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International Conference on Natural Computation (ICNC)

Research on Quantum Neural Networks and Its Convergence Property

Li-liang Ding, Li Chen

Published Jan 1, 2008• 4 citations
Publisher

Abstract

The training algorithm and the structure of quantum neural networks (QNN) that based on multilevel activation function are presented in this paper. Aiming at the influence of the activation function of output layer and the phenomenon of error saturation in the training process on the output values and convergence property, a linear superposition of arctangent function is introduced in as hide layer activation function, and error saturation prevention (ESP) function is constructed to improve the convergence property of QNN. The results of simulation program show that the convergence property is improved obviously.

DOI
10.1109/icnc.2008.578

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The training algorithm and the structure of quantum neural networks (QNN) that based on multilevel activation function are presented in this paper. Aiming at the influence of the activation function of output layer and the phenomenon of error saturation in the training process on the output values and convergence property, a linear superposition of arctangent function is introduced in as hide layer activation function, and error saturation prevention (ESP) function is constructed to improve the convergence property of QNN. The results of simulation program show that the convergence property is improved obviously.
Abstract Since the multi-level activation function quantum neural network (QNN) for pattern recognition was firstly proposed by Purushothaman and Karayiannis, more and more researches have been conducted on improving it. However, they all ignore that the QNN only uses multi-level activation function to simulate the concept of quantum superposition rather than really using quantum computing. In this paper, we propose a real QNN model based on multi-layer activation function. In addition, we present algorithms for updating weight parameters and quantum intervals, and also improve the learning algorithm for weight parameters using famous Levenberg–Marquardt algorithm. We also use the QNN for lie detection, and the simulation results of MATLAB prove that the performance of the model based on the corresponding algorithm are very strong.
In this paper an improved quantum neural network(QNN) is presented based on multilevel activation function to solve the problems of precision inadequacy and low convergence rate of the BP neural network used in character recognition.Firstly,momentum term is used to updating the weights to accelerate the convergence rate of learning algorithm in QNN.Secondly,a linear superposition of hyperbolic tangent function is used as activation function of hidden unit in the new networks to classify pattern recognition problems that have uncertainty and overlapping data between two patterns.Finally,The experimental results for number,letter,and Chinese character recognition is provided and compared with both BP neural networks and the original Qnn.Results indicate that the improved Qnn not only takes great recognition rate,but also decreases the number of the training time comparing with the original one.The superiority is demonstrated by simulation.
Inspired by the principle of superposing states in quantum mechanics,a new kind of feedforward neural network with single hidden layer was designed and named as Quantum Neural Networks.It has mainly been used for data classification.Multilevel activation functions is adopted in Quantum Neural Networks and a different objective function is used for the learning of quantum intervals of the multilevel hidden units;minimizing the class-conditional variances at the outputs of the hidden units.Quantum Neural Networks is endowed with a special ability of identifying uncertainty in data classification by its unique design.However,as different objective functions are used for the learning of synaptic weights and quantum intervals,conflict is observed in the iterative training process which will cause more iteration times for training and degrades the training results.Using the theory of Constrained Optimization,a new training algorithm is proposed in this paper by introducing penalty function into the steepest descent method.In the new training algorithm, the conflict is removed.Experimental results indicate that the new algorithm can increase the training speed and improve the performance of the trained network remarkably.
In the structure of original Quantum Neural Network (QNN), only multi-sigmoid transfer function is adopted. Besides that, due to the conflict of the two objective functions in original training algorithm, the training process converges slowly and presents constant variation. In this paper, the QNN with multi-tan-sigmoid transfer function and a novel training algorithm which combines the two objective functions are proposed. Experimental results demonstrate the effectiveness of the structure improvement and the new training algorithm. Streszczenie. W oryginalnym algorytmie kwantowej sieci neuronowej QNN tylko multisigmoidalna funkcja przejścia jest wykorzystywana. W pracy zaprezentowano siec z multi-tan-sigmoidalną funkcją przejścia z nowym algorytmem uczenia. (Nowa struktura i algorytm uczenia w kwantowej sieci neuronowej)
This article proposes a model of a quantum neural network based on a multilevel activation function, which has high performance. This performance is achieved by combining such unique components as: the quantum weight vector, quantum activity values and the dot product operator. In addition, algorithms for learning weight parameters and quantum intervals are presented, in particular, the Levenberg-Marquardt algorithm is improved to improve the quality of the error back propagation method in the process of learning weight parameters, which will also reduce the likelihood of quantum errors.
The current status of Quantum Neural Network (QNN) research is analyzed, it deeply studies the model Quantum Gate Circuit Neural Network (QGCNN) and QGCNN Learning Algorithm (QGCA). Replacing the mean square error function by using the Widrow function and the Rumelhart function, it creates two quantum neural network learning algorithms based on performance function, including Learning Algorithm of QGCNN based on the Widrow functions (WQGCA) and Learning Algorithm of QGCNN based on the Rumelhart functions (RQGCA). New algorithms overcome the inherent defects of the training result is not ideal and unrealistic, which is because the use of mean square error function training network will appear excessive punishment phenomenon. Three algorithms are trained by three data sets. Simulation Experiments on three kinds of algorithms was carried out by using these data sets in the case of the best learning rate. Research prove WQGCA and RQGCA have better pattern classification ability relative to QGCA and RQGCA has a higher classification accuracy than WQGCA.