Generalized Quantum Signal Processing and Non-Linear Fourier Transform Are Equivalent

Explore the mathematical equivalence between generalized quantum signal processing and non-linear Fourier transforms in this 54-minute conference talk. Discover how quantum signal processing (QSP) serves as a unifying technique for quantum algorithms through eigenvalue and singular value transformations of block-encoded matrices. Learn about the established connection between QSP and non-linear Fourier analysis, where QSP protocols can be computed by inverting the non-linear Fourier transform (NLFT). Examine the strengthened relationship demonstrating that NLFT over general complex sequences can be converted into generalized QSP protocols and vice versa. Understand how the complete theory of single-qubit QSP and NLFT over SU(2) are mathematically identical, providing QSP with a robust theoretical foundation. Gain insights into both generalized quantum signal processing and non-linear Fourier transform concepts, and see how this equivalence advances quantum algorithm development.