Partial Differential Equations (PDEs) are transversal to all scientific fields such as aero and fluidodynamics, 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 socalled 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 HarrowHassidimLloyd (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.
Partial Differential Equations (PDEs) are transversal to all scientific fields such as aero and fluidodynamics, 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 socalled 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 HarrowHassidimLloyd (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.
Quantum algorithms for the solution of partial differential equations with applications in the aerospace sector
GRILLI, ALESSANDRO
2023/2024
Abstract
Partial Differential Equations (PDEs) are transversal to all scientific fields such as aero and fluidodynamics, 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 socalled 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 HarrowHassidimLloyd (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.File  Dimensione  Formato  

Grilli_Alessandro.pdf
accesso aperto
Dimensione
1.61 MB
Formato
Adobe PDF

1.61 MB  Adobe PDF  Visualizza/Apri 
The text of this website © Università degli studi di Padova. Full Text are published under a nonexclusive license. Metadata are under a CC0 License
https://hdl.handle.net/20.500.12608/66542