Abstract
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.
Highlights
C OMBINATORIAL optimization problems have immense real-world applications, including financial portfolio optimization, bioinformatics, drug discovery, cryptography, operations research, resource allocation, satellite-based target tracking, and trajectory and route planning [1]–[4]
By comparing with Markov chain Monte Carlo (MCMC) simulations, we show that our Ising solver behaves like a low-temperature Ising spin system, indicating its effectiveness in solving optimization problems
Through experimentally calibrated numerical simulations, we delineate the notion of creating attractor states in the phase space of the coupled phasetransition nano-oscillators (PTNOs) network that will correspond to the minima of the Ising Hamiltonian
Summary
C OMBINATORIAL optimization problems have immense real-world applications, including financial portfolio optimization, bioinformatics, drug discovery, cryptography, operations research, resource allocation, satellite-based target tracking, and trajectory and route planning [1]–[4]. The fundamental advantage in the CTDS approach compared with a digital system comes from the inherently distributed nature and highly parallel processing capability based on the continuous physical interaction between compute elements This allows the CTDS to dynamically find the ground-state or near-optimum solution with immense speed-up compared with a sequentially working digital computer. This ground-state search can be further improved by exploiting the inherent stochasticity of the PTNOs and introducing annealing schemes as described later While both experimental as well numerical simulations have highlighted a clear advantage of PTNO-CTDS-based Ising solver over other aforementioned proposals in terms of time-and energy-to-solution [28], [29], a deeper understanding of the inherent dynamics of the PTNO network is still remaining. By comparing with Markov chain Monte Carlo (MCMC) simulations, we show that our Ising solver behaves like a low-temperature Ising spin system, indicating its effectiveness in solving optimization problems
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