**5. Conclusions**

This chapter presented two different quantum algorithms with possible applications in computational fluid dynamics. Beyond their very different areas of application, the key differences are the computational model with regard the quantum coprocessor model of quantum computing. The hybrid quantum/classical algorithm for the vortex-in-cell method involves repeated exchanges of information between classical and quantum hardware, i.e., at each time step in the time integration. In contrast, the quantum algorithm implementing a discrete-velocity method for kinetic flow modeling can be performed on the quantum processor for the duration of the simulation, with classical information exchange only required at the start and end of the simulation.

This work addressed a number of key challenges that remain to be investigated further. Firstly, the need for further efficient quantum algorithms as well as a further understanding of how to apply the quantum coprocessor model for this type of flow simulations was investigated. Secondly, the measurement-based extraction of

classical information fundamentally changes the way quantum algorithms for CFD application will most likely be used. Finally, obtaining detailed information on the full flow field will be a challenge, so applications for which only certain characteristics of the solution are desired would present a good choice for future applications.
