Vortex Detection from Quantum Data

TL;DR

This paper introduces quantum algorithms for detecting vortices in quantum data representing fluid flows, using specialized quantum circuits for feature extraction and classification, demonstrating efficient analysis of complex quantum flow states.

Contribution

It develops novel quantum circuit techniques for vortex detection, including contour-based and Fourier analysis methods, advancing quantum data analysis tools for fluid dynamics.

Findings

Quantum circuits can effectively identify vortex regions in quantum flow data.

Fourier analysis on quantum states enables classification of vortex presence.

Parallel window techniques improve efficiency in vortex detection.

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.