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PRZEGLĄD ELEKTROTECHNICZNY

A Novel Structure Design and Training Algorithm for Quantum Neural Network

Jian Sun, Xiongwei Zhang, Tieyong Cao, Jibin Yang, Xinjian Sun, Qibin Liao

Published Jan 1, 2012• 1 citation
OpenAlex

Abstract

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)

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A new training algorithm for Quantum Neural Networks

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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.

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LM Based Training Algorithm for Quantum Neural Networks

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Aiming at the question that the result trained by quantum neural networks is easy to fall into the local least value,the Levenberg-Marquardt algorithm was introduced into the original training algorithm to increase the training speed and improve the performance of the network.In addition,the conflict between different objective functions used for the training synaptic weights and quantum intervals can cause mean square error fluctuates.In order to solve this problem,the iteration order of the original training algorithm was adjusted.The experimental results show that,compared with the original training algorithm,the algorithm using LM can significantly reduce the number of iterations,significantly decrease the mean square error when the network convergences,and improve the classification results of quantum neural network.

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Research on Quantum Neural Networks and Its Convergence Property

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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.

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This paper investigates the application of topology optimization techniques to enhance the performance of quantum neural networks (QNNs). Traditional QNN architectures often suffer from inefficiencies in information processing due to suboptimal connections between neurons. This work proposes a novel approach utilizing topology optimization algorithms to dynamically adjust the connectivity topology within a QNN, aiming to maximize computational capacity and efficiency. The core claim is that optimizing the neuronal connection topology is a key factor in improving QNN performance. The proposed mechanism involves the iterative application of a topology optimization algorithm, which iteratively modifies the network's connectivity structure based on a defined objective function. The results demonstrate the potential of this method to significantly improve QNN performance, offering a pathway to more powerful and efficient quantum computing architectures. The specific objective function utilized focuses on maximizing the fidelity of quantum state transformations while minimizing the number of connections, representing a novel approach to QNN design. Further exploration will involve investigating different optimization algorithms and network architectures to fully realize the potential of this topology-optimized QNN design.

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A novel quantum neural network based on multi-level activation function

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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.

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Hybrid quantum neural network structures for image multi-classification

Mingrui Shi, Haozhen Situ, Cai Zhang

Abstract Image classification is a fundamental problem in computer vision, and neural networks provide an effective solution. With the advancement of quantum technology, quantum neural networks have attracted a lot of attention. However, they are only suitable for low-dimensional data and require dimensionality reduction and quantum encoding. Two image classification methods have recently emerged: one employs PCA for dimensionality reduction and angular encoding, and the other integrates QNN into a CNN to improve performance. Despite numerous algorithms, the differences between them remain unclear. This study explores these algorithms’ performance in multi-class image classification and proposes an optimized hybrid quantum neural network suitable for the current environment. As the number of classes increases, research on PCA-based quantum algorithms reveals the barren plateau problem of QNN, which is not suitable for multiple classes in a hybrid setting. Our proposed model combining traditional CNN with QNN addresses QNN’s multi-class training difficulties to some extent and achieves satisfactory classification results. Nevertheless, its accuracy remains below that of the top-performing CNN models. Furthermore, we investigate transfer learning in hybrid quantum neural network models and assess the performance of our models on the quantum hardware from IBM. In conclusion, quantum neural networks show promise but require further research and optimization, facing challenges ahead.

arXiv:2308.16005•Physica Scripta•Apr 12, 2024•32 citations
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)
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.
Aiming at the question that the result trained by quantum neural networks is easy to fall into the local least value,the Levenberg-Marquardt algorithm was introduced into the original training algorithm to increase the training speed and improve the performance of the network.In addition,the conflict between different objective functions used for the training synaptic weights and quantum intervals can cause mean square error fluctuates.In order to solve this problem,the iteration order of the original training algorithm was adjusted.The experimental results show that,compared with the original training algorithm,the algorithm using LM can significantly reduce the number of iterations,significantly decrease the mean square error when the network convergences,and improve the classification results of quantum neural network.
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.
This paper investigates the application of topology optimization techniques to enhance the performance of quantum neural networks (QNNs). Traditional QNN architectures often suffer from inefficiencies in information processing due to suboptimal connections between neurons. This work proposes a novel approach utilizing topology optimization algorithms to dynamically adjust the connectivity topology within a QNN, aiming to maximize computational capacity and efficiency. The core claim is that optimizing the neuronal connection topology is a key factor in improving QNN performance. The proposed mechanism involves the iterative application of a topology optimization algorithm, which iteratively modifies the network's connectivity structure based on a defined objective function. The results demonstrate the potential of this method to significantly improve QNN performance, offering a pathway to more powerful and efficient quantum computing architectures. The specific objective function utilized focuses on maximizing the fidelity of quantum state transformations while minimizing the number of connections, representing a novel approach to QNN design. Further exploration will involve investigating different optimization algorithms and network architectures to fully realize the potential of this topology-optimized QNN design.
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.
Abstract Image classification is a fundamental problem in computer vision, and neural networks provide an effective solution. With the advancement of quantum technology, quantum neural networks have attracted a lot of attention. However, they are only suitable for low-dimensional data and require dimensionality reduction and quantum encoding. Two image classification methods have recently emerged: one employs PCA for dimensionality reduction and angular encoding, and the other integrates QNN into a CNN to improve performance. Despite numerous algorithms, the differences between them remain unclear. This study explores these algorithms’ performance in multi-class image classification and proposes an optimized hybrid quantum neural network suitable for the current environment. As the number of classes increases, research on PCA-based quantum algorithms reveals the barren plateau problem of QNN, which is not suitable for multiple classes in a hybrid setting. Our proposed model combining traditional CNN with QNN addresses QNN’s multi-class training difficulties to some extent and achieves satisfactory classification results. Nevertheless, its accuracy remains below that of the top-performing CNN models. Furthermore, we investigate transfer learning in hybrid quantum neural network models and assess the performance of our models on the quantum hardware from IBM. In conclusion, quantum neural networks show promise but require further research and optimization, facing challenges ahead.