Quantum Algorithm for Lattice Boltzmann (QALB) Simulation of Incompressible Fluids with a Nonlinear Collision Term

We propose a quantum algorithm for solving physical problems represented by the lattice Boltzmann formulation. Specifically, we deal with the case of a single phase, incompressible fluid obeying the Bhatnagar-Gross-Krook model. We use the framework introduced by Kowalski that links the nonlinear dynamics of a system to the evolution of bosonic modes, assigning a Carleman linearization order to the truncation in the bosonic Fock space of the bosons. The streaming and collision steps are both achieved via unitary operators. A quantized version of the nonlinear collision term has been implemented, without introducing variables of discrete densities coupled from neighbouring sites, unlike the classical Carleman technique. We use the compact mapping of the bosonic modes to qubits that uses a number of qubits which scales logarithmically with the size of truncated bosonic Fock space. The work can be readily extended to the multitude of multiphysics problems which could adapt the lattice Boltzmann formulation.