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.
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.
Accurately predicting turbulent flows remains a central challenge in fluid dynamics due to their high dimensionality and intrinsic nonlinearity. Recent developments in quantum algorithms and machine learning offer new opportunities for overcoming the computational barriers inherent in turbulence modeling. Here we present a new hybrid quantum-classical framework that enables faster-than-real-time turbulence prediction by integrating machine learning, quantum computation, and fluid dynamics modeling, in particular, the reduced-order modeling. The novel framework combines quantum proper orthogonal decomposition (QPOD) with a quantum-enhanced deep kernel learning (QDKL) approach. QPOD employs quantum circuits to perform efficient eigenvalue decomposition for low-rank flow reconstruction, while QDKL exploits quantum entanglement and nonlinear mappings to enhance kernel expressivity and dynamic prediction accuracy. The new method is demonstrated on three benchmark turbulent flows, our architecture achieves significantly improved predictive accuracy at reduced model ranks, with training speeds up to 10 times faster and parameter counts reduced by a factor of 1/N compared to classical counterparts, where N is the input dimensionality. Although constrained by current noisy intermediate-scale quantum (NISQ) hardware, our results demonstrate the potential of quantum machine learning to transform turbulence simulation and lay a solid foundation for scalable, real-time quantum fluid modeling in future quantum computers.
This research investigates the potential of quantum mechanics to enhance geometric modeling of fluid dynamics, specifically addressing the challenges posed by complex flow scenarios. We propose a novel approach that leverages quantum-inspired methods to represent and manipulate fluid dynamics parameters, aiming to improve the accuracy and efficiency of simulations. This work explores the application of quantum-based representations to streamline calculations and improve the representation of turbulent flows, ultimately leading to more robust and accurate fluid dynamics models. The research focuses on creating a new framework for modeling complex flows, potentially offering a significant advancement over traditional methods.
In this study, we propose a new approach to describing certain macroscopic objects
that can arise in a quantum fluid. These objects are formed by means of quantum entanglement from the circular-shaped mesoscale and microscale vortices, and can be interpreted as a vortex filaments with any shape and size. The method is based on a quantization scheme for classical closed vortex filaments that was proposed by the author early \cite{Tal18,Tal22_1,Tal_Chaos25J}. The model we consider examines the instantaneous picture of the locations in space R3 of such filaments with a small, but non-zero, core diameter.
Both energy and circulation of the studied filaments are calculated using the proposed approach. We demonstrate that the adopted concept leads to the emergence of secondary vortices around these investigated filament-like objects.
We also study the specific mechanisms by which large vortex loops can disconnect and create the filament fragments . From our point of view, the proposed approach to describing vortex filaments within a vortex tangle can be seen as an important step toward understanding the appearance of quantum turbulence.
This paper explores the potential of quantum-enhanced geometric simulation to revolutionize the representation and analysis of complex fluid dynamics. Traditional numerical methods often struggle to accurately model the intricate quantum effects that govern fluid flow, leading to inaccuracies and computational bottlenecks. We propose a novel simulation technique, incorporating a quantum-enhanced geometric framework, designed to address these limitations. This work details the algorithm's core principles, the quantum-mechanical elements employed, and the expected impact on simulation accuracy and speed. The research focuses on leveraging quantum entanglement and superposition to enhance the representation of fluid wave propagation, turbulence, and other crucial fluid dynamics phenomena. The ultimate goal is to provide a more robust and efficient method for simulating complex fluid dynamics, opening avenues for advancements in fields ranging from fluid mechanics to materials science.
I present a unified theoretical and numerical framework that couples quantum wave dynamics (Schrödinger) with classical viscous flow (Navier–Stokes) through an emergent quantum-π field (π_q) that encodes phase-topology and coherence. The model reproduces Schrödinger dynamics in the conservative limit, Navier–Stokes turbulence in the dissipative limit, and novel intermediate regimes where quantum coherence and fluid turbulence coexist and interact. I derive the governing equations by (i) applying a Madelung decomposition to a complex field ψ, (ii) introducing a controlled viscous regularization and non-linear coupling terms, and (iii) coupling a dynamically evolving π_q scalar (or tensor) field that modulates local coherence, effective mass, and information flux. I then present a robust hybrid numerical method (QHFVM — Quantum Hydrodynamic Finite-Volume Method) combining split-step spectral propagation for dispersive quantum terms and conservative finite-volume solvers for advective, viscous and pressure dynamics. I validate the approach on a set of canonical problems (quantum vortex shedding in a viscous background, π-phase revival in confined geometries, and turbulence spectra with quantum corrections), show numerical convergence and conservation properties, and outline applications spanning quantum fluids, nanoscale bio-fluids, materials, and hybrid QEC architectures. Flash explanations highlight intuition and immediate experimental tests.
Abstract Chapter 5 delves into quantum turbulence in superfluid helium and atomic Bose-Einstein condensates (BECs). The foundation of quantum turbulence research lies in classical fluid dynamics and turbulence, which is why we begin by covering essential concepts like the Reynolds number and Kolmogorov’s -5/3 power law in the energy spectrum. These principles are crucial for understanding quantum turbulence. We then explore the shared aspects of quantum turbulence in superfluid helium and atomic BECs, such as the differences in vortex configurations compared to classical turbulence, energy spectra, cascades, and the distinction between quasiclassical (Kolmogorov) and ultraquantum (Vinen) turbulence, focusing on their decay behaviors. In superfluid helium, we emphasize experimental studies in thermal counterflow and numerical simulations using the Vortex Filament Model (VFM). The advent of visualization experiments in the mid-2000s was transformative, allowing the observation of normal fluid velocity profiles and accelerations via tracer particles, which led to more accurate simulations coupling the VFM with normal fluid dynamics. Another significant topic is the energy spectrum of quantum turbulence, and whether it mirrors classical turbulence remains a key question. In addition to thermal counterflow, localized quantum turbulence generated by oscillating objects has been a major area of study. We present research showing how quantized vortices grow and evolve into turbulence. Superfluid 3He-B also provides a platform for quantum turbulence, with advancements in microfabrication bringing MEMS and NEMS into focus for studying quantum hydrodynamics at micro- and nanoscale, influenced by boundary conditions. In atomic BECs, confined by potentials, turbulence is induced through techniques like shaking or moving potentials. A unique aspect of BECs is two-dimensional quantum turbulence, featuring inverse energy cascades, Onsager vortices, and negative temperature states. Finally, atomic BECs, being compressible, serve as a platform for both vortex and wave turbulence. Multicomponent BECs, such as spinor BECs, introduce spin turbulence, further diversifying the field.