Experimental Investigation of the Dynamics of Coupled Oscillators as Ising Machines

Abstract

Coupled electronic oscillator networks, under second harmonic injection, have recently been shown to behave as Ising machines capable of solving computationally hard combinatorial optimization problems. In this work, we experimentally investigate the dynamical properties of a reconfigurable network of up to 30 oscillators ( $\equiv $ spins) configured as an Ising machine. Specifically, we analyze the characteristics of the solutions to the Ising model produced by the oscillators and show that as the system evolves towards the ground state through the high-dimensional phase space, it gets trapped in local minima resulting in sub-optimal solutions. Moreover, the exact local minima where the system gets trapped also changes implying that the trajectory of evolution of the system also changes with each trial. Finally, we illustrate experimentally how an appropriately designed annealing scheme can help the coupled oscillators escape a local minimum and attain a lower energy state.

Keywords

• Analog computing
• combinatorial optimization
• oscillator Ising machine
• MaxCut