Neural networks using two-component Bose-Einstein condensates.

The authors previously considered a method of solving optimization problems by using a system of interconnected network of two component Bose-Einstein condensates (Byrnes, Yan, Yamamoto New J. Phys. 13, 113025 (2011)). The use of bosonic particles gives a reduced time proportional to the number of bosons N for solving Ising model Hamiltonians by taking advantage of enhanced bosonic cooling rates. Here we consider the same system in terms of neural networks. We find that up to the accelerated cooling of the bosons the previously proposed system is equivalent to a stochastic continuous Hopfield network. This makes it clear that the BEC network is a physical realization of a simulated annealing algorithm, with an additional speedup due to bosonic enhancement. We discuss the BEC network in terms of neural network tasks such as learning and pattern recognition and find that the latter process may be accelerated by a factor of N.