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

TL;DR

This paper introduces a robust quantum-enhanced method for accurately estimating tail risk (CVaR) in complex structural mechanics problems with correlated uncertainties, outperforming classical Monte Carlo approaches in efficiency.

Contribution

It develops a stabilized iterative quantum amplitude estimation framework with confidence guarantees for CVaR evaluation under correlated random fields, extending prior quantum methods.

Findings

Achieves lower oracle complexity than classical Monte Carlo methods.

Provides finite-sample confidence guarantees and reduced estimator variance.

Demonstrates effectiveness on benchmark problems with correlated material properties.

Abstract

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.