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<p>Ising machines are specialized devices designed to efficiently solve combinatorial optimization problems. Among such problems, Boolean Satisfiability (SAT) is particularly relevant in industrial applications. To solve SAT problems using Ising machines, it is crucial to incorporate higher-order interactions. However, in analog Ising machines, interactions of different orders scale unevenly with the continuous spin amplitudes, introducing imbalances that can significantly degrade performance. Here we present a numerical comparison of methods to mitigate these imbalances, evaluating time-to-solution and success rate on uniform random 3-SAT and 4-SAT instances. Our results show that the most effective approach employs spin interactions that are proportional to the signs of spins, rather than their continuous amplitudes. We further demonstrate that smooth approximations of this method make it compatible with analog hardware. These findings underscore the central role of spin-sign-based interactions in enabling robust and scalable analog Ising machine dynamics.</p>

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Discretized spin interactions enhance higher-order analog Ising machines

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年8月5日

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  • Robbe De Prins,
  • Guy Van der Sande,
  • Peter Bienstman,
  • Thomas Van Vaerenbergh

摘要

Ising machines are specialized devices designed to efficiently solve combinatorial optimization problems. Among such problems, Boolean Satisfiability (SAT) is particularly relevant in industrial applications. To solve SAT problems using Ising machines, it is crucial to incorporate higher-order interactions. However, in analog Ising machines, interactions of different orders scale unevenly with the continuous spin amplitudes, introducing imbalances that can significantly degrade performance. Here we present a numerical comparison of methods to mitigate these imbalances, evaluating time-to-solution and success rate on uniform random 3-SAT and 4-SAT instances. Our results show that the most effective approach employs spin interactions that are proportional to the signs of spins, rather than their continuous amplitudes. We further demonstrate that smooth approximations of this method make it compatible with analog hardware. These findings underscore the central role of spin-sign-based interactions in enabling robust and scalable analog Ising machine dynamics.