An Intuitive Implementation of a Quantum Linear Solver for Electrostatic Propulsion for Spacecraft

The need for a resilient and enhanced satellite constellation is crucial for the scientific and societal challenges of the future. Resilient satellites for Low Earth Orbit (LEO) can also be achieved through advanced propulsion systems, namely Electric Propulsion Systems (EPs). High-precision design tools would be extremely useful for understanding complex phenomena such as particle kinetics, transport, and acceleration in advanced propulsion systems for spacecraft. Quantum methods have the potential to increase the speed of simulation and, more interestingly, allow for further physical phenomena to be implemented in the numerical experiments. The purpose of this paper is to provide a step-by-step guide to applying quantum algorithms to practical engineering problems. Quantum computing addresses time complexity issues in these simulations to look at small-scale, higher-resolution problems.In our case, it is advanced satellite propulsion systems, and the current results are promising. EP systems that accelerate the propellant by an electric field fall under the electrostatic group; these thrusters include Hall Effect Thrusters (HETs) and Electrospray Thrusters (ESPs). The calculation of the electric potential, central to electrospray and Hall Effect Thrusters, is a stepping stone in the implementation of quantum computing and is the focus of the current paper. The expectation is to also provide guidance for other applications.