Experimental Demonstration of a Reconfigurable Coupled Oscillator Platform to Solve the Max-Cut Problem

In this work, we experimentally demonstrate an integrated circuit (IC) of 30 relaxation oscillators with reconfigurable capacitive coupling to solve the NP-Hard maximum cut (Max-Cut) problem. We show that under the influence of an external second-harmonic injection signal, the oscillator phases exhibit a bipartition that can be used to calculate a high-quality approximate Max-Cut solution. Leveraging the all-to-all reconfigurable coupling architecture, we experimentally evaluate the computational properties of the oscillators using randomly generated graph instances of varying size and edge density ( $\eta $ ). Furthermore, comparing the Max-Cut solutions with the optimal values, we show that the oscillators (after simple postprocessing) produce a Max-Cut that is within 99% of the optimal value in 28 of the 36 measured graphs; importantly, the oscillators are particularly effective in dense graphs with the Max-Cut being optimal in seven out of nine measured graphs with $\eta =0.8$ . Our work marks a step toward creating an efficient, room-temperature-compatible non-Boolean hardware-based solver for hard combinatorial optimization problems.