Work

The quantum Euclid algorithm and its application to factoring

Year: 2026

Type: article

Abstract: We present a quantum implementation of the Euclid algorithm for calculating the Greatest Common Divisor when one of the integers involved is a compound of two odd-valued primes. We discuss a possible application to the quantum factoring problem, for which modular exponentiation is no longer required, and the factors are revealed directly by measurements, although the method does not scale for large numbers in a favourable manner.

Source: EPJ Quantum Technology

DOI: 10.1140/epjqt/s40507-026-00587-8

Authors: Asma Al-Qasimi, Daniel F. V. James

Institutions: University of Liverpool, University of Toronto

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,190

Funders: Natural Sciences and Engineering Research Council of Canada, Engineering and Physical Sciences Research Council