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

Quantum Physics 2026-03-16 v3

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 10210^{-2}. The algorithm scales as O(log22(N)+Q3)O(log_2^2(N)+Q^3) each time step with NN the number of lattice sites of the 2D lattice and QQ the number of channels with a constant number of qubits when using dynamical circuits.

Keywords

Cite

@article{arxiv.2511.13072,
  title  = {Quantum lattice Boltzmann method for several time steps: A local Carleman linearization algorithm},
  author = {Antonio David Bastida Zamora and Ljubomir Budinski and Valtteri Lahtinen and Pierre Sagaut},
  journal= {arXiv preprint arXiv:2511.13072},
  year   = {2026}
}

Comments

14 pages, 14 figures

R2 v1 2026-07-01T07:40:38.747Z