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Quantum lattice Boltzmann method for several time steps: A local Carleman linearization algorithm
Antonio David Bastida Zamora, Ljubomir Budinski, Valtteri Lahtinen, Pierre Sagaut·November 17, 2025·DOI: 10.1103/kbx3-c35d
Quantum Physics
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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 $O(log_2^2(N)+Q^3)$ 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.