– Europe/Lisbon
Room P3.10, Mathematics Building
— Online
Diogo Oliveira e Silva, CAMGSD & Instituto Superior Técnico
Quantum signal processing and nonlinear Fourier analysis I
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 compactly supported sequences and square-summable sequences on the half-line, and prove that the inverse map is well-defined on $SU(2n)$-valued functions whose diagonal $n \times n$ blocks are outer matrix functions. As an application, we prove infinite generalized quantum signal processing in the fully coherent regime.
Bibliography:
- L. Lin, Lecture Notes on Quantum Algorithms for Scientific Computation, https://arxiv.org/pdf/2201.08309
- D. Oliveira e Silva, Inequalities in nonlinear Fourier analysis. CIM Bulletin 38-39 (2017), 31-35
- T. Tao and C. Thiele, Nonlinear Fourier Analysis, https://arxiv.org/abs/1201.5129