Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2510.14099 · Brazilian Journal of Physics

A Review of Quantum Machine Learning and Quantum-inspired Applied Methods to Computational Fluid Dynamics

Cesar A. Amaral, Vinícius L. Oliveira, Juan P. L. C. Salazar, Eduardo I. Duzzioni

Published Dec 12, 2025• 4 citations
arXivHTMLPDF
DOI
10.1007/s13538-025-01959-8

Related papers

Quantum Machine Learning for Computational Fluid Dynamics

Nathan Wiebe

Bulletin of the American Physical Society•Nov 22, 2021•0 citations

Magic of the Well: assessing quantum resources of fluid dynamics data

Antonio Francesco Mello, Mario Collura, E. Miles Stoudenmire +1 more

We investigate the quantum resource requirements of a dataset generated from simulations of two-dimensional, periodic, incompressible shear flow, aimed at training machine learning models. By measuring entanglement and non-stabilizerness on MPS-encoded functions, we estimate the computational complexity encountered by a stabilizer or a tensor network solver applied to Computational Fluid Dynamics (CFD) simulations across different flow regimes. Our analysis reveals that, under specific initial conditions, the shear width identifies a transition between resource-efficient and resource-intensive regimes for non-trivial evolution. Furthermore, we find that the two resources qualitatively track each other in time, and that the mesh resolution along with the sign structure play a crucial role in determining the resource content of the encoded state. These findings offer useful guidelines for the development of scalable, quantum-inspired approaches to fluid dynamics.

quant-pharXiv:2512.03177•Dec 4, 2025•0 citations

Quantum Computing CFD Simulations for Aeronautical Heat Exchangers

Giulio Malinverno, Javier Blasco Alberto, Jon Lecumberri SanMartin

This document is meant to review and discuss the possible applications of Quantum computing to computational fluid dynamics (CFD) problems.A review of the current state-of-the-art of quantum computing applied to computational fluid dynamics has been carried out, highlining how the technology is still in an early stage of development but very promising.Quantum computing is a type of computation that harnesses the collective properties of quantum states, such as superposition, interference, and entanglement, to perform calculations.The devices that perform quantum computations are known as quantum computers.Quantum Computing is currently a very active field of study and development, with expected applications in various fields, including engineering problems.Indeed, several approaches have been proposed for the solutions of CFD problems with the use of quantum algorithms and / or quantum computers.Possible approaches, applicable to compact heat exchangers used in aeronautics, include the development of quantum algorithms, e.g., based on the solutions of Navier Stokes equations or the Lattice Boltzmann Method., the design of an "analog" quantum computer able to mimic the thermal fluid system under investigation, and, finally, the implementation of a scientific machine learning approach.

Proceedings of the International Conference on Fluid Flow and Thermal Science, ICFFTS ...•Dec 1, 2023•5 citations

Quantum-Inspired Computational Fluid Dynamics for Transient Turbulent Compressible Flows

Shang Xian Matthew Lee, Melissa Kozul, Muhammad Usman +3 more

Quantum-inspired algorithms are an emerging class of algorithms for computational fluid dynamics (CFD) with potentially favourable scaling for large problems compared to classical methods. However, their applications have been limited to incompressible flows due to arithmetic limitations, which are addressed in this work. This work introduces the first true end-to-end quantum-inspired computational fluid dynamics (QICFD) solver for direct numerical simulation of the compressible Navier-Stokes equations, that is, all arithmetic operations, as well as initialisation and post-processing, are undertaken in the tensor train (TT) format. Importantly, new division and square-root algorithms using TTs enable the use of Sutherland's law for viscosity, and leverages recent improvements in TT arithmetic algorithms for reduced runtime and memory cost. The new QICFD solver is validated by comparison with the classical CFD solver HiPSTAR and by way of a challenging fluid-flow test case, the low resolution Taylor-Green Vortex (TGV) at Mach numbers of 0.8 and 0.1. The TGV test case is a transient turbulent case that is very sensitive to accumulating errors, yet our QICFD solver achieves excellent agreement with the classical CFD reference. This work demonstrates the correctness of the new TT division and square-root algorithms, and that QICFD is capable of compressible flow simulations. The new QICFD solver is also able to perform simultaneous simulations, running multiple TGV-like cases initialised differently in parallel with reduced extra cost. Finally, the demonstrated TGV test case reveals additional challenges of QICFD as well as highlight the need for future advances to make TT methods viable for industrially-relevant conditions.

physics.flu-dynCross-listedarXiv:2608.26995•Aug 28, 2026

Quantum-Ready and Quantum-Inspired Computing for Fluid Dynamics

Peyman Givi

Bulletin of the American Physical Society•Nov 22, 2021•0 citations

Quantum Fluid Dynamics and Quantum Computational Fluid Dynamics

Chia‐Liang Lin, Jenn‐Kun Kuo, Tsu-Hsu Yen

Journal of Computational and Theoretical Nanoscience•Apr 1, 2009•2 citations
We investigate the quantum resource requirements of a dataset generated from simulations of two-dimensional, periodic, incompressible shear flow, aimed at training machine learning models. By measuring entanglement and non-stabilizerness on MPS-encoded functions, we estimate the computational complexity encountered by a stabilizer or a tensor network solver applied to Computational Fluid Dynamics (CFD) simulations across different flow regimes. Our analysis reveals that, under specific initial conditions, the shear width identifies a transition between resource-efficient and resource-intensive regimes for non-trivial evolution. Furthermore, we find that the two resources qualitatively track each other in time, and that the mesh resolution along with the sign structure play a crucial role in determining the resource content of the encoded state. These findings offer useful guidelines for the development of scalable, quantum-inspired approaches to fluid dynamics.
This document is meant to review and discuss the possible applications of Quantum computing to computational fluid dynamics (CFD) problems.A review of the current state-of-the-art of quantum computing applied to computational fluid dynamics has been carried out, highlining how the technology is still in an early stage of development but very promising.Quantum computing is a type of computation that harnesses the collective properties of quantum states, such as superposition, interference, and entanglement, to perform calculations.The devices that perform quantum computations are known as quantum computers.Quantum Computing is currently a very active field of study and development, with expected applications in various fields, including engineering problems.Indeed, several approaches have been proposed for the solutions of CFD problems with the use of quantum algorithms and / or quantum computers.Possible approaches, applicable to compact heat exchangers used in aeronautics, include the development of quantum algorithms, e.g., based on the solutions of Navier Stokes equations or the Lattice Boltzmann Method., the design of an "analog" quantum computer able to mimic the thermal fluid system under investigation, and, finally, the implementation of a scientific machine learning approach.
Quantum-inspired algorithms are an emerging class of algorithms for computational fluid dynamics (CFD) with potentially favourable scaling for large problems compared to classical methods. However, their applications have been limited to incompressible flows due to arithmetic limitations, which are addressed in this work. This work introduces the first true end-to-end quantum-inspired computational fluid dynamics (QICFD) solver for direct numerical simulation of the compressible Navier-Stokes equations, that is, all arithmetic operations, as well as initialisation and post-processing, are undertaken in the tensor train (TT) format. Importantly, new division and square-root algorithms using TTs enable the use of Sutherland's law for viscosity, and leverages recent improvements in TT arithmetic algorithms for reduced runtime and memory cost. The new QICFD solver is validated by comparison with the classical CFD solver HiPSTAR and by way of a challenging fluid-flow test case, the low resolution Taylor-Green Vortex (TGV) at Mach numbers of 0.8 and 0.1. The TGV test case is a transient turbulent case that is very sensitive to accumulating errors, yet our QICFD solver achieves excellent agreement with the classical CFD reference. This work demonstrates the correctness of the new TT division and square-root algorithms, and that QICFD is capable of compressible flow simulations. The new QICFD solver is also able to perform simultaneous simulations, running multiple TGV-like cases initialised differently in parallel with reduced extra cost. Finally, the demonstrated TGV test case reveals additional challenges of QICFD as well as highlight the need for future advances to make TT methods viable for industrially-relevant conditions.