Quantum computation and quantum information encompasses processing and transmission of data stored in quantum states (see [8] and references therein).

On the other hand, Artificial Neural Networks (**ANNs**) is a rapidly
expanding area of current research, attracting people from a wide variety
of disciplines due to its capabilities for pattern recognition, classification
and modeling of brain information processing [2].
Simply stated an ANN is a computing system composed by very specialized
units called *neurons* which are linked by *synaptic* junctions.
Learning is the fundamental feature of ANNs. Learning occurs when modifications
are made to the coupling properties between neurons, at the synaptic junction
[2].

From this scenario, emerge the field of artificial neural networks based
on quantum theoretical concepts and techniques. They are called Quantum
Neural Networks (**QNNs**).

The first systematic and deeply examination of quantum theory applied to ANNs was done by Menneer [7] in her PhD thesis. The basic approach comes from the multiple universes view of quantum theory: the neural network is seen as a physical system and its multiple occurrences (component networks) are trained according to the set of patterns of interest. The superposition of the trained components gives the final QNN.

Several works about QNNs have been done since Menneer's thesis. Shafee
worked with a quantum neural network with nearest neighbor nodes connected
by c-NOT gates [10].
Altaisky [1]
proposed a quantum *inspired* version of the perceptron - the basic
model for neurons in ANNs.

Gupta at al. [5]
defined a new model of quantum computation by introducing a nonlinear and
irreversible gate (D-Gate). Authors justify the models as a solution for
the *localization* problem, that is, the reflexion of the computational
trajectory, causing the computation to turn around. In another way, D-Gate
would be a run-time device (that means, a gate) sensitive to the probability
amplitude.

From the point of view of ANNs all of these works shares the same limitation: from the actual state-of-the-art for quantum computers it is not clear the hardware requirements to implement such models. The key problem here is the need of nonlinearity and irreversible operations (dissipation). This is the starting point for our research in QNN models.

Firstly, we describe the work of Behrman at al. [4]. They used discretized Feynman path integrals and found that the real time evolution of a quantum dot molecule coupled to the substrate lattice through optical phonons, and subject to a time-varying external field, can be interpreted as a neural network. Starting from this interpretation, we observe that this model is a kind of quantum perceptron and discuss the learning rules and nonlinearity in the context of QNNs.

The material presented is organized as follows. Section 2 present some ANNs concepts used in neural networks. In section 3 we present basic concepts for quantum computation, discuss nonlinearity for QNNs and the quantum dot molecule model is described. We present our analysis in section 4. Finally, we present the conclusions (section 5).