Ising Machines for Diophantine Problems in Physics

Abstract

Diophantine problems arise frequently in physics, in for example anomaly cancellation conditions, string consistency conditions and so forth. We present methods to solve such problems to high order on annealers that are based on the quadratic Ising Model. This is the intrinsic framework for both quantum annealing and for common forms of classical simulated annealing. We demonstrate the method on so-called Taxicab numbers (discovering some apparently new ones), and on the realistic problem of anomaly cancellation in $U(1)$ extensions of the Standard Model.

13 pages, 5 figures

References in corpus (9)

• CP Violation in Leptonic Rare $B_s^0$ Decays as a Probe of New Physics
• Computational complexity of the landscape I
• Machine Learning in the String Landscape
• Evolving neural networks with genetic algorithms to study the String Landscape
• Branes with Brains: Exploring String Vacua with Deep Reinforcement Learning
• Genetic Algorithms and the Search for Viable String Vacua
• Getting CICY High
• Breeding realistic D-brane models
• Kahler Moduli Stabilization and the Propagation of Decidability