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Quantum State Preparation Representation
An SU(2n)-valued nonlinear Fourier transform
arXiv
Authors: Michel Alexis, Lars Becker, Diogo Oliveira e Silva, Christoph Thiele
Year
2026
Paper ID
4127
Status
Preprint
Abstract Read
~2 min
Abstract Words
79
Citations
N/A
Abstract
We define a nonlinear Fourier transform which maps sequences of contractive n times n matrices to SU(2n)-valued functions on the circle mathbb{T}. We characterize the image of finitely supported sequences and square-summable sequences on the half-line, and construct an inverse for SU(2n)-valued functions whose diagonal n times n blocks are outer matrix functions. As an application, we relate this nonlinear Fourier transform with quantum signal processing over U(2n) and multivariate quantum signal processing.
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- This paper contributes to the Quantum State Preparation & Representation research area in the Quantum Articles archive.
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- We define a nonlinear Fourier transform which maps sequences of contractive n times n matrices to SU(2n)-valued functions on the circle mathbbT.
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