- Applications of quantum computing follow the **quantum coprocessor model**, where selected parts of the computational task for which efficient quantum algorithms exist are executed on the quantum hardware. ### Approximate Quantum Fourier Transform For example, in computational fluid dynamics algorithm, this hybrid quantum/classical approach is discussed, and in particular it is shown how the **approximate quantum Fourier transform (AQFT) **can be used in the **Poisson solvers** of the considered method for the incompressible-flow Navier-Stokes equations. The analysis shows that despite the inevitable errors introduced by applying AQFT, **the method produces meaningful results** for three-dimensional example problems. - **vortex-in-cell method** was used to solve the incompressible-flow Navier-Stokes equations in a regular domain - In this algorithm, the Poisson solvers dominating CPU time requirements are based on the quantum computing equivalent of the fast Fourier transform, i.e., the quantum Fourier transform. - Specifically, the effect of applying an approximate QFT instead of the full QFT is analyzed for different levels of approximation or truncating of rotation gates in the quantum circuit implementation. ### Quantum Algorithms for Flow Simulations - quantum discrete-velocity algorithm for kinetic flow modeling - method based on kinetic modeling of the flow was developed to r**educe the information transfer between quantum and classical hardware in the quantum coprocessor model.** - It is shown that this quantum algorithm can be executed fully on quantum hardware during a simulation.