How to represent a function in a quantum computer

We define the SU(2)-valued nonlinear Fourier transform and explain its connection with quantum signal processing, a quantum algorithm on one qubit. In particular, we provide an algorithm to compute the inverse nonlinear Fourier transform in a special case, which allows one to "represent" most functions in a quantum computer. Finally, we mention the several qubit analog with the SU(2n)-valued nonlinear Fourier transform. This talk includes joint work with L. Becker, L. Lin, G. Mnatsakanyan, D. Oliveira e Silva, C. Thiele and J. Wang.