Prime factorization using quantum annealing and computational algebraic geometry

In this paper 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. We also explain how Gr\"obner bases can be used to reduce the degree of Hamiltonians.