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

2026-02-10

AI Summary

This work proposes an efficient quantum amplitude estimation–based algorithm to address the high computational cost of traditional Monte Carlo methods in evaluating Conditional Value-at-Risk (CVaR) for structural systems under high-dimensional material uncertainties. By reformulating CVaR assessment as a maximum-likelihood amplitude estimation problem with confidence constraints, the approach embeds explicit maximum-likelihood inference within an interval-tracking framework and incorporates a stabilization mechanism—combining multi-hypothesis feasibility tracking, periodic low-depth disambiguation, and bounded restart strategies—to ensure global correctness and statistical reliability under finite sampling. Leveraging a Nystrom low-rank Gaussian kernel to model lognormal Young’s modulus fields and integrating Grover-amplified response processing, the method significantly reduces oracle complexity while achieving lower estimation variance and rigorous statistical guarantees at comparable confidence levels.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

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.

Problem

• Conditional Value-at-Risk
• spatially correlated uncertainty
• stochastic structural mechanics
• tail-risk quantification
• high-dimensional uncertainty

Innovation

• Quantum Amplitude Estimation
• Conditional Value-at-Risk (CVaR)
• Iterative Quantum Algorithm
• Stabilized Maximum-Likelihood Inference
• Spatially Correlated Random Fields