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Quantum Carleman Linearization of the Lattice Boltzmann Equation with Boundary Conditions
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The Lattice Boltzmann Method (LBM) is widely recognized as an efficient algorithm for simulating fluid flows in both single-phase and multi-phase scenarios. In this research, a quantum Carleman Linearization formulation of the Lattice Boltzmann equation is described, employing the Bhatnagar Gross and Krook equilibrium function. Our approach addresses the treatment of boundary conditions with the commonly used bounce back scheme. The accuracy of the proposed algorithm is demonstrated by simulating flow past a rectangular prism, achieving agreement with respect to fluid velocity In comparison to classical LBM simulations. This improved formulation showcases the potential to provide computational speed-ups in a wide range of fluid flow applications. Additionally, we provide details on read in and read out techniques.
Forward citations
Cited by 2 Pith papers
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A Scalable Approach to Solve the Carleman Linearized Burgers' Equation on a Quantum Computer
LCNU loading plus multigrid-warmed VQLS solves Carleman-linearized 1D Burgers on quantum hardware/simulators, with circuits scaling to 2^80 points.
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Linearization Scheme of Shallow Water Equations for Quantum Algorithms
A Carleman linearization maps 1D shallow water equations to a linear system for quantum solvers, but validation is limited to small-amplitude test cases and the speedup remains conditional.
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