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Quantum implicit representation of vortex filaments in turbulence

Published online by Cambridge University Press:  07 July 2025

Chenjia Zhu ,
Ziteng Wang ,
Shiying Xiong Open the ORCID record for Shiying Xiong [Opens in a new window] ,
Yaomin Zhao Open the ORCID record for Yaomin Zhao [Opens in a new window]  and
Yue Yang Open the ORCID record for Yue Yang [Opens in a new window]
Chenjia Zhu
Affiliation:
Department of Engineering Mechanics, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, PR China
Ziteng Wang
Affiliation:
Department of Engineering Mechanics, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, PR China
Shiying Xiong*
Affiliation:
Department of Engineering Mechanics, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, PR China
Yaomin Zhao
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, PR China HEDPS-CAPT, Peking University, Beijing 100871, PR China
Yue Yang
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, PR China HEDPS-CAPT, Peking University, Beijing 100871, PR China
*
Corresponding author: Shiying Xiong, shiying.xiong@zju.edu.cn
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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 a quantum implicit representation of vortex filaments in turbulence, employing a levelset 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 optimisation 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.

JFM classification

Vortex Flows: Vortex dynamics Turbulent Flows: Turbulence modelling Mathematical Foundations: Topological fluid dynamics

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JFM Papers
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Journal of Fluid Mechanics , Volume 1014 , 10 July 2025 , A31
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© The Author(s), 2025. Published by Cambridge University Press

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Footnotes

†

Co-first author.

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