稳定的最大似然迭代量子振幅估计用于相关随机场下的结构CVaR
Stabilized Maximum-Likelihood Iterative Quantum Amplitude Estimation for Structural CVaR under Correlated Random Fields
AI总结：
本文提出一种稳定最大似然迭代量子振幅估计方法，用于在相关随机场下计算结构CVaR，通过量子计算提升效率并保证统计可靠性。
摘要：
条件价值在风险（CVaR）是随机结构力学中的核心尾风险度量，然而在高维、空间相关材料不确定性下准确评估仍然对经典蒙特卡洛方法来说计算上是不可行的。利用与量子振幅估计兼容的CVaR有界期望重述，我们开发了一个量子增强的推断框架，将CVaR评估作为统计上一致、置信度约束的最大似然振幅估计问题。所提出的方法通过在严格控制的区间跟踪架构中嵌入显式的最大似然推断来扩展迭代量子振幅估计（IQAE）。为确保在有限样本噪声和由Grover放大引起的非单射振荡响应下的全局正确性，我们引入了一种稳定推断方案，结合多假设可行性跟踪、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置机制。该方法在保持振幅估计的二次Oracle复杂度优势的同时，提供了有限样本置信度保证和降低的估计器方差。该框架在具有空间相关对数正态杨氏模量场的基准问题上得到验证，这些场使用Nystrom低秩高斯核模型生成。数值结果表明，所提出的估计器在可比的置信度水平下比经典蒙特卡洛CVaR估计显著降低了Oracle复杂度，同时保持了严谨的统计可靠性。本工作建立了一种在随机连续力学中量化尾风险的实用稳健且理论基础扎实的量子增强方法。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
