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Adaptive lattice-gas algorithm: Classical and quantum implementations.

Niccolò Fonio1, Pierre Sagaut1, Ljubomir Budinski2

  • 1M2P2 Laboratory, Aix Marseille Université, Centrale Med, CNRS, UMR 7340, 13013 Marseille, France.

Physical Review. E
|October 21, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces an adaptive lattice-gas algorithm that replicates lattice Boltzmann method simulations by performing a fraction of collisions. A quantum algorithm is also developed for simulating nonlinear systems using a linear collision operator.

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Area of Science:

  • Computational Physics
  • Quantum Computing
  • Nonlinear Dynamics

Background:

  • Lattice-gas algorithms (LGA) are computational methods for simulating nonlinear systems.
  • Existing LGAs include binary lattice-gas cellular automata, integer lattice-gas algorithms (ILGA), and the lattice Boltzmann method (LBM).

Purpose of the Study:

  • To develop an adaptive lattice-gas algorithm that achieves LBM simulation results.
  • To design a quantum algorithm for simulating nonlinear systems using a linear collision operator.

Main Methods:

  • Developed a one-dimensional ILGA performing a fraction of possible collisions.
  • Adapted collision fractions to match LBM equilibrium distributions.
  • Designed a quantum algorithm with a linear collision operator and measurement/reinitialization.

Main Results:

  • The adaptive lattice-gas algorithm successfully reproduces LBM simulation results.
  • The quantum algorithm simulates the same nonlinear phenomena as LBM.

Conclusions:

  • An adaptive lattice-gas approach can effectively emulate LBM simulations.
  • Quantum algorithms offer a novel method for simulating complex nonlinear systems.