arXiv:2602.09847stat.MLcs.LG2026-02被引 1

量子算法提升结构风险评估精度,显著降低计算成本。

Stabilized Maximum-Likelihood Iterative Quantum Amplitude Estimation for Structural CVaR under Correlated Random Fields

  • 将尾部风险评估转化为带置信约束的最大似然量子振幅估计。
  • 在相同置信水平下,量子方法比经典蒙特卡洛减少约90%的计算次数。
  • 适合高维相关材料不确定性下的工程结构风险分析。

条件风险价值(CVaR)是随机结构力学中的核心尾部风险度量,但在高维、空间相关材料不确定性下,经典蒙特卡洛方法的计算成本过高。本文利用与量子振幅估计兼容的有界期望重构形式,提出一种量子增强推断框架,将CVaR评估建模为统计一致、置信约束的最大似然振幅估计问题。所提方法扩展了迭代量子振幅估计(IQAE),在严格控制的区间追踪架构中嵌入最大似然推断。为应对有限采样噪声及格罗弗放大的非单射振荡响应,引入稳定化推断方案,包含多假设可行性跟踪、周期性低深度消歧和基于显式失败概率预算的有界重启机制。该框架保持了振幅估计的二次查询复杂度优势,同时提供有限样本置信保证并降低估计方差。在使用奈斯特罗姆低秩高斯核模型生成的空间相关对数正态弹性模量场的基准问题上验证,所提估计器在相同置信水平下,相比经典蒙特卡洛方法显著降低查询复杂度,且保持严格的统计可靠性。本工作建立了一种实际稳健且理论严谨的量子增强尾部风险量化方法,适用于随机连续介质力学。

原文摘要 · Abstract (English)

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.

量子计算风险评估结构力学振幅估计

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