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

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.

💡 Research Summary

This paper introduces a robust quantum‑enhanced framework for estimating the Conditional Value‑at‑Risk (CVaR) of structural responses subject to spatially correlated material uncertainties. Classical Monte‑Carlo (MC) methods become infeasible for high‑confidence CVaR because they require an enormous number of expensive finite‑element simulations. The authors first model the Young’s modulus field as a log‑normal random field and compress its high‑dimensional correlation structure using a Nyström low‑rank approximation of an anisotropic Gaussian kernel. This yields a small set of latent Gaussian variables (r ≪ N) that can be sampled efficiently while preserving the essential spatial correlation.

The CVaR definition is then reformulated as a bounded expectation: after computing the discrete Value‑at‑Risk threshold ηα, the tail contribution is expressed through a normalized hinge function g_i = max(Q_i − ηα, 0)/(Q_max − ηα) that lies in