This article presents an encoding for the quantum Lattice Boltzmann method algorithm using Carleman linearization. In contrast to previous articles [C. Sanavio et al., AVS Quantum Sci. 6, 023802 (2024); Phys. Fluids 37, 037123 (2025)], the encoding used allows for local collision rules while keeping a higher probability to obtain the correct result, which is of the order of ${10}^{-2}$. The algorithm scales as $O[{log}_2^2\left(N\right)+Q^3]$ at each time step with $N$ the number of lattice sites of the two-dimensional lattice and $Q$ the number of channels with a constant number of qubits when using dynamical circuits.

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• Nonlinear dynamics in fluids
• Quantum algorithms & computation
• Lattice gases
• Lattice-Boltzmann methods