Stochastic optimization of spin-glasses on cellular neural/nonlinear network based processors

Nowadays, Cellular Neural/Nonlinear Networks (CNN) are practically implemented in parallel, analog computers, showing a fast developing trend. It is important also for physicists to be aware that such computers are appropriate for implementing in an elegant manner practically important algorithms, which are extremely slow on the classical digital architecture. Here, CNN is used for optimization of spin-glass systems. We prove, that a CNN in which the parameters of all cells can be separately controlled, is the analog correspondent of a two-dimensional Ising type spin-glass system. Using the properties of CNN we show that one single operation on the CNN chip would yield a local minimum of the spin-glass energy function. By using this property a fast optimization method, similar to simulated annealing, can be built. After estimating the simulation time needed for this algorithm on CNN based computers, and comparing it with the time needed on normal digital computers using the classical simulated annealing algorithm, the results look promising: a speed-up of the order 10¹² is expected already at 50×50 lattice sizes. Hardwares realized nowadays are of 128×128 size. Also, there seem to be no technical difficulties adapting CNN chips for such problems and the needed local control of the parameters could be fully developed in the near future.