Ising Machines for Diophantine Problems in Physics

Abel, Steven A.; Nutricati, Luca A.

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.

Citation

Abel, S. A., & Nutricati, L. A. (2022). Ising Machines for Diophantine Problems in Physics. Fortschritte der Physik, 70(11), Article 2200114. https://doi.org/10.1002/prop.202200114

• Journal Article Type: Article
• Online Publication Date: Sep 11, 2022
• Publication Date: Nov 7, 2022
• Deposit Date: Oct 7, 2022
• Publicly Available Date: Oct 25, 2022
• Journal: Fortschritte der Physik
• Print ISSN: 0015-8208
• Electronic ISSN: 1521-3978
• Publisher: Wiley-VCH Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 70
• Issue: 11
• Article Number: 2200114
• DOI: https://doi.org/10.1002/prop.202200114
• Public URL: https://durham-repository.worktribe.com/output/1190109