Quantum Signal Processing via Hamiltonian Neural Networks

We show that projectors proposed in the framework of Quantum Signal Processing can be implemented as Hamiltonian Neural Network based orthogonal filters. Moreover, such filters can be used as Universal Signal Processors. The structures of such processors rely on a family of Hurwitz-Radon matrices. To illustrate, we propose a procedure of nonlinear mapping synthesis. The problem of anticipation is reformulated as a problem of supervised learning.