Welcome to the Future of Quantum in Computational Fluid Dynamics!

by Amara Graps

Quantum in Computational Fluid Dynamics (QCFD) has taken the research world by storm in recent times. While Rolls Royce’s collaborations and use cases are well-known, there are other groundbreaking examples being explored in pilot projects today. CFD plays a crucial role in various industries such as automotive, aerospace, civil engineering, wind energy, and defense. These industries are collectively known as ‘Advanced Industries’ in the realm of Quantum Information (QI) as shown in the figure below.

One noteworthy example of the impact of classical CFD is seen in SpaceX’s rocket design and optimization, leading to near-perfect launch performances like the one that propelled the ESA Hera asteroid defense mission on its interplanetary journey on October 7.

Quantum CFD Scientific Literature

Delving into the algorithms, a primary source for CFD research is Dalzell et al. (2023), offering insights into computational fluid dynamics. Most simulations focus on air or fluid movement on solid objects, but it’s essential to replicate other processes like foaming. Quantum algorithms have shown promise in handling large CFD simulations, with some notable approaches highlighted in the following table. The papers are grouped based on their approaches for a better understanding.

QCFD Introductions

• Bharadwaj et al. (2020) provides a broad introduction to quantum scientific computing with a focus on CFD implementation using various quantum devices, making it a great starting point for beginners.

• Gaitan’s articles (2020, 2021) explore steps involved in solving Navier-Stokes equations on quantum computers, emphasizing techniques like Kacewicz quantum ODE algorithm.

A New Middle Ground

GQI’s Quantum Algorithms Outlook report highlights a ‘new middle ground’ approach in quantum computing:

While VQE (low depth for NISQ applications) is often viewed in contrast to QPE (high depth requiring FTQC), interest has grown in other techniques that might offer a middle ground.

QCFD algorithms seem to fit this category, bridging the gap between Linear Algebra-Forward and Native Quantum classes, adapting successfully to NISQ devices.

QCFD Algorithms: Linear Algebra-Forward

• Gourianov et al. (2021) utilize tensor network theory for structure-resolving turbulent flow, showcasing a significant reduction in parameters compared to direct numerical simulation.
• Kiffner and Jaksch (2023) apply a tensor network algorithm to reproduce stationary state data for flow dynamics, achieving exponential speed benefits using appropriate quantum algorithms.
• Jaksch et al. (2022) showcase the application of variational quantum algorithms (VQAs) to CFD, demonstrating quantum advantages in solving nonlinear optimization problems.

• Bosco et al. (2024) describe the Hybrid Quantum-Classical Finite Method (HQCFM), proving high accuracy in solving complex fluid equations, showcasing quantum computers’ potential over conventional methods.
• Oz et al. (2022) present a QCFD solver tailored for Burgers’ equation, exhibiting effectiveness in handling various flow scenarios.

• Lapworth et al. (2022) introduce a hybrid quantum-classical CFD methodology using the HHL algorithm to solve linear systems effectively.
• Succi et al. (2024) explore the functional Liouville formulation for ensemble simulations on quantum computers, emphasizing the need for reliable qubit performance.

QCFD Algorithms: Quantum Native

• Itani et al. (2023) unveil a full quantum algorithm for the Lattice Boltzmann method, offering efficient qubit scalability for simulating fluid flows.
• Li et al. (2024) demonstrate the efficient simulation of turbulence using quantum solvers, emphasizing a significant improvement over classical algorithms.

Quantum Computing Use Cases Live Tracker

These studies highlight the integration of quantum and classical components to enhance CFD algorithms, setting a path for exciting applications in Quantum Information. Stay tuned for Parts 2 and 3 to explore advanced Quantum CFD Use Cases!

If you are interested to learn more, please don’t hesitate to contact info@global-qi.com.

October 8, 2024