An interesting feature of this approach is that the proposed hardware doesn't rely on non-linear elements, memristors, or even active elements (besides an optional noise source). It is simply a passive network of oscillators with a DC bias on each cell. That said, the hardware to implement this at scale does not currently seem to exist. To my knowledge, the state of the art is https://app.normalcomputing.ai/composer
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.
The relationship with Hopfield networks sounds fascinating, would love to discuss further. As you mentioned, there is a connection to annealing in that we are encoding the solution to our problem in the minimization of a physical system's energy. Indeed, the all-to-all coupling is the hard part!