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Structural Safety

An efficient quantum computing based structural reliability analysis method using quantum amplitude estimation

Jingran He

Published Dec 7, 2024• 7 citations
Publisher
DOI
10.1016/j.strusafe.2024.102555

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Abstract Structural reliability analysis is essential for ensuring the safety of engineering structures, particularly complex systems like space trusses used in various industries. These 3D truss structures face uncertain loading conditions and deterioration, making reliability crucial. Traditional methods, such as Monte Carlo simulation, can be computationally intensive, especially for large systems. Quantum computing may offer a promising solution that utilizes qubits to process large amounts of information and simulate probabilistic models more efficiently. In this study, we explore the use of quantum circuits to represent the reliability problem, employing quantum algorithms like quantum Monte Carlo to estimate failure probabilities. The results indicate that quantum computing can perform structural reliability analysis, possibly reducing computational time and resources compared to classical methods. This approach shows potential to solve larger, more complex systems, providing scalable solutions for reliability analysis of engineering structures. Integrating quantum computing with structural reliability analysis could lead to more efficient, cost-effective designs of complex structures.
We propose an approach for quantum amplitude estimation (QAE) designed to enhance computational efficiency while minimizing the reliance on quantum resources. Our method leverages quantum computers to generate a sequence of signals, from which the quantum amplitude is inferred through classical post-processing techniques. Unlike traditional methods that use quantum phase estimation (QPE), which requires numerous controlled unitary operations and the quantum Fourier transform, our method avoids these complex and resource-demanding steps. By integrating quantum computing with classical post-processing techniques, our method significantly reduces the need for quantum gates and qubits, thus optimizing the utilization of quantum hardware. We present numerical simulations to validate the effectiveness of our method and provide a comprehensive analysis of its computational complexity and error. This hybrid strategy not only improves the practicality of QAE but also broadens its applicability in quantum computing.
To enable an in-depth study of power system operation and planning, the assessment of standard reliability indices is inevitable. The Monte Carlo Simulation (MCS) approach is a broadly used method in replacing the analytical methods in reliability indices assessment. The accuracy of MCS, however, highly depends on the sampling size, and hence, a complicated system with large number of components requires a large sampling size and daunting computational effort. To address this shortcoming, this paper attempts to take advantage of potentials of the quantum computing (QC) for power system reliability assessment by realizing the following contributions: 1) an innovative quantum model designed for reliability assessment; 2) a quantum circuit that achieves the quadratic speed up compared to the classical MCS method; 3) an efficient quantum amplitude estimation (QAE) algorithm to accurately evaluate the reliability indices. The accuracy and efficacy of the quantum reliability method are extensively verified and demonstrated on both radial and mesh distribution systems.