Quantum signal processing and nonlinear Fourier analysis
Michel Alexis, Gevorg Mnatsakanyan, Christoph Thiele
TL;DR
This paper explores the connection between quantum signal processing and nonlinear Fourier analysis, extending existing algorithms to represent signals with square summable sequences where coefficients vary Lipschitz continuously with the signal.
Contribution
It introduces an extension of quantum signal processing algorithms to nonlinear Fourier analysis, enabling representation of signals with continuous coefficient variation.
Findings
Extended quantum signal processing algorithms to nonlinear Fourier analysis.
Coefficients of the sequence are Lipschitz continuous functions of the signal.
Provides a new framework for representing signals in quantum computing contexts.
Abstract
Elucidating a connection with nonlinear Fourier analysis, we extend a well known algorithm in quantum signal processing to represent measurable signals by square summable sequences. Each coefficient of the sequence is Lipschitz continuous as a function of the signal.
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Taxonomy
TopicsBlind Source Separation Techniques · Quantum Information and Cryptography