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arXiv · 2511.13072

Quantum lattice Boltzmann method for several time steps: A local Carleman linearization algorithm

Antonio David Bastida Zamora·Ljubomir Budinski·Valtteri Lahtinen·Pierre Sagaut
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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.

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Antonio David Bastida Zamora, Ljubomir Budinski, Valtteri Lahtinen, Pierre Sagaut. 2025-11-17. Quantum lattice Boltzmann method for several time steps: A local Carleman linearization algorithm. https://doi.org/10.1103/kbx3-c35d

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