  We propose a method for preparing the quantum state for a given velocity
field, e.g., in fluid dynamics, via the spherical Clebsch wave function (SCWF).
Using the pointwise normalization constraint for the SCWF, we develop a
variational ansatz comprising parameterized controlled rotation gates.
Employing the variational quantum algorithm, we iteratively optimize the
circuit parameters to transform the target velocity field into the SCWF and its
corresponding discrete quantum state, enabling subsequent quantum simulation of
fluid dynamics. Validations for one- and two-dimensional flow fields confirm
the accuracy and robustness of our method, emphasizing its effectiveness in
handling multiscale and multidimensional velocity fields. Our method is able to
capture critical flow features like sources, sinks, and saddle points.
Furthermore, it enables the generation of SCWFs for various vector fields,
which can then be applied in quantum simulations through SCWF evolution.
