AI 中文总结
针对结构可靠性分析中估计小失效概率难的问题，提出贝叶斯序贯量子幅度估计方法，将结构失效编码为量子幅度，通过贝叶斯更新处理测量数据，实验表明该方法比直接蒙特卡罗模拟误差低，能实现精度与不确定性量化。
AI 中文摘要
结构可靠性分析常需在不确定性下估计小失效概率，直接蒙特卡罗模拟因失效观测稀缺而效率低下。量子幅度估计有望在有界期望估计的查询复杂度上实现二次提升，但实际迭代公式需从有限放大测量数据进行可靠推断。本文为罕见事件结构失效概率估计开发了迭代量子幅度估计的贝叶斯序贯公式。将结构失效表示为有限随机集合上的二元指标并通过查找表预言机编码，把失效概率当作量子幅度。通过对幅度角的贝叶斯更新同化不同格罗弗深度收集的测量结果，得出后验估计、可信区间和不确定性感知收敛诊断。在随机有限元基准问题上评估该框架，结果表明幅度放大将罕见失效事件转化为可测量的成功概率，在相同理想化预言机查询预算下比直接蒙特卡罗模拟估计误差低得多。贝叶斯公式实现了与最大似然IQAE相当的点估计精度，还提供后验不确定性量化、可信区间和透明收敛评估。该研究证明贝叶斯IQAE是量子辅助罕见事件可靠性分析的具有统计可解释性的概念验证，尽管依赖理想化预言机访问。
英文摘要
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.
