Arbeitsgemeinschaft: Quantum Signal Processing and Nonlinear Fourier Analysis

Abstract

A pivotal algorithm in quantum signal processing represents a real-valued function as a specific entry in a product of $SU(2)$ matrices, where an argument matrix alternates with a sequence of coefficient matrices. Recently, this framework has been identified as a nonlinear Fourier series, a concept studied across various mathematical disciplines. This Arbeitsgemeinschaft explored the intersection of quantum computing and harmonic analysis, emphasizing the potential of this connection.