ABSTRACT Encoding velocity fields as quantum states poses a significant challenge in the development of quantum algorithms for fluid dynamics. Conventional methods, often based on direct normalization of discrete velocity data, do not intrinsically capture the structure and dynamics of vortex flows, potentially introducing artifacts that affect accuracy in modeling flow evolution. We propose a method for encoding velocity fields as quantum states of a spinor field using the spherical Clebsch representation. By applying a pointwise normalization constraint, we develop an ansatz with parameterized controlled rotation gates, optimized through a variational quantum algorithm. This approach encodes target velocity fields into spinor‐based quantum states, offering a pathway to more efficient quantum simulations of fluid dynamics. Furthermore, the encoded quantum state can be mapped to the vortex‐surface field, providing a useful approach for analyzing vortex dynamics and characterizing flow structures. While the calculation of the loss function encounters exponential complexity per training step, and the measurement of all qubits is inevitable, leading to high computational complexity for implementation on quantum hardware and requiring further optimization, its effectiveness has been validated across various scenarios through quantum simulation. This method enables spinor‐based encoding and quantum simulation, with potential applications to diverse vector fields and complex flows, including magnetohydrodynamics and reactive flows.
Su et al. (2026) studied this question.