Quantum linear solvers for potential flow problems: assessing efficiency and challenges

We leverage quantum algorithms to solve linear equations that govern canonical potential flow problems. Although the development of quantum processors with continuous quantum error correction and high-fidelity (number of qubits) capable of handling practical fluid flow problems may be distant, recent advancements in quantum algorithms, particularly linear solvers, have paved the way for quantum counterparts to classical fluid flow solvers. Assessing the capability of quantum linear systems algorithms (QLSA) in solving ideal flow equations on real hardware is crucial for their future development in practical fluid flow applications. In this study, we test the capability of various QLSA for accurately solving the system of linear equations. Our ongoing preliminary efforts are focused on analyzing the accuracy and computational cost of these solvers. We also evaluate the stability and convergence of the solvers using shots-based simulations of quantum simulators. We employ different state-of-the-art techniques to model and mitigate the effect of noise from quantum hardware. We will also share our experiences with running the algorithms on different quantum hardware.