  Computational fluid dynamics (CFD) simulations often entail a large
computational burden on classical computers. At present, these simulations can
require up to trillions of grid points and millions of time steps. To reduce
costs, novel architectures like quantum computers may be intrinsically more
efficient at the appropriate computation. Current quantum algorithms for
solving CFD problems use a single quantum circuit and, in some cases,
lattice-based methods. We introduce the a novel multiple circuits algorithm
that makes use of a quantum lattice Boltzmann method (QLBM). The two-circuit
algorithm we form solves the Navier-Stokes equations with a marked reduction in
CNOT gates compared to existing QLBM circuits. The problem is cast as a stream
function--vorticity formulation of the 2D Navier-Stokes equations and verified
and tested on a 2D lid-driven cavity flow. We show that using separate circuits
for the stream function and vorticity lead to a marked CNOT reduction: 35% in
total CNOT count and 16% in combined gate depth. This strategy has the
additional benefit of the circuits being able to run concurrently, further
halving the seen gate depth. This work is intended as a step towards practical
quantum circuits for solving differential equation-based problems of scientific
interest.
