**DLR institute**

# ToQuaFlics

## Towards Quantum Fluid Dynamics

## Objective

We are investigating ways in which the flow around aircraft can be simulated more efficiently and faster with quantum computers than with classical supercomputers, and what requirements must the hardware meet in order to do so.

The simulation of aerodynamics during take-off, landing or cruise plays a fundamental role in the development of new aircraft. In order to accelerate the introduction of innovative technologies for more economical, environmentally friendly and quiet flying, and to better manage technological risks, a very large number of highly accurate simulations must be performed to assess different aircraft configurations. These simulations are very time-consuming and expensive, even on today’s supercomputers.

Since no exact analytical solutions for the equations of fluid mechanics are known for complicated application cases such as the flow around airplanes, we want to investigate which type of approximation of the equations is suitable for solution on quantum computers and which requirements the hardware has to fulfill in order to solve relevant problems in aerodynamics. For this purpose, we use quantum simulators and real quantum computers of the DLR QCI.

## Motivation

The aviation industry faces the challenge of having to make significant contributions to achieving the ambitious global climate and environmental targets. To achieve this, future aircraft must consume significantly less fuel than today’s or use more environmentally friendly engines, and also be quieter, especially during takeoff and landing. In order to be able to assess these properties as early as possible in the development of a new aircraft, a very large number of computer simulations are required, which are barely feasible even on today’s high-performance computers.

Accelerating the simulations, which can only be achieved through the use of quantum computers, promises to close this gap in the future. Unexpected characteristics of an aircraft that would only become evident later in flight testing can be uncovered in advance through a large number of simulations and remedied during the design process. As a vision, a complete flight from takeoff to landing could be simulated on a quantum computer long before the real first flight, thus creating an accurate image of the aircraft and its environmental effects in advance.

## Innovation

The simulations of the various flight conditions are based on solving complex mathematical equations describing the interaction between the surrounding air and the aircraft. Classically, these equations are numerically approximated in an approximate form and solved using increasingly finely subdivided computational grids. A simulation becomes more expensive the finer the subdivision of the flow domain. These approaches seem unsuitable for quantum computing. Instead, the focus of the methods investigated in the project is to merge machine learning methods and quantum computing.

This focuses on the use of neural networks and variational algorithms. The approach is based on the fact that a solution of the considered equation can be approximated by a neural network. This universal approximation capability inspires the development of a data-driven solution to these equations. The idea of the solution strategy is to reformulate the problem arising from the equation in such a way that an equivalent minimization problem is solved. Complementary to this exist parameterized quantum circuits, sometimes called quantum neural networks. The study of how these topics can be brought together to make quantum computing useful for flow simulation, among other topics, is an important core of the project.