Neural networks with quantum architecture and quantum learning

A method is proposed for solving the two key problems facing quantum neural networks: introduction of nonlinearity in the neuron operation and efficient use of quantum superposition in the learning algorithm. The former is indirectly solved by using suitable Boolean functions. The latter is based on the use of a suitable nonlinear quantum circuit. The resulting learning procedure does not apply any optimization method. The optimal neural network is obtained by applying an exhaustive search among all the possible solutions. The exhaustive search is carried out by the proposed quantum circuit composed of both linear and nonlinear components.