Feasibility of accelerating incompressible computational fluid dynamics simulations with fault-tolerant quantum computers

Abstract: Across industries, traditional design and engineering workflows are being upgraded to simulation-driven processes. Many workflows include computational fluid dynamics (CFD). Simulations of turbulent flow are notorious for high compute costs and reliance on approximate methods that compromise accuracy. Improvements in the speed and accuracy of CFD calculations would potentially reduce design workflow costs by reducing computational costs and eliminating the need for experimental testing. This study explores the feasibility of using fault-tolerant quantum computers to improve the speed and accuracy of CFD simulations in the incompressible or weakly compressible regime. For the example of simulation-driven ship design, we consider simulations for calculating the drag force in steady-state flows, and provide analysis on economic utility and classical hardness. As a waypoint toward assessing the feasibility of our chosen quantum approach, we estimate the quantum resources required for the simpler case of drag force on a sphere. We estimate the product of (logical qubits)$\times$($T$ gates) to range from $10^{22}$ to $10^{28}$. These high initial estimates suggest that future quantum computers are unlikely to provide utility for incompressible CFD applications unless significant algorithmic advancements or alternative quantum approaches are developed. Encouraged by applications in quantum chemistry that have realized orders-of-magnitude improvements as they matured, we identify the most promising next steps for quantum resource reduction as we work to scale up our estimates from spheres to utility-scale problems with more complex geometry.