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Introduction

In the last two decades we observed a growing interest in Quantum Computation and Quantum Information due to the possibility to solve efficiently hard problem for conventional computer science paradigms.

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). 


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Gilson Giraldi 2002-07-02