Quantum algorithm for the lattice Boltzmann method with applications on real quantum devices

TL;DR

This paper presents a new quantum algorithm for the lattice Boltzmann method that offers greater flexibility and efficiency, demonstrated through applications in linear acoustics and nonlinear fluid dynamics on real quantum hardware.

Contribution

A novel quantum algorithm for the lattice Boltzmann method that improves flexibility and efficiency, enabling practical applications on current quantum devices.

Findings

Successful implementation of linear acoustics simulation on IBM QPU

Demonstrated nonlinear Navier-Stokes problem solution in hybrid quantum-classical loop

Algorithm maintains computational efficiency with reduced qubit and gate complexity

Abstract

We introduce a novel quantum algorithm for the lattice Boltzmann method (LBM) based on the one-step simplified LBM. The structure of the algorithm allows for more flexibility in modelling different physics in contrast to earlier quantum algorithms for the LBM, while retaining computational efficiency in terms of the gate and qubit complexity. The new algorithm has potential for full end-to-end quantum utility especially for linear problems. We discuss the implementation of examples in linear acoustics, as well as a nonlinear Navier-Stokes problem that was solved on an IBM QPU in a hybrid simulation loop.