We develop a quantum representation for Newtonian viscous fluid flows by establishing a mapping between the Navier-Stokes equation (NSE) and the Schr\"odinger-Pauli equation (SPE). The proposed nonlinear SPE incorporates the two-component wave function and the imaginary diffusion. Consequently, classical fluid flow can be interpreted as a non-Hermitian quantum spin system. Using the SPE-based numerical simulation of viscous flows, we demonstrate the quantum/wave-like behavior in flow dynamics. Furthermore, the SPE equivalent to the NSE can facilitate the quantum simulation of fluid dynamics.
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Meng et al. (2024) studied this question.
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