Biological evidence shows that there are neural networks specialized for recognition of signals and patterns acting as associative memories. The spiking neural networks are another kind which receive input from a broad range of other brain areas to produce output that selects particular cognitive or motor actions to perform. An important contribution of this work is to consider the geometric processing in the modeling of feed-forward neural networks. Since quaternions are well suited to represent 3D rotations, it is then well justified to extend real-valued neural networks to quaternion-valued neural networks for task of perception and control of robot manipulators. This work presents the quaternion spiking neural networks which are able to control robots, where the examples confirm that these artificial neurons have the capacity to adapt on-line the robot to reach the desired position. Also, we present the quaternionic quantum neural networks for pattern recognition using just one quaternion neuron. In the experimental analysis, we show the excellent performance of both quaternion neural networks.

Since the introduction of quaternion by Hamilton in 1843, quaternions have been used in a lot of applications. One of the most interesting qualities is that we can use quaternions to carry out rotations and operate on other quaternions; this characteristic of the quaternions inspired us to investigate how the quantum states and quantum operator work in the field of quaternions and how we can use it to construct a quantum neural network. This new type of quantum neural network (QNN) is developed in the quaternion algebra framework that is isomorphic to the rotor algebra [Formula: see text] of the geometric algebra and is based on the so-called qubit neuron model. The quaternion quantum neural network (QQNN) is tested and shows robust performance.