
• quantum amplitude estimation
• Bayesian inference
• reliability analysis

Innovation

• Bayesian sequential inference
• quantum amplitude estimation
• rare-event probability
• structural reliability
• Grover amplification