Carleman-Grad approach to the quantum simulation of fluids

TL;DR

This paper explores a Carleman-Grad linearization method for quantum simulation of classical fluids, comparing it to existing lattice Boltzmann and Navier-Stokes approaches, highlighting its intermediate properties and potential for quantum computing.

Contribution

It introduces a Carleman-Grad approach for quantum fluid simulation, analyzing its convergence and implementation prospects relative to prior methods.

Findings

Carleman-Grad exhibits intermediate properties between lattice Boltzmann and Navier-Stokes.

Convergence occurs over a few tens of timesteps.

Potential for quantum circuit implementation exists, but requires further improvements.

Abstract

We discuss the Carleman linearization approach to the quantum simulation of classical fluids based on Grad's generalized hydrodynamics and compare it to previous investigations based on lattice Boltzmann and Navier-Stokes formulations. We show that the Carleman-Grad procedure exhibits intermediate properties between the two. Namely, convergence of the Carleman iteration over a few tens of timesteps and a potentially viable quantum circuit implementation using quantum linear algebra solvers. However, both features still need substantial improvements to yield a viable quantum algorithm for fluid flows.