Understanding the Continuous-Time Dynamics of Phase-Transition Nano-Oscillator-Based Ising Hamiltonian Solver
Understanding the Continuous-Time Dynamics of Phase-Transition Nano-Oscillator-Based Ising Hamiltonian Solver
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DOI：
10.1109/jxcdc.2020.3045074
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发表时间：
2020-12-01
影响因子：
2.4
通讯作者：
Datta, Suman
中科院分区：
文献类型：
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作者：
Dutta, Sourav;Khanna, Abhishek;Datta, Suman
许多组合优化问题可以映射到伊辛模型的基态搜索问题。利用耦合相变纳米振荡器(PTNO)网络的连续时间动力学，可以建立一个Ising哈密顿求解器，在离散时间迭代数字硬件上以较大的加速获得最优解或接近最优解。在这里，我们提供了对这种基于PTNO的伊辛哈密顿解算器的连续时间动力学的见解。我们着重讨论了利用二次谐波注入锁定(SHIL)在耦合PTNO网络的相空间中形成稳定吸引子的过程，该二次谐波注入锁定对应于Ising哈密顿量的极小值。结果表明，PTNO网络的同步动力学在振子相位双稳临界点附近达到极大值，超过该临界点，网络的同步动力学将受到冻结效应的限制。这种动态冻结严重限制了基于PTNO的Ising求解器获得全局最优解的性能。我们强调了通过引入一种与恒定SHIL幅度相比线性增加SHIL幅度的退火法来提高到达基态的成功几率。最后，通过与马尔可夫链蒙特卡罗模拟的比较，我们估计了基于PTNO的Ising求解器的“有效温度”。基于PTNO的伊辛解算器的行为类似于低温伊辛自旋系统，表明其对于优化任务的有效性。
Many combinatorial optimization problems can be mapped onto the ground-state search problem of an Ising model. Exploiting the continuous-time dynamics of a network of coupled phase-transition nano-oscillators (PTNOs) allows building an Ising Hamiltonian solver for obtaining optimum or near-optimum solution with a large speed-up over discrete-time iterative digital hardware. Here, we provide insights into the continuous-time dynamics of such a PTNO-based Ising Hamiltonian solver. We highlight the formation of stable attractor states in the phase space of the coupled PTNO network using second-harmonic injection locking (SHIL) that corresponds to the minima of the Ising Hamiltonian. We show that the emergent synchronized dynamics of the PTNO network is maximized near the critical point of oscillator phase bistability beyond which the dynamics is limited by freeze-out effects. Such dynamical freeze-out severely limits the performance of the PTNO-based Ising solver from obtaining the global optimum. We highlight an improvement in the success probability of reaching the ground state by introducing an annealing scheme with linearly increasing SHIL amplitude compared with a constant SHIL. Finally, we estimate the "effective temperature" of the PTNO-based Ising solver by comparing it with the Markov chain Monte Carlo simulations. The PTNO-based Ising solver behaves like a low-temperature Ising spin system, indicating its effectiveness for optimization tasks.