Abstract
This article presents a novel encoding for quantum Lattice Boltzmann method algorithm using Carleman linearization. In contrast to previous articles \cite{Sanavio2024LatticeBC,sanavio2025carleman}, the encoding used allows for local collision rules while keeping a higher probability to obtain the right result, which is of the order of 10⁻². The algorithm scales as O(log₂²(N)+Q³) each time step with N the number of lattice sites of the 2D lattice and Q the number of channels with a constant number of qubits when using dynamical circuits.