Stable factorization for phase factors of quantum signal processing

TL;DR

This paper introduces a numerically stable factorization algorithm for quantum signal processing phase factors that avoids high-degree polynomial root finding, demonstrated through various quantum simulation applications.

Contribution

A novel factorization method leveraging Prony's technique that enhances numerical stability in quantum signal processing tasks.

Findings

Effective in Hamiltonian simulation

Improves stability over existing methods

Applicable to multiple quantum algorithms

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.