Quantum implicit representation of vortex filaments in turbulence

TL;DR

This paper introduces a quantum implicit representation method for vortex filaments in turbulence, leveraging quantum computing techniques to efficiently model complex fluid structures and topological properties.

Contribution

It presents a novel quantum framework reformulating vortex filament modeling as an eigenvalue problem solved via variational quantum eigensolvers, enabling efficient turbulence analysis.

Findings

Achieves near-linear time complexity in vortex filament modeling

Provides exponential reduction in storage requirements

Maintains accuracy and robustness in turbulence representation

Abstract

Entangled vortex filaments are essential to turbulence, serving as coherent structures that govern nonlinear fluid dynamics and support the reconstruction of fluid fields to reveal statistical properties. This study introduces an quantum implicit representation of vortex filaments in turbulence, employing a level-set method that models the filaments as the intersection of the real and imaginary zero iso-surfaces of a complex scalar field. Describing the fluid field via the scalar field offers distinct advantages in capturing complex structures, topological properties, and fluid dynamics, while opening new avenues for innovative solutions through quantum computing platforms. The representation is reformulated into an eigenvalue problem for Hermitian matrices, enabling the conversion of velocity fields into complex scalar fields that embed the vortex filaments. The resulting optimization is addressed using a variational quantum eigensolver, with Pauli operator truncation and deep learning techniques applied to improve efficiency and reduce noise. The proposed quantum framework achieves a near-linear time complexity and a exponential storage reduction while maintaining a balance of accuracy, robustness, and versatility, presenting a promising tool for turbulence analysis, vortex dynamics research, and machine learning dataset generation.