Not all computing problems are created equal. The inherent complexity of processing certain classes of problems using digital computers has inspired the exploration of alternate computing paradigms. Coupled oscillators exhibiting rich spatio-temporal dynamics have been proposed for solving hard optimization problems. However, the physical implementation of such systems has been constrained to small prototypes. Consequently, the computational properties of this paradigm remain inadequately explored. Here, we demonstrate an integrated circuit of thirty oscillators with highly reconfigurable coupling to compute optimal/near-optimal solutions to the archetypally hard Maximum Independent Set problem with over 90% accuracy. This platform uniquely enables us to characterize the dynamical and computational properties of this hardware approach. We show that the Maximum Independent Set is more challenging to compute in sparser graphs than in denser ones. Finally, using simulations we evaluate the scalability of the proposed approach. Our work marks an important step towards enabling application-specific analog computing platforms to solve computationally hard problems.

并非所有的计算问题都是平等的。使用数字计算机处理某些类别问题的固有复杂性激发了对替代计算范式的探索。已经提出了表现出丰富时空动态的耦合振荡器来解决硬优化问题。但是，此类系统的物理实现仅限于小型原型。因此，这种范式的计算特性仍未得到充分探索。在这里，我们展示了具有高度可重构耦合的三十个振荡器的集成电路，以超过 90% 的准确度计算原型困难的最大独立集问题的最佳/接近最佳解决方案。该平台独特地使我们能够表征这种硬件方法的动态和计算特性。我们表明，在稀疏图中计算最大独立集比在密集图中更具挑战性。最后，我们使用模拟来评估所提出方法的可扩展性。我们的工作标志着朝着使特定于应用程序的模拟计算平台能够解决计算难题迈出了重要的一步。