Quantum algorithms for the solution of partial differential equations with applications in the aerospace sector

Partial Differential Equations (PDEs) are transversal to all scientific fields such as aero- and fluido-dynamics, plasma physics and finance. A technique for efficiently finding numerical approximations to the PDEs’ solutions is based on the introduction of a finite mesh to discretize the space of the parameters, the so-called Finite Element Method (FEM). With this approach the solution of the PDEs ultimately reduces to the solution of a large system of linear equations. This thesis explores the potential of quantum algorithms, with a specific focus on the Harrow-Hassidim-Lloyd (HHL) algorithm, in accelerating the solution of PDEs relevant in the context of electromagnetic simulations for Earth Observation (EO). We present a comprehensive implementation of the HHL algorithm, that allows full control over input parameters and associated subroutines. By classically emulating HHL, we critically examine its limitations, and highlight the regimes where a speedup over classical methods is expected. This work represents the output of a six month internship with the research division of Thales Alenia Space Italia (TASI), aimed at exploring potential applications of quantum computing in the EO scenario.