Inverse nonlinear fast Fourier transform on SU(2) with applications to quantum signal processing
Year: 2025
Type: preprint
Abstract: The nonlinear Fourier transform (NLFT) extends the classical Fourier transform by replacing addition with matrix multiplication. While the NLFT on $\mathrm{SU}(1,1)$ has been widely studied, its $\mathrm{SU}(2)$ variant has only recently attracted attention due to emerging applications in quantum signal processing (QSP) and quantum singular value transformation (QSVT). In this paper, we investigate the inverse NLFT on $\mathrm{SU}(2)$ and establish the numerical stability of the layer stripping algorithm for the first time under suitable conditions. Furthermore, we develop a fast and numerically stable algorithm, called inverse nonlinear fast Fourier transform, for performing inverse NLFT with near-linear complexity. This algorithm is applicable to computing phase factors for both QSP and the generalized QSP (GQSP).
Source: arXiv (Cornell University)
Authors: Ni, Hongkang, Sarkar, Rahul, Ying, Lexing, Lin, Lin
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417301689
Cites:
Cited by:
Related to: