In this work, we experimentally demonstrate an integrated circuit (IC) of 30 relaxation oscillators with reconfigurable capacitive coupling to solve the NP-Hard Maximum Cut (Max-Cut) problem. We show that under the influence of an external second-harmonic injection signal, the oscillator phases exhibit a bi-partition which can be used to calculate a high quality approximate Max-Cut solution. Leveraging the all-to-all reconfigurable coupling architecture, we experimentally evaluate the computational properties of the oscillators using randomly generated graph instances of varying size and edge density . Further, comparing the Max-Cut solutions with the optimal values, we show that the oscillators (after simple post-processing) produce a Max-Cut that is within 99% of the optimal value in 28 of the 36 measured graphs; importantly, the oscillators are particularly effective in dense graphs with the Max-Cut being optimal in seven out of nine measured graphs with edge density 0.8. Our work marks a step towards creating an efficient, room-temperature-compatible non-Boolean hardware-based solver for hard combinatorial optimization problems.

中文翻译：

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解决最大切割问题的可重构耦合振荡器平台的实验演示

在这项工作中，我们通过实验证明了 30 个张弛振荡器的集成电路 (IC) 具有可重构电容耦合，以解决 NP-Hard 最大切割 (Max-Cut) 问题。我们表明，在外部二次谐波注入信号的影响下，振荡器相位表现出双分区，可用于计算高质量的近似 Max-Cut 解。利用全方位可重构耦合架构，我们使用随机生成的不同大小和边缘密度的图实例，通过实验评估振荡器的计算特性。此外，将 Max-Cut 解与最优值进行比较，我们表明振荡器（经过简单的后处理）产生的 Max-Cut 在 36 个测量图中的 28 个图中处于最优值的 99% 以内；重要的，振荡器在密集图中特别有效，Max-Cut 在边密度为 0.8 的九个测量图中有七个是最佳的。我们的工作标志着朝着为硬组合优化问题创建高效、室温兼容的非布尔硬件求解器迈出了一步。