Conditional Value-at-Risk (CVaR) is a central tail-risk measure in stochastic structural mechanics, yet its accurate evaluation under high-dimensional, spatially correlated material uncertainty remains computationally prohibitive for classical Monte Carlo methods. Leveraging bounded-expectation reformulations of CVaR compatible with quantum amplitude estimation, we develop a quantum-enhanced inference framework that casts CVaR evaluation as a statistically consistent, confidence-constrained maximum-likelihood amplitude estimation problem. The proposed method extends iterative quantum amplitude estimation (IQAE) by embedding explicit maximum-likelihood inference within a rigorously controlled interval-tracking architecture. To ensure global correctness under finite-shot noise and the non-injective oscillatory response induced by Grover amplification, we introduce a stabilized inference scheme incorporating multi-hypothesis feasibility tracking, periodic low-depth disambiguation, and a bounded restart mechanism governed by an explicit failure-probability budget. This formulation preserves the quadratic oracle-complexity advantage of amplitude estimation while providing finite-sample confidence guarantees and reduced estimator variance. The framework is demonstrated on benchmark problems with spatially correlated lognormal Young's modulus fields generated using a Nystrom low-rank Gaussian kernel model. Numerical results show that the proposed estimator achieves substantially lower oracle complexity than classical Monte Carlo CVaR estimation at comparable confidence levels, while maintaining rigorous statistical reliability. This work establishes a practically robust and theoretically grounded quantum-enhanced methodology for tail-risk quantification in stochastic continuum mechanics.

翻译：条件风险价值（CVaR）是随机结构力学中的核心尾部风险度量，然而在高维空间相关材料不确定性下，其精确评估对于经典蒙特卡洛方法在计算上仍然难以实现。利用与量子振幅估计兼容的CVaR有界期望重构，我们开发了一种量子增强推理框架，将CVaR评估转化为一个统计一致、置信度约束的最大似然振幅估计问题。所提出的方法通过将显式最大似然推理嵌入严格控制的区间跟踪架构中，扩展了迭代量子振幅估计（IQAE）。为了在有限测量噪声和Grover放大引起的非单射振荡响应下确保全局正确性，我们引入了一种稳定推理方案，该方案融合了多假设可行性跟踪、周期性低深度歧义消除以及由显式失败概率预算控制的有界重启机制。此表述在保持振幅估计二次预言机复杂度优势的同时，提供了有限样本置信度保证并降低了估计量方差。该框架在采用Nyström低秩高斯核模型生成的空间相关对数正态杨氏模量场的基准问题上进行了验证。数值结果表明，在可比置信水平下，所提出的估计量相比经典蒙特卡洛CVaR估计实现了显著更低的预言机复杂度，同时保持了严格的统计可靠性。这项工作为随机连续介质力学中的尾部风险量化建立了一种实用稳健且理论坚实的量子增强方法论。