  Finding the distribution of the velocities and pressures of a fluid by
solving the Navier-Stokes equations is a principal task in the chemical,
energy, and pharmaceutical industries, as well as in mechanical engineering and
the design of pipeline systems. With existing solvers, such as OpenFOAM and
Ansys, simulations of fluid dynamics in intricate geometries are
computationally expensive and require re-simulation whenever the geometric
parameters or the initial and boundary conditions are altered. Physics-informed
neural networks are a promising tool for simulating fluid flows in complex
geometries, as they can adapt to changes in the geometry and mesh definitions,
allowing for generalization across fluid parameters and transfer learning
across different shapes. We present a hybrid quantum physics-informed neural
network that simulates laminar fluid flows in 3D Y-shaped mixers. Our approach
combines the expressive power of a quantum model with the flexibility of a
physics-informed neural network, resulting in a 21% higher accuracy compared to
a purely classical neural network. Our findings highlight the potential of
machine learning approaches, and in particular hybrid quantum physics-informed
neural network, for complex shape optimization tasks in computational fluid
dynamics. By improving the accuracy of fluid simulations in complex geometries,
our research using hybrid quantum models contributes to the development of more
efficient and reliable fluid dynamics solvers.
