  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
bi-partition which 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 . Further,
comparing the Max-Cut solutions with the optimal values, we show that the
oscillators (after simple post-processing) 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 edge density 0.8. Our work
marks a step towards creating an efficient, room-temperature-compatible
non-Boolean hardware-based solver for hard combinatorial optimization problems.
