[en] Solving Helmholtz problems using finite elements leads to the resolution of a
linear system which is challenging to solve for classical computers. In this
paper, we investigate how quantum annealers could address this challenge. We
first express the linear system arising from the Helmholtz problem as a
generalized eigenvalue problem (gEVP). The obtained gEVP is mapped into
quadratic unconstrained binary optimization problems (QUBOs) which we solve
using an adaptive quantum annealing eigensolver (AQAE) and its classical
equivalent. We identify two key parameters in the success of AQAE for solving
Helmholtz problems: the system condition number and the integrated control
errors (ICE) in the quantum hardware. Our results show that a large system
condition number implies a finer discretization grid for AQAE to converge,
leading to larger QUBOs and that AQAE is either tolerant or not with respect to
ICE depending on the gEVP.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Remi, Arnaud ; Université de Liège - ULiège > Montefiore Institute of Electrical Engineering and Computer Science
Damanet, François ; Université de Liège - ULiège > Complex and Entangled Systems from Atoms to Materials (CESAM)
Geuzaine, Christophe ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Applied and Computational Electromagnetics (ACE)
Language :
English
Title :
Solving Helmholtz problems with finite elements on a quantum annealer
