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        "description":"Quantum Signal Processing (QSP) is an algorithmic process by which one represents a signal $f:[0,1] \\to (-1,1)$ as the upper left entry of a product of SU(2) matrices parametrized by the input variable $x \\in [0,1]$ and some \"phase factors'' $\\{\\psi_k\\}_{k \\geq 0}$ depending on $f$. We show that, after a change of variables, QSP is actually the SU(2)-valued nonlinear Fourier transform, and the phase factors correspond to the nonlinear Fourier coefficients. By exploiting a nonlinear Plancherel identity and using some basic spectral theory, we show that QSP can be done for any signal f satisfying the log integrability condition\r\n\r\n\\int\\limits_{0} ^1 \\log (1-f(x)^2) \\frac{dx}{\\sqrt{1-x^2}} > - \\infty .\r\n\r\nEmail eblackst@umich.edu for the zoom link.",
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