Quantum Machine Learning for Computational Fluid Dynamics

Cesar A. Amaral, Vinícius L. Oliveira, Juan P. L. C. Salazar +1 more

Achraf Hsain, F. M. Abbou

This paper presents the first application of quantum generative models to learned latent space representations of computational fluid dynamics (CFD) data. While recent work has explored quantum models for learning statistical properties of fluid systems, the combination of discrete latent space compression with quantum generative sampling for CFD remains unexplored. We develop a GPU-accelerated Lattice Boltzmann Method (LBM) simulator to generate fluid vorticity fields, which are compressed into a discrete 7-dimensional latent space using a Vector Quantized Variational Autoencoder (VQ-VAE). The central contribution is a comparative analysis of quantum and classical generative approaches for modeling this physics-derived latent distribution: we evaluate a Quantum Circuit Born Machine (QCBM) and Quantum Generative Adversarial Network (QGAN) against a classical Long Short-Term Memory (LSTM) baseline. Under our experimental conditions, both quantum models produced samples with lower average minimum distances to the true distribution compared to the LSTM, with the QCBM achieving the most favorable metrics. This work provides: (1)~a complete open-source pipeline bridging CFD simulation and quantum machine learning, (2)~the first empirical study of quantum generative modeling on compressed latent representations of physics simulations, and (3)~a foundation for future rigorous investigation at this intersection.

Jeffrey Yepez

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.

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.

Peyman Givi