Given the fundamental importance of combinatorial optimization across many diverse domains, there has been widespread interest in the development of unconventional physical computing architectures that can deliver better solutions with lower resource costs. However, a theoretical understanding of their performance remains elusive. We develop such understanding for the case of the coherent Ising machine (CIM), a network of optical parametric oscillators that can be applied to any quadratic unconstrained binary optimization problem. We focus on how the CIM finds low-energy solutions of the Sherrington-Kirkpatrick spin glass. As the laser gain of this system is annealed, the CIM interpolates between gradient descent on coupled soft spins to descent on coupled binary spins. By combining the Kac-Rice formula, the replica method, and supersymmetry breaking, we develop a detailed understanding of the evolving geometry of the high-dimensional energy landscape of the CIM as the laser gain increases, finding several phase transitions in the landscape, from flat to rough to rigid. Additionally, we develop a novel cavity method that provides a geometric interpretation of supersymmetry breaking in terms of the reactivity of a rough landscape to specific external perturbations. Our energy landscape theory successfully matches numerical experiments, provides geometric insights into the principles of CIM operation, and yields optimal annealing schedules. Published by the American Physical Society 2024

中文翻译：

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几何景观退火作为相干 Ising 机器的优化原则


鉴于组合优化在许多不同领域中的重要性，人们对开发非常规物理计算架构产生了广泛的兴趣，这些架构可以以更低的资源成本提供更好的解决方案。然而，对它们性能的理论理解仍然难以捉摸。我们针对相干 Ising 机 （CIM） 的情况进行了这样的理解，CIM 是一个光学参量振荡器网络，可以应用于任何二次无约束二进制优化问题。我们重点介绍 CIM 如何找到 Sherrington-Kirkpatrick 旋转玻璃的低能耗解决方案。当该系统的激光增益退火时，CIM 在耦合软自旋的梯度下降与耦合二进制自旋的下降之间进行插值。通过结合 Kac-Rice 公式、复制方法和超对称性打破，我们详细了解了随着激光增益的增加，CIM 高维能量景观的演变几何形状，在景观中发现了几个相变，从平面到粗糙再到刚性。此外，我们开发了一种新的空腔方法，该方法根据粗糙景观对特定外部扰动的反应性，对超对称性打破进行几何解释。我们的能源景观理论成功地匹配了数值实验，提供了对 CIM 操作原理的几何见解，并产生了最佳的退火时间表。 美国物理学会 2024 年出版