标题： 耦合Kerr参量振荡器的参数不稳定图谱 显示英文标题

标题： The parametric instability landscape of coupled Kerr parametric oscillators

摘要： 耦合Kerr参数振荡器（KPOs）网络有望用于神经形态和量子计算的实现。 然而，它们丰富的分岔结构仍大多未被理解。 在这里，我们采用长期摄动理论来绘制这些网络的稳定性区域，并确定系统可以映射到伊辛模型的区域。 从两个耦合的KPO开始，我们展示了分岔如何源于全局参数驱动与KPO之间线性耦合之间的竞争。 然后我们将这一框架扩展到具有全连接等耦合的更大网络，推导出分岔转变全过程的解析表达式。 在热力学极限下，我们发现这些转变变得均匀间隔，从而形成高度规则的结构。 我们的结果揭示了KPO网络具有类似伊辛解空间的精确界限，从而为其实验实现提供了关键指导。 显示英文摘要

摘要： Networks of coupled Kerr parametric oscillators (KPOs) hold promise as for the realization of neuromorphic and quantum computation. Yet, their rich bifurcation structure remains largely not understood. Here, we employ secular perturbation theory to map the stability regions of these networks, and identify the regime where the system can be mapped to an Ising model. Starting with two coupled KPOs, we show how the bifurcations arise from the competition between the global parametric drive and linear coupling between the KPOs. We then extend this framework to larger networks with all-to-all equal coupling, deriving analytical expressions for the full cascade of bifurcation transitions. In the thermodynamic limit, we find that these transitions become uniformly spaced, leading to a highly regular structure. Our results reveal the precise bounds under which KPO networks have an Ising-like solution space, and thus provides crucial guidance for their experimental implementation.