Vortex Detection from Quantum Data

Abstract: Quantum solutions to differential equations represent quantum data -- states that contain relevant information about the system's behavior, yet are difficult to analyze. We propose a toolbox for reading out information from such data, where customized quantum circuits enable efficient extraction of flow properties. We concentrate on the process referred to as quantum vortex detection (QVD), where specialized operators are developed for pooling relevant features related to vorticity. Specifically, we propose approaches based on sliding windows and quantum Fourier analysis that provide a separation between patches of the flow field with vortex-type profiles. First, we show how contour-shaped windows can be applied, trained, and analyzed sequentially, providing a clear signal to flag the location of vortices in the flow. Second, we develop a parallel window extraction technique, such that signals from different contour positions are coherently processed to avoid looping over the entire solution mesh. We show that Fourier features can be extracted from the flow field, leading to classification of datasets with vortex-free solutions against those exhibiting Lamb-Oseen vortices. Our work exemplifies a successful case of efficiently extracting value from quantum data and points to the need for developing appropriate quantum data analysis tools that can be trained on them.