From what I see, it's like mimicking the annealing process and the "derivative" automatically drives you to the solution. If that's the case, implementing such hardware should be not that hard except for the programmable coupling part. A bit off-topic, this reminds me of the duality between any deep forward network and a modern Hopfield network with some special energy functions, in which the duality is based on the fact that the forward running process can be seen as an energy minimization process.

I haven't read the paper, so maybe completely irrelevant, but isn't there an analytical solution for a system of N coupled oscillators?