Fast Phase Factor Finding for Quantum Signal Processing

Abstract. This paper presents two efficient and stable algorithms for recovering phase factors in quantum signal processing (QSP), a crucial component of many quantum information processing applications. The first algorithm, the Half Cholesky (HC) 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 (FFPI), offers 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. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://github.com/HongkangNi/Fast-Phase-Factor-Finding-for-QSP and in the supplementary materials ( Fast-Phase-Factor-Finding-for-QSP-main.zip [135KB]). [Formula: see text]