Prime factorization using quantum annealing and computational algebraic geometry

TL;DR

This paper introduces a new scalable algorithm that combines quantum annealing and computational algebraic geometry to factorize numbers, successfully factoring all bi-primes up to just over 200,000 using a quantum processor.

Contribution

It presents a novel hybrid algorithm that integrates quantum annealing with computational algebraic geometry for prime factorization, achieving the largest number factored with a quantum processor to date.

Findings

Successfully factored all bi-primes up to just over 200,000.

Demonstrated the effectiveness of combining quantum annealing with algebraic geometry.

Achieved the largest number factored using a quantum processor so far.

Abstract

We investigate prime factorization from two perspectives: quantum annealing and computational algebraic geometry, specifically Gr\"obner bases. We present a novel scalable algorithm which combines the two approaches and leads to the factorization of all bi-primes up to just over $200 \, 000$, the largest number factored to date using a quantum processor.