Stable factorization for phase factors of quantum signal processing

Abstract: This paper proposes a new factorization algorithm for computing the phase factors of quantum signal processing. The proposed algorithm avoids root finding of high degree polynomials by using a key step of Prony's method and is numerically stable in the double precision arithmetics. Experimental results are reported for Hamiltonian simulation, eigenstate filtering, matrix inversion, and Fermi-Dirac operator.