Quantum computation encodes and operates on data in a radically different way than classical logic. This difference allows researchers in nearly all applied sciences to explore how quantum-accelerated computing could enhance the efficiency of their most computationally demanding tasks.
This thesis studies the introduction of quantum-accellerated computing in structural mechanics, a field that traditionally leverages computational techniques at both industrial and research scales. The scope is limited to practical and mostly near-term quantum computing. Therefore, the algorithms analyzed or proposed are evaluated for their runtime as end-to-end routines and for their ability to run on near-term quantum devices.
Given the vastness of the application domain, the research was developed in three separate threads. The first is a review of quantum algorithms applicable to partial differential equations (PDEs) in structural mechanics. The second is an application of a variational quantum algorithm for linear systems of equations to the discrete Poisson equation, while the last studies how quantum machine learning, specifically quantum kernel methods, discriminates damage-inducing loading states in a composite plate with a cutout.
Each of the three parts reveals the potentials and limitations of practical quantum-accelerated computing.
The PDE review questions the end-to-end advantage of fault-tolerant quantum algorithms and highlights the need to specialize near-term alternatives to problems in mechanics.
The work on the variational quantum linear solver emphasizes the matrix decomposition bottleneck and proposes a method to factorize the discrete Poisson equation matrix.
Finally, the work on kernel methods for damage identification shows how heuristically selected and trained quantum kernels reach scores comparable to classical best-practice kernels, but also hints at the fact that potential quantum advantage requires more systematic kernel optimization and retaining performance when scaling quantum systems beyond classical simulation.

This paper explores the potential application of quantum and hybrid quantum–classical neural networks in power flow analysis. Experiments are conducted using two datasets based on 4-bus and 33-bus test systems. A systematic performance comparison is also conducted among quantum, hybrid quantum–classical, and classical neural networks. The comparison is based on (i) generalization ability, (ii) robustness, (iii) training dataset size needed, (iv) training error, and (v) training process stability. The results show that the developed hybrid quantum–classical neural network outperforms both quantum and classical neural networks, and hence can improve deep learning-based power flow analysis in the noisy-intermediate-scale quantum (NISQ) and fault-tolerant quantum (FTQ) era.

The wide adoption of composite structures in the aerospace industry requires reliable numerical methods to account for the effects of various damage mechanisms, including delamination. Cohesive elements are a versatile and physically representative way of modelling delamination. However, using their standard form which conforms to solid substrate elements, multiple elements are required in the narrow cohesive zone, thereby requiring an excessively fine mesh and hindering the applicability in practical scenarios. The present work focuses on the implementation and testing of triangular thin plate substrate elements and compatible cohesive elements, which satisfy C¹-continuity in the domain. The improved regularity meets the continuity requirement coming from the Kirchhoff Plate Theory and the triangular shape allows for conformity to complex geometries. The overall model is validated for mode I delamination, the case with the smallest cohesive zone. Very accurate predictions of the limit load and crack propagation phase are achieved, using elements as large as 11 times the cohesive zone.

Structural mechanics is commonly modeled by (systems of) partial differential equations (PDEs). Except for very simple cases where analytical solutions exist, the use of numerical methods is required to find approximate solutions. However, for many problems of practical interest, the computational cost of classical numerical solvers running on classical, that is, silicon-based computer hardware, becomes prohibitive. Quantum computing, though still in its infancy, holds the promise of enabling a new generation of algorithms that can execute the most cost-demanding parts of PDE solvers up to exponentially faster than classical methods, at least theoretically. Also, increasing research and availability of quantum computing hardware spurs the hope of scientists and engineers to start using quantum computers for solving PDE problems much faster than classically possible. This work reviews the contributions that deal with the application of quantum algorithms to solve PDEs in structural mechanics. The aim is not only to discuss the theoretical possibility and extent of advantage for a given PDE, boundary conditions and input/output to the solver, but also to examine the hardware requirements of the methods proposed in literature.