Coupled electronic oscillators have recently been explored as a compact, integrated circuit- and room temperature operation- compatible hardware platform to design Ising machines. However, such implementations presently require the injection of an externally generated second-harmonic signal to impose the phase bipartition among the oscillators. In this work, we experimentally demonstrate a new electronic autaptic oscillator (EAO) that uses engineered feedback to eliminate the need for the generation and injection of the external second harmonic signal to minimize the Ising Hamiltonian. The feedback in the EAO is engineered to effectively generate the second harmonic signal internally. Using this oscillator design, we show experimentally, that a system of capacitively coupled EAOs exhibits the desired bipartition in the oscillator phases, and subsequently, demonstrate its application in solving the computationally hard Maximum Cut (MaxCut) problem. Our work not only establishes a new oscillator design aligned to the needs of the oscillator Ising machine but also advances the efforts to creating application specific analog computing platforms.

中文翻译：

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创建没有外部注射锁定的基于电子振荡器的 Ising 机器

耦合电子振荡器最近被探索为一种紧凑的、集成电路和室温操作兼容的硬件平台来设计 Ising 机器。然而，此类实现目前需要注入外部生成的二次谐波信号以在振荡器之间施加相位二分。在这项工作中，我们通过实验证明了一种新的电子自调振荡器 (EAO)，它使用工程反馈来消除对外部二次谐波信号的生成和注入的需要，以最小化伊辛哈密顿量。EAO 中的反馈经过精心设计，可在内部有效地生成二次谐波信号。使用这种振荡器设计，我们通过实验表明，电容耦合 EAO 系统在振荡器相位中表现出所需的二分，随后，演示其在解决计算困难的最大切割 (MaxCut) 问题中的应用。我们的工作不仅建立了符合振荡器 Ising 机需求的新振荡器设计，而且还推动了创建特定于应用程序的模拟计算平台的努力。