Fast Phase Factor Finding for Quantum Signal Processing
<|reference_start|>Fast Phase Factor Finding for Quantum Signal Processing: 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.<|reference_end|>
@article{ni2024fast,
    title={Fast Phase Factor Finding for Quantum Signal Processing},
    author={Hongkang Ni, Lexing Ying},
    journal={arXiv preprint arXiv:2410.06409},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.06409},
    primaryClass={quant-ph cs.NA math.NA}
}