论文标题
将XY Hamiltonian映射到耦合激光器网络上
Mapping the XY Hamiltonian onto a Network of Coupled Lasers
论文作者
论文摘要
近年来，人们对通过光学振荡器网络对经典自旋模型的物理实施的兴趣越来越大。但是，此映射中的一个关键缺失步骤是正式证明这种非线性动力学系统的动力学是为了最大程度地降低与自旋模型Hamiltonian等效的全局成本函数。在这里，我们引入了一个最小的动力学模型，用于散发耦合的光振荡器网络，并证明这种系统的动力学受Lyapunov函数的控制，该功能是系统的成本函数。通常，此成本函数通常是振荡器的阶段和强度的函数，并且在很大程度上取决于泵参数。如果是两分网络拓扑，则振荡器的幅度在稳态下变得相同，成本函数降低了XY Hamiltonian。但是，在非平凡网络拓扑的一般情况下，成本函数仅在强泵极限下接近XY Hamiltonian。我们表明，通过绝热调整泵参数，网络可以很大程度上避免捕获到管理成本函数的局部最小值中，并稳定在相关的XY Hamiltonian的基态中。这些结果表明，激光网络对于非常规计算的巨大潜力。
In recent years there has been a growing interest in the physical implementation of classical spin models through networks of optical oscillators. However, a key missing step in this mapping is to formally prove that the dynamics of such a nonlinear dynamical system is toward minimizing a global cost function which is equivalent with the spin model Hamiltonian. Here, we introduce a minimal dynamical model for a network of dissipatively coupled optical oscillators and prove that the dynamics of such a system is governed by a Lyapunov function that serves as a cost function for the system. This cost function is in general a function of both phases and intensities of the oscillators and depends strongly on the pump parameter. In case of bipartite network topologies, the amplitudes of the oscillators become identical in the steady state and the cost function reduces to the XY Hamiltonian. In the general case for non-trivial network topologies, however, the cost function approaches the XY Hamiltonian only in the strong pump limit. We show that by adiabatically tuning the pump parameter, the network can largely avoid trapping into the local minima of the governing cost function and stabilize into the ground state of the associated XY Hamiltonian. These results show the great potential of laser networks for unconventional computing.
