Quantum Prime Factorization: A Novel Approach Based on Fermat Method

Abstract: In this paper, we introduce a novel quantum algorithm for the factorization of composite odd numbers. This work makes two significant contributions. First, we present a new improvement to the classical Fermat method, fourfold reducing the computational complexity of factoring. Second, we reformulate Fermat factorization method as an optimization problem suitable for Quantum Annealers which allowed us to factorize 8,689,739, the biggest number ever factorized using a quantum device to our knowledge.