Hybrid quantum algorithms for flow problems

Quantum computing (QC) has advantages of speed and storage over classical computing, but it is based on a linear paradigm. However, many problems of interest are nonlinear. A viable QC algorithm includes a suitable preparation of a nonlinear problem into a linearized setting, doing computations quantum mechanically and reading out the results in classical terms. This end-to-end process usually diminishes the quantum advantage. We solve Poiseuille and Couette flows by introducing an in-house quantum simulator, named Quantum Flow Simulator, for computational fluid dynamics, and highlight the limitations of QC while preserving the quantum advantage. The quantum algorithmic as well as the classical software machinery developed here sets the stage for future quantum simulations.