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

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.