Understanding the Continuous-Time Dynamics of Phase-Transition Nano-Oscillator-Based Ising Hamiltonian Solver

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.