  For quantum computing (QC) to emerge as a practically indispensable
computational tool, there is a need for quantum protocols with an end-to-end
practical applications -- in this instance, fluid dynamics. We debut here a
high performance quantum simulator which we term QFlowS (Quantum Flow
Simulator), designed for fluid flow simulations using QC. Solving nonlinear
flows by QC generally proceeds by solving an equivalent infinite dimensional
linear system as a result of linear embedding. Thus, we first choose to
simulate two well known flows using QFlowS and demonstrate a previously unseen,
full gate-level implementation of a hybrid and high precision Quantum Linear
Systems Algorithms (QLSA) for simulating such flows at low Reynolds numbers.
The utility of this simulator is demonstrated by extracting error estimates and
power law scaling that relates $T_{0}$ (a parameter crucial to Hamiltonian
simulations) to the condition number $\kappa$ of the simulation matrix, and
allows the prediction of an optimal scaling parameter for accurate eigenvalue
estimation. Further, we include two speedup preserving algorithms for (a) the
functional form or sparse quantum state preparation, and (b) \textit{in-situ}
quantum post-processing tool for computing nonlinear functions of the velocity
field. We choose the viscous dissipation rate as an example, for which the
end-to-end complexity is shown to be $\mathcal{O}(\textrm{polylog}
(N/\epsilon)\kappa/\epsilon_{QPP})$, where $N$ is the size of the linear system
of equations, $\epsilon$ is the the solution error and $\epsilon_{QPP}$ is the
error in post processing. This work suggests a path towards quantum simulation
of fluid flows, and highlights the special considerations needed at the gate
level implementation of QC.
