A Quantum Annealing Approach to Fluid Dynamics Problems Solving Navier-Stokes Equations

Partial differential equations (PDEs) present important computational challenges in several scientific disciplines. Classical numerical methods, while effective, often encounter scalability issues and high computational costs, particularly for complex problems. Quantum computing seems to address these challenges, offering a potential exponential speedup over classical methods. The presented work studies the application of quantum computing, specifically Quantum Annealing, to the computational complexities inherent in solving the Navier-Stokes equations within Computational Fluid Dynamics (CFD). Our study examines the quantum annealing methodology, conducting two different experiments and analyzing the error between the simulation and the analytical solution. The results obtained demonstrate that quantum annealing paradigm can solve this problems and the errors obtained are acceptable in comparison with other methods in the state of the art. By combining theoretical insights with practical implementation, this research clarifies the potential of quantum annealing, providing a comprehensive overview of the simulation framework, analyzing the obtained results, and suggesting future research avenues.