  We report on an analog computing system with coupled non-linear oscillators
which is capable of solving complex combinatorial optimization problems using
the weighted Ising model. The circuit is composed of a fully-connected 4-node
LC oscillator network with low-cost electronic components and compatible with
traditional integrated circuit technologies. We present the theoretical
modeling, experimental characterization, and statistical analysis our system,
demonstrating single-run ground state accuracies of 98% on randomized MAX-CUT
problem sets with binary weights and 84% with 5-bit weight resolutions.
Solutions are obtained within 5 oscillator cycles, and the time-to-solution has
been demonstrated to scale directly with oscillator frequency. We present
scaling analysis which suggests that large coupled oscillator networks may be
used to solve computationally intensive problems faster and more efficiently
than conventional algorithms. The proof-of-concept system presented here
provides the foundation for realizing such larger scale systems using existing
hardware technologies and could pave the way towards an entirely novel
computing paradigm.
