Accurately simulating turbulent, compressible fluids remains a major computational challenge for the aviation industry and a key to achieving future climate goals. Despite advances in computational fluid dynamics (CFD), limitations in turbulence models and the immense cost of high-fidelity simulations make scale-resolving full-aircraft simulations unrealistic. Quantum computing could overcome these barriers, as even few qubits can represent vast degrees of freedom. However, due to numerous obstacles such as the restriction to unitary operators, the read-out problem, and the limited availability of actual quantum hardware, the development of efficient algorithms for solving fluid mechanics equations is a real scientific challenge. This presentation highlights current efforts within the DLR QCI project ToQuaFlics to explore the potential of quantum computing for aerodynamic simulations.
Accurately simulating turbulent, compressible fluids remains a major computational challenge for the aviation industry and a key to achieving future climate goals. Despite advances in computational fluid dynamics (CFD), limitations in turbulence models and the immense cost of high-fidelity simulations make scale-resolving full-aircraft simulations unrealistic. Quantum computing could overcome these barriers, as even few qubits can represent vast degrees of freedom. However, due to numerous obstacles such as the restriction to unitary operators, the read-out problem, and the limited availability of actual quantum hardware, the development of efficient algorithms for solving fluid mechanics equations is a real scientific challenge. This presentation highlights current efforts within the DLR QCI project ToQuaFlics to explore the potential of quantum computing for aerodynamic simulations.
The accurate simulation of turbulent compressible fluids is a major computational challenge for the aviation industry and possibly a key technology for improving the efficiency of future aircraft so that the ambitious climate targets can be achieved. Even though great progress has been made in the field of CFD in recent decades, and simulation software is available to a wide range of users from both commercial providers and research institutes, it still has two major shortcomings: a) The accuracy of the results is usually limited by the quality of the turbulence models. Even very advanced turbulence models such as Reynolds-Stress models are not able to accurately reproduce a wide range of flows, in particular at the border of the flight envelope. For unseen test cases involving complex physical phenomena or unconventional aircraft configurations, selecting an appropriate turbulence model is often challenging and not straightforward. b) In order to overcome the shortcomings resulting from turbulence modeling, scale-resolving methods such as large eddy simulations or even direct numerical simulations are increasingly being carried out. However, the cost of these simulations for flight Reynolds numbers is so high that even under very optimistic assumptions about the development of future HPC resources and advances in algorithms, full-aircraft simulations seem unrealistic. Even though the possibilities for the use of quantum computers in CFD are still limited due to their current stage of development, they may offer the potential to accelerate calculations in such a way that scale-resolving methods for complete aircraft seem possible. Since algorithms that can be efficiently implemented on quantum computers for solving compressible nonlinear transport equations are also largely not yet available, the time is now to deal with them.
Computational Fluid Dynamics (CFD) plays a central role in mechanical system design by enabling the simulation of complex flow phenomena such as turbulence, phase transitions, and fluid–structure interactions. However, high-fidelity CFD simulations—particularly those involving turbulent and multiphase flows—are often limited by the computational cost of solving large-scale, nonlinear, and high-dimensional systems of equations. This study explores the potential of quantum-enhanced computational fluid dynamics, focusing on hybrid quantum–classical solvers as a next-generation approach to overcoming these limitations. By integrating quantum algorithms with classical numerical methods, hybrid frameworks aim to accelerate key CFD tasks such as linear system solving, optimization, and high-dimensional state exploration while preserving the stability and accuracy of established solvers. The paper examines how quantum principles such as superposition and entanglement can be leveraged to improve convergence rates and design-space exploration in turbulence modeling and multiphase flow simulations. Through a conceptual and methodological analysis, this work highlights the opportunities, current constraints, and future implications of quantum-enhanced CFD for mechanical system design, offering a forward-looking perspective on the convergence of quantum computing and fluid mechanics.
This paper presents an algorithmic quantum simulation approach to modeling complex fluid dynamics, specifically targeting the intricacies of turbulence. Traditional CFD simulations struggle to accurately capture the multi-scale dynamics inherent in turbulent flows, often requiring extensive computational resources and approximations. We introduce a novel 'Quantum Flow Lattice' – a quantum-mechanical representation of fluid motion – designed to overcome these limitations by explicitly modeling fluid dynamics across multiple scales. This research explores the feasibility of utilizing quantum algorithms to enhance the fidelity of fluid dynamics simulations, offering a potentially transformative advancement in computational fluid dynamics.
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.
High-performance computing (HPC) refers to the use of advanced computational models and technologies to significantly enhance the performance of processing highly complex problems. HPC has evolved dramatically since the first supercomputer was commissioned in the 1960s. Nowadays, HPC is characterized by the pursuit of exascale computing, i.e., the ability to perform 1018 calculations per second. In November 2024, Lawrence Livermore National Laboratory, California announced the new El Capitan System as the most powerful exascale supercomputer, capable of performing over 1.742 exaFlops. Over the past few years, HPC platforms have evolved from CPU-centric architecture to GPU-accelerated systems. Such computing capability empowers researchers to tackle a diverse array of scientific applications across numerous domains, including stock market prediction, task scheduling, weather forecasting, gene sequencing, drug discovery, and Computational Fluid Dynamics (CFD) (Netto et al., 2018; Jamshed, 2015). CFD is an applied science field that is concerned with the simulation and analysis of the physics of fluid flow using computational models and technologies. CFD finds extensive applications in diverse industries and scientific disciplines, including aircraft design optimization to facilitate the analysis of aerodynamic performance, drag reduction, and fuel efficiency enhancement (Moin and Apte, 2006). In addition, CFD plays a crucial role in oil reservoir simulation and recovery (Britto et al. 2020). Overall, CFD serves as a powerful tool for understanding and predicting fluid flow phenomena, enabling engineers and scientists to make informed decisions, optimize designs, and improve the performance of various systems and processes. Recently, Quantum Computing has emerged as a new computing approach that leverages quantum physics phenomena such as superposition and entanglement to provide computational speedup over classical computers. With the rapid progress of quantum computing, it is projected that future HPC platforms are venturing into Quantum Processing Unit (QPU)-based systems to tackle previously unsolvable problems. Several researchers have studied the potential use of quantum computing in solving complex CFD problems (Gaitan, 2020; Jaksch et al. 2023). Quantum computing can offer several advantages in CFD applications. First, quantum computing can address the exponential growth of computational complexity associated with high-resolution and turbulent flow simulations. Accordingly, more accurate and detailed simulations can be performed. For example, Berry et al. (2014) presented quantum algorithms that can effectively handle large-scale linear algebraic calculations, such as solving sparse matrix equations and eigenvalue problems, which are fundamental in CFD. Furthermore, quantum computers have the potential to accelerate optimization algorithms that facilitate faster design and optimization of fluid systems (Preskill, 2018). While quantum computing is still in its nascent stage, ongoing research in quantum hardware and algorithms demonstrates huge potential for future applications in solving complex CFD problems.
This paper explores the application of quantum-inspired algorithms to accelerate the simulation of fluid dynamics. Traditional computational fluid dynamics (CFD) methods, particularly those solving the Navier-Stokes equations, are often computationally expensive, limiting their applicability in real-time simulations and complex scenarios. This research investigates the potential of mimicking quantum phenomena, specifically wave interference and amplitude estimation, through the design and implementation of novel algorithms. The core idea is to leverage techniques inspired by quantum computing to achieve a significant speedup in solving these equations. We present a framework utilizing amplitude estimation to efficiently approximate solutions, offering a potential pathway to overcome the computational bottlenecks inherent in conventional CFD. The presented approach provides a novel methodology for simulating fluid dynamics with reduced computational cost, opening opportunities for advancements in areas such as aerospace, automotive, and weather forecasting.