Quantum Carleman linearization efficiency in nonlinear fluid dynamics
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Abstract
Computational fluid dynamics (CFD) is a specialized branch of fluid mechanics that utilizes numerical methods and algorithms to solve and analyze fluid-flow problems. One promising avenue to enhance CFD is the use of quantum computing, which has the potential to resolve nonlinear differential equations more efficiently than classical computers. Here, we try to answer the question of which regimes of nonlinear partial differential equations for fluid dynamics can have an efficient quantum algorithm. We propose a connection between the numerical parameter R, which guarantees efficiency in the truncation of the Carleman linearization, and the physical parameters that describe the fluid flow. This link can be made thanks to the Kolmogorov scale, which determines the minimum size of the grid needed to properly resolve the energy cascade induced by the nonlinear term. Additionally, we introduce the formalism for vector field simulation in different spatial dimensions, providing the discretization of the operators and the boundary conditions. Published by the American Physical Society 2025