Author:
Alexis Michel,Mnatsakanyan Gevorg,Thiele Christoph
Abstract
AbstractElucidating a connection with nonlinear Fourier analysis (NLFA), we extend a well known algorithm in quantum signal processing (QSP) to represent measurable signals by square summable sequences. Each coefficient of the sequence is Lipschitz continuous as a function of the signal.
Funder
Rheinische Friedrich-Wilhelms-Universität Bonn
Publisher
Springer Science and Business Media LLC
Reference26 articles.
1. Ablowitz, M.J., Kaup, D.J., Newell, A.C., Segur, H.: The inverse scattering transform-Fourier analysis for nonlinear problems. Stud. Appl. Math. 53(4), 249–315 (1974)
2. Beals, R., Coifman, R.R.: Scattering and inverse scattering for first order systems. Commun. Pure Appl. Math. 37(1), 39–90 (1984)
3. Rui, C., Dawei, D., András, G., Cupjin, H., and Mario, S.: Finding angles for quantum signal processing with machine precision, 2020, arXiv:2003.02831
4. Christ, M., Kiselev, A.: Maximal functions associated to filtrations. J. Funct. Anal. 179(2), 409–425 (2001)
5. Andrew, M.C., Dmitri, M., Yunseong, N., Neil, J.R., and Yuan, S.: Toward the first quantum simulation with quantum speedup. In: Proceedings of the National Academy of Sciences 115 (2018), 38, pp. 9456–9461