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Simulating fluid dynamics on a quantum computer is intrinsically difficult due to the nonlinear and non-Hamiltonian nature of the Navier-Stokes equation (NSE). We propose a framework for quantum computing of fluid dynamics based on the hydrodynamic Schrödinger equation (HSE), which can be promising in simulating threedimensional turbulent flows in various engineering applications. The HSE is derived by generalizing the Madelung transform to compressible/incompressible flows with finite vorticity and dissipation. Since the HSE is expressed as a unitary operator on a two-component wave function, it is more suitable than the NSE for quantum computing. The flow governed by the HSE can resemble a turbulent flow consisting of tangled vortex tubes with the five-thirds scaling of energy spectrum. We develop a prediction-correction quantum algorithm to solve the HSE. This algorithm is implemented for simple flows on the quantum simulator Qiskit with exponential speedup. I. INTRODUCTIONQuantum computing has emerged to be the next disruptive technology since Feynman pointed out the enormous potential of quantum simulation [1]. Compared to conventional digital computing, quantum computing can dramatically reduce the execution time, memory usage, and energy consumption [2]. There are various hardware techniques for quantum logic gates [3][4][5][6][7][8], quantum algorithms for specific tasks [9][10][11][12], and applications [13][14][15][16]

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