Quantum Prime Factorization: A Novel Approach Based on Fermat Method

TL;DR

This paper introduces a new quantum algorithm that improves classical Fermat factorization and reformulates it for quantum annealers, successfully factoring a large number with a quantum device for the first time.

Contribution

It presents a novel quantum approach to Fermat factorization, significantly reducing classical complexity and enabling large number factorization on quantum hardware.

Findings

Reduced Fermat method complexity fourfold

First quantum device factorization of 8,689,739

Reformulation of Fermat as an optimization problem

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.