Calvanese Strinati Marcello, Bello Leon, Dalla Torre Emanuele G, Pe'er Avi
Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel.
Dipartimento di Fisica, Università di Roma "La Sapienza," Piazzale Aldo Moro 5, I-00185 Rome, Italy.
Phys Rev Lett. 2021 Apr 9;126(14):143901. doi: 10.1103/PhysRevLett.126.143901.
We study large networks of parametric oscillators as heuristic solvers of random Ising models. In these networks, known as coherent Ising machines, the model to be solved is encoded in the coupling between the oscillators, and a solution is offered by the steady state of the network. This approach relies on the assumption that mode competition steers the network to the ground-state solution of the Ising model. By considering a broad family of frustrated Ising models, we show that the most efficient mode does not correspond generically to the ground state of the Ising model. We infer that networks of parametric oscillators close to threshold are intrinsically not Ising solvers. Nevertheless, the network can find the correct solution if the oscillators are driven sufficiently above threshold, in a regime where nonlinearities play a predominant role. We find that for all probed instances of the model, the network converges to the ground state of the Ising model with a finite probability.
我们将参数振荡器的大型网络作为随机伊辛模型的启发式求解器进行研究。在这些被称为相干伊辛机的网络中，待求解的模型被编码在振荡器之间的耦合中，并且网络的稳态提供了一个解决方案。这种方法依赖于模式竞争将网络引导至伊辛模型基态解的假设。通过考虑一类广泛的受挫伊辛模型，我们表明最有效的模式通常并不对应于伊辛模型的基态。我们推断接近阈值的参数振荡器网络本质上不是伊辛求解器。然而，如果振荡器被驱动到足够高于阈值的状态，在非线性起主要作用的 regime 中，网络可以找到正确的解决方案。我们发现对于该模型的所有探测实例，网络以有限概率收敛到伊辛模型的基态。
