Quantum Algorithms for Solving Differential Equations with Application to Computational Fluid Dynamics

Quantum computing offers the potential to transform the way solutions to large-scale computational fluid dynamics (CFD) problems are obtained. This requires the development of efficient quantum algorithms for differential equations that are classically intractable. By bridging quantum mechanics with classical numerical methods and machine learning, this research advances the emerging interdisciplinary field of quantum scientific computing in fluid dynamics. This thesis develops a series of quantum algorithms, protocols and models that collectively form a quantum computational pipeline for CFD applications, from data loading and differential equation solving to circuit construction and feature extraction. The proposed methods incorporate data encoding, quantum iterative solvers, preconditioning, variational hybrid strategies, generative modelling, quantum data processing and physics-informed quantum machine learning. These methods are demonstrated on representative CFD use cases, capturing essential flow features while accounting for quantum resource constraints. The thesis concludes that combining hybrid quantum-classical solving strategies with physics-based modelling and data-driven techniques offers a promising path toward practical quantum algorithms for computational physics and engineering applications. By establishing core algorithmic components, this research provides a foundation for developing industrially relevant and competitive quantum CFD pipelines.<p></p>

Author dc:creator

• Chelsea Williams (21042788)

• Computational Fluid Dynamics
• Differential Equations
• Quantum Algorithms
• Computational Physics

Statement dc:rights

• All rights reserved

Identifier

10779/exe.32092057.v1

OAI identifier oai:identifier

oai:figshare.com:article/32092057