Towards Quantum Machine Learning of Lattice Boltzmann Collision Operators for Fluid Dynamic Simulations

TL;DR

This paper explores using quantum algorithms to simulate lattice Boltzmann collision operators for fluid dynamics, highlighting current limitations and potential for future quantum machine learning applications.

Contribution

It introduces a quantum approach to approximate collision operators, incorporating symmetry hard-wiring and modified encoding to improve quantum simulation of fluid dynamics.

Findings

Quantum approximation limited to low velocities in cavity flow

Modified amplitude encoding avoids classical renormalization

Insights into nonlinear quantum simulations for fluid dynamics

Abstract

We attempt the use of a unitary operator to approximate the lattice Boltzmann collision operator. We use a modified amplitude encoding to bypass the renormalization that would have required classical processing at every step (thus eroding any quantum advantage to be had). We describe the hard-wiring of the lattice Boltzmann symmetries into the quantum circuit and show that, for the specific case of the cavity flow, approximating the nonlinear system is limited to low velocities. These findings may help us understand better the possibilities of nonlinear simulations on a quantum computer, and also pave the way for a discussion on how quantum machine learning might be harnessed to address more complex problems.