Quantum system decomposition for the semi-classical quantum Fourier transform

For classical simulation, the quantum Fourier transform (QFT) requires very large matrix operations. Previous work has shown that the semi-classical quantum Fourier transform (SCQFT) can use these individual coefficients to perform the QFT using only single-quantum bit (qubit) unitary gates and measurement operators. However, the SCQFT requires these individual decomposed qubits of the quantum system as input to the algorithm. We devise two methods to find separable approximations of quantum systems to serve as inputs to the SCQFT. We introduce an application of the approach on classical radio frequency signals represented through a quantum model. The resulting decomposition and QFT are computed on several simulated results, and an example is given using an experimental signal.