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First of all, let me come out and say that I know very little about Quantum Computing (QC), even though it's a subject which fascinates me. I'd say I'm generally aware of the basic principles (with a lot of misconceptions thrown in, quite probably), but not naive enough to think I have a firm grasp of them, so please go easy on me.

I also know little about the Lattice-Boltzmann Method as my day to day at work involves using Navier-Stokes based commercial solvers for our commercial Computational Fluid Dynamics (CFD) work, and that's what I was taught in my integrated Masters. I've only briefly checked out a couple of open-source LBM codes while at work.

So, from what little understanding I have of both these topics, and from the following explanation of the LBM method - Everything you need to know about the Lattice Boltzmann Method - is it plausible to assume that this method would be inherently more suitable to implement in a QC CFD code, or am I just erroneously conflating the role that probability plays in both these topics?

Best regards,

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If I understand correctly, the Lattice Boltzmann Method computes the probability density on a lattice. It doesn't consider sampling from that probability distribution. So, from a very remote perspective, both methods are computing some quantity over a lattice using some finite-difference approximations of differential operators. From this perspective, LBM doesn't involve more or less probability. Therefore, both equations should be equally suitable for implementing on a quantum computer.

They may have different challenges, though, because of the different operators they involve (I can't comment on that, as I haven't read in-depth any works that proposed quantum CFD).

Quantum computers would have an edge in problems where it is hard to sample such a probability distribution. For example, the evolution of a quantum Hamiltonian can lead to a probability distribution that is (believed to be) hard to sample from using a classical computer but easily implemented with a quantum one (e.g. see this article; it is very technical but the introduction seems accessible to non-experts).

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