Julien Mellaerts | Searcharxiv

arXiv2025

Quantum Prime Factorization: A Novel Approach Based on Fermat Method

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.

cs.CR↗

arXiv2023

Quantum-inspired anomaly detection, a QUBO formulation

Anomaly detection is a crucial task in machine learning that involves identifying unusual patterns or events in data. It has numerous applications in various domains such as finance, healthcare, and cybersecurity. With the advent of quantum computing, there has been a growing interest in developing quantum approaches to anomaly detection. After reviewing traditional approaches to anomaly detection relying on statistical or distance-based methods, we will propose a Quadratic Unconstrained Binary Optimization (QUBO) model formulation of anomaly detection, compare it with classical methods, and discuss its scalability on current Quantum Processing Units (QPU).

quant-ph↗