Variational quantum algorithm towards quantum computing for fluid mechanics

Quantum computation has shown a fast development trend in the past few years.  The quantum devices, superposition state, and the representability of the Hilbert space span by the quantum vectors show great potentials for achieving exponential speedup over classical computers, which have stimulated great interests in quantum computing in many fields, such as communication, finance, and life sciences.  The study of quantum algorithms for fluid mechanics problems is still at an infancy stage.  Here we present a variational quantum algorithm for solving key building blocks of the Navier-Stokes equations.  Using a parameterized quantum circuit, solutions can be obtained through a training process.  Using numerical experiments, we compare the computational cost of the algorithm with the previous methods and the results indicate that a significant speedup is possible.