Quantum neurons and their fluctuation

A new model of symmetric neural networks is presented, where each neuron takes one of the quantized values (e.g. integers) rather than just a binary values (i.e. 0 or 1) or continuous values (i.e. real numbers). By applying this model to combinatorial optimization problems which take integers as solutions, the number of neurons and connections between neurons, and computation time decrease greatly as compared with the traditional counting method. Therefore, it is possible to get better solutions in the same total computation time. The simulation of Hitchcock problem is made to show these advantages. It is also illustrated, by the simulation, that some fluctuation coming from this quantization makes it possible to get a better or best solution more easily. This fluctuation suggests an effective way to escape from the local minimum.