Quantum algorithm to solve unsteady nonlinear flows and its execution

The uprise of quantum computing (QC) has been facilitated by its success in some niche domains. For QC to emerge as a versatile tool, it also needs to demonstrate its utility in classical engineering applications that are often highly nonlinear. Here, we present a quantum algorithm and its end-to-end execution to simulate unsteady nonlinear fluid flows by attempting to preserve any quantum speed up. We develop a customized Quantum Linear System Algorithm based on Linear Combination of Unitaries (LCU) and analyze different methods to perform forward time marching of the fluid flow PDEs that have been appropriately cast in a linearized form. The algorithm also includes an optimal quantum state preparation strategy and a quantum post-processing unit to compute viscous energy dissipation and skin friction coefficient. We present results for both 1D and 2D cases of linear and nonlinear flows, in particular the Poiseuille and Burgers flow respectively. We implement a full gate-level circuit and simulation on an in-house developed, high performance Quantum Flow Simulator -- QFlowS and outline the algorithm's accuracy and performance. We finally provide insight into pragmatic quantum resource estimates required to simulate current state-of-the-art computational sizes of classical nonlinear flows.