Title:  Generalized quantum signal processing and non-linear Fourier transform are equivalent Speaker:  Lorenzo Laneve (Università della Svizzera Italiana) Date & Time:  September 18, 2025, 2:00pm Where to Attend: Virtual Via Zoom: https://umd.zoom.us/j/9893676372?pwd=VVNOd2xNZ3FCblk4aFdTMjkzTllvQT09&omn=98702890920 Meeting ID: 989 367 6372 Passcode: abc123
Quantum signal processing (QSP) is a technique that was shown to unify and simplify many new and known quantum algorithms. Its powerfulness lies in the possibility of carrying out eigenvalue or singular value transformations of block-encoded matrices. Recent works have found a connection between QSP and non-linear Fourier analysis, showing that a QSP protocol for a desired transformation can be stably computed by inverting the so-called non-linear Fourier transform (NLFT). In this work we strengthen the connection between NLFT and QSP, by showing that the NLFT over general complex sequences can be turned into a generalized QSP (GQSP) protocol [Motlagh, Wiebe ’24] and viceversa. In other words, the full theory of single-qubit QSP and the theory of NLFT over SU(2) are the same, giving the former a solid mathematical foundation. In this talk I will introduce both (G)QSP and NLFT and show how QSP benefits from this insight.
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