End-to-end quantum computational simulation of fluid flows on QuOn

In the recent past, quantum algorithms have shown promise to accelerate computational research in various fields. However, nonlinear classical systems are still quite arduous to simulate on quantum machines. To evaluate their viability, one needs a full gate level quantum simulation, while also extracting the velocity fields for benchmarking. To this end, we develop a new, high performance quantum simulator, specific to fluid dynamics called "QuOn" equipped with full gate level simulation capabilities. Using QuOn and Qiskit (IBM) we first perform a full end-to-end simulation of time-dependent Poiseuille and Couette flows, using a modified quantum linear solver algorithm and evaluating its performance. We show as a proof-of-concept, that these quantum algorithms can capture the physics quite accurately given the near-term quantum resources with quantum advantage. We describe how to design these circuits to perform accurate simulations. We also discuss ongoing efforts to encode nonlinearity in the problem of solving 1D Burgers flow.