2024/10/08 by Hongkang Ni, Lexing Ying, Ni, Hongkang +1 · 9 citations
Computer Science · #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2410.06409
This paper presents two efficient and stable algorithms for recovering phase factors in quantum signal processing (QSP), a crucial component of many quantum algorithms. The first algorithm, the ``Half Cholesky" method, which is based on nonlinear Fourier analysis and fast solvers for structured matrices, demonstrates robust performance across all regimes. The second algorithm, ``Fast Fixed Point Iteration," provides even greater efficiency in the non-fully-coherent regime. Both theoretical analysis and numerical experiments demonstrate the significant advantages of these new methods over all existing approaches.