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Ising Machines for Diophantine Problems in Physics

Abel, Steven A.; Nutricati, Luca A.

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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.


Abel, S. A., & Nutricati, L. A. (2022). Ising Machines for Diophantine Problems in Physics. Fortschritte der Physik, 70(11), Article 2200114.

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


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Copyright Statement
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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