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

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This study introduces a new quantum Lattice Boltzmann method encoding using Carleman linearization. The novel approach enables local collision rules with improved accuracy for quantum simulations.

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Area of Science:

  • Quantum Computing
  • Computational Physics
  • Fluid Dynamics

Background:

  • The Lattice Boltzmann method is a powerful tool for simulating fluid dynamics.
  • Quantum algorithms offer potential speedups for complex simulations.
  • Previous quantum Lattice Boltzmann method encodings faced limitations in collision rule implementation and accuracy.

Purpose of the Study:

  • To present a novel encoding for the quantum Lattice Boltzmann method algorithm.
  • To enable local collision rules within the quantum Lattice Boltzmann method.
  • To improve the accuracy and efficiency of quantum fluid dynamics simulations.

Main Methods:

  • Utilized Carleman linearization for encoding the quantum Lattice Boltzmann method.
  • Developed an algorithm allowing for local collision rules.
  • Analyzed the computational scaling of the proposed encoding.

Main Results:

  • Achieved a higher probability of obtaining correct results, on the order of 10^{-2}.
  • The algorithm exhibits a computational scaling of O[log_{2}^{2}(N)+Q^{3}] per time step.
  • The encoding is compatible with dynamical circuits using a constant number of qubits.

Conclusions:

  • The proposed Carleman linearization encoding enhances the quantum Lattice Boltzmann method.
  • This advancement facilitates more accurate and potentially faster quantum simulations of fluid dynamics.
  • The method offers a promising direction for future research in quantum computational physics.