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.

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We study negative refraction and focusing of elastic waves in a simple mechanical system comprised of a free standing plate with a step change in thickness. A point focused and intensity modulated laser source is used to excite backward propagating Lamb waves on one side of the step, and the displacement field is probed using an optical interferometer. Conversion between forward and backward propagating modes at the interface leads to negative refraction, and we demonstrate for the first time the operation of a flat lens, similar to that predicted by Veselago in negative index media, for guided elastic waves in isotropic media. We propose that guided elastic waves provide a convenient and powerful experimental test bed for the study of negative index physics.2