A network-theoretical perspective on oscillator-based Ising machines

The standard van Neumann computer excels at many things. However, it can be very inefficient in solving optimization problems with a large solution space. For that reason, a novel analog approach, the oscillator-based Ising machine, has been proposed as a better alternative for dealing with such problems. In this work, we review the concept of oscillator-based Ising machine and address how optimization problems can be mapped onto such machines when the quadratic unconstrained binary optimization (QUBO) formulation is given. Furthermore, we provide an ideal circuit that can be used in combination with the wave digital concept for real-time simulated annealing. The functionality of this circuit is explained on the basis of a Lyapunov stability analysis. The latter also provides an answer for the decision-making question: When has the Ising machine solved a mapped problem? At the end, we provide emulation results demonstrating the correlation between functionality and stability. Our results are based on an eigenvalue analysis of the linearized system and demonstrate that all eigenvalues converge to the left complex half plane, once an optimization problem has been optimally solved. This implies that the system enters an attractor region and is hence forced to eventually converge to the optimal solution.