Quantum Approach to Accelerate Finite Volume Method on Steady Computational Fluid Dynamics Problems.

Computational fluid dynamics (CFD) is a branch of fluid mechanics that solves fluid flows by numerical methods. Recently, quantum computing has been proven to outperform a classical computer on specific computational tasks. However, using a quantum computer to accelerate the CFD solver remains a challenge. Existed quantum differential equation solvers, which are limited to the linearity of the equation, cannot be applied in the CFD because the fluid equations are highly nonlinear. Here, we propose a quantum approach to accelerate the finite volume method, which is typical in the classical CFD domain. We focus on how a quantum computer handles classical input and output, designing a specific quantum data structure that allows fast memory update throughout the calculation, resulting in an exponential speedup over the classical counterpart. Numerical tests show that this algorithm adapts to various CFD problems, including problems with high nonlinearity. This approach complements existed quantum methods for nonlinear differential equations and allows new frontiers of the CFD by allowing a breakthrough of the cell number and the solution speed. [ABSTRACT FROM AUTHOR]