Infinite quantum signal processing for arbitrary Szeg\H{o} functions
Abstract
We provide a complete solution to the problem of infinite quantum signal processing for the class of Szeg\H{o} functions, which are functions that satisfy a logarithmic integrability condition and include almost any function that allows for a quantum signal processing representation. We do so by introducing a new algorithm called the Riemann-Hilbert-Weiss algorithm, which can compute any individual phase factor independent of all other phase factors. Our algorithm is also the first provably stable numerical algorithm for computing phase factors of any arbitrary Szeg\H{o} function. The proof of stability involves solving a Riemann-Hilbert factorization problem in nonlinear Fourier analysis using elements of spectral theory.
Cite
@article{arxiv.2407.05634,
title = {Infinite quantum signal processing for arbitrary Szeg\H{o} functions},
author = {Michel Alexis and Lin Lin and Gevorg Mnatsakanyan and Christoph Thiele and Jiasu Wang},
journal= {arXiv preprint arXiv:2407.05634},
year = {2026}
}
Comments
45 pages, 5 figures. Final version published in Communications on Pure and Applied Mathematics