Reducing quantum resources for the quantum lattice Boltzmann method

We present a two-circuit approach for solving the Navier-Stokes equations to model fluid flows, which exhibits quantum resource efficiency gains over the existing quantum lattice Boltzmann method. The streamfunction-vorticity formulation of the Navier-Stokes equations is used, and we show that using separate circuits to evolve streamfunction and vorticity leads to a reduction in CNOT gates in the collision and streaming steps. In addition, a technique is shown to eliminate CNOT gates entirely from the macro step of the simulation. This reduces the quantum resources necessary for the simulation, and the circuits can be run concurrently. In addition, the gate depths of the circuits are lower than present single-circuit QLBM variants. This algorithm is validated on the two-dimensional lid-driven cavity flow and shows good agreement with the classical lattice Boltzmann simulations. The research presents simulation results of a quantum algorithm and quantum resource estimations, indicating considerable advantages over current methods.