Prime factorization using quantum annealing and computational algebraic geometry

Erratum: Prime factorization using quantum annealing and computational algebraic geometry

We investigate prime factorization from two perspectives: quantum annealing and computational algebraic geometry, specifically Gröbner bases. We present a novel autonomous algorithm which combines the two approaches and leads to the factorization of all bi-primes up to just over 200000, the largest number factored to date using a quantum processor. We also explain how Gröbner bases can be used ...

Computational algebraic geometry

Algebraic geometry is a powerful combination of algebra and geometry, with a rich history and many applications, both theoretical and practical. It also has an intimidating reputation. Hence it is important to have a variety of introductory texts at different levels of sophistication. We will see that Schenck's book offers an interesting path into this wonderful subject. 1. What is algebraic ge...

Computational Algebraic Geometry

Prime Factorization on a Quantum Computer

complete problems eeciently is a Holy Grail of theoretical computer science which very few people expect to be possible on a classical computer. Finding polynomial-time algorithms for solving these problems on a quantum computer would be a momentous discovery. There are some weak indications that quantum computers are not powerful enough to solve NP-complete problems Bennett et al. 1996a], but ...

38 COMPUTATIONAL and QUANTITATIVE REAL ALGEBRAIC GEOMETRY

Computational and quantitative real algebraic geometry studies various algorithmic and quantitative questions dealing with the real solutions of a system of equalities, inequalities, and inequations of polynomials over the real numbers. This emerging field is largely motivated by the power and elegance with which it solves a broad and general class of problems arising in robotics, vision, compu...