  The authors previously considered a method 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 was found to give a reduced time proportional to the number
of bosons N for solving Ising model Hamiltonians by taking advantage of
enhanced bosonic cooling rates. In this paper 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 typical neural
network tasks such as learning and pattern recognition and find that the latter
process may be accelerated by a factor of N.
