Ising Machines for Diophantine Problems in Physics

• URL: http://arxiv.org/abs/2206.09956v2
• Date: Tue, 19 Jul 2022 11:15:04 GMT
• Title: Ising Machines for Diophantine Problems in Physics
• Authors: Steven Abel and Luca A. Nutricati
• Abstract summary: We present methods to solve Diophantine problems on annealers based on the quadratic Ising Model. We demonstrate the method on so-called Taxicab numbers, and on the realistic problem of anomaly cancellation in $U(1)$ extensions of the Standard Model.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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