All-to-All Connected Oscillator Ising Machines and Their Application as Associative Memory

Dynamic behaviors of the classical Kuramoto models have been widely studied. The dynamics of the all-to-all connected oscillator Ising machines (OIMs) is similar to that of the classical Kuramoto models, with the main difference being that there is an additional term in OIMs, called the second harmonic term. However, the dynamic behavior of an all-to-all connected OIM is significantly different and its intricate properties are largely unexplored. In this article, we study in detail the properties of the all-to-all connected OIMs and explore their application as associative memory. The number of patterns such an OIM can store increases exponentially with respect to the number of oscillators. To improve the performance of the OIMs for associative memory, we propose a new harmonic term so that the resulting OIM achieves pattern retrieval with high accuracy in the presence of a high level of noise.