  Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses
numerical methods to solve fluid flows. The finite volume method (FVM) is an
important one. In FVM, space is discretized to many grid cells. When the number
of grid cells grows, massive computing resources are needed correspondingly.
Recently, quantum computing has been proven to outperform a classical computer
on specific computational tasks. However, the quantum CFD (QCFD) solver remains
a challenge because the conversion between the classical and quantum data would
become the bottleneck for the time complexity. Here we propose a QCFD solver
with exponential speedup over classical counterparts and focus on how a quantum
computer handles classical input and output. By utilizing quantum random access
memory, the algorithm realizes sublinear time at every iteration step. The QCFD
solver could allow new frontiers in the CFD area by allowing a finer mesh and
faster calculation.
