Quantum linear system algorithm for solving an ill-posed quasi-linear elliptic problem by preconditioning operator

• Published in: European physical journal plus Vol. 140; no. 5; p. 467
• Main Authors: Salehi Shayegan, Amir Hossein, Dejam, Laya
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 31.05.2025; Springer Nature B.V
• Subjects: Algorithms; Applied and Technical Physics; Atomic; Complex Systems; Condensed Matter Physics; Data compression; Discretization; Eigenvalues; Expected values; Finite element analysis; Finite element method; Fourier transforms; Ill-conditioned problems (mathematics); Linear systems; Mathematical and Computational Physics; Molecular; Operators (mathematics); Optical and Plasma Physics; Physics; Physics and Astronomy; Preconditioning; Regular Article; Sobolev space; Sparsity; Theoretical

The HHL quantum algorithm for solving a well-conditioned linear system of equations provides an exponential speedup over the best classical methods. To be exact, in the quantum algorithm to achieve exponential speedup, the condition number of the matrix can scale at most poly logarithmically with th...