To enhance the approximation and generalization ability of process neural networks (PNNs), by studying the quantum implementation mechanism of information processing of process neuron, a new idea of designing quantum process neuron is proposed in this paper, based on the quantum rotation gates and the quantum controlled-non gates. In the proposed approach, the discrete process inputs are expressed by the qubits, which, as the control qubits of controlled-non gates after being rotated by the quantum rotation gates, control the target qubits to reverse. The model outputs are described by the probability amplitude of state |1 in the target qubits. Then the quantum process neural networks (QPNNs) are designed by the quantum process neurons for the hidden layer and the normal neurons for the output layer. The algorithm of QPNN is derived through the quantum computing. The proposed approach is utilized to predict the smoothed yearly mean sunspot numbers, and the results indicate that the QPNN has higher prediction accuracy than the normal PNN, thus it has a certain theoretical meaning and practical value for the complex prediction.
To enhance the approximation and generalization ability of process neural networks (PNNs), by studying the quantum implementation mechanism of information processing of process neuron, a new idea of designing quantum process neuron is proposed in this paper, based on the quantum rotation gates and the quantum controlled-non gates. In the proposed approach, the discrete process inputs are expressed by the qubits, which, as the control qubits of controlled-non gates after being rotated by the quantum rotation gates, control the target qubits to reverse. The model outputs are described by the probability amplitude of state |1 in the target qubits. Then the quantum process neural networks (QPNNs) are designed by the quantum process neurons for the hidden layer and the normal neurons for the output layer. The algorithm of QPNN is derived through the quantum computing. The proposed approach is utilized to predict the smoothed yearly mean sunspot numbers, and the results indicate that the QPNN has higher prediction accuracy than the normal PNN, thus it has a certain theoretical meaning and practical value for the complex prediction.
To enhance the approximation and generalization ability of classical artificial neural networks,a quantum-inspired neural network model,whose input of each dimension is a discrete sequence,is proposed.This model concludes three layers,in which the hidden layer consists of quantum-inspired neurons,and the output layer consists of common neurons.The quantum-inspired neuron consists of the quantum rotation gates and the multi-qubits controlled-rotation gates.By using the information feedback of target qubit from output to input in multi-qubits controlled-rotation gate,the overall memory of input sequences is realized.The output of quantum-inspired neuron is obtained from the entanglements of multi-qubits in controlled-rotation gates.The learning algorithm is designed in detail according to the basic principles of quantum computation.The characteristics of input sequence can be effectively obtained by way ofbreadthanddepth.The simulation results show that,when the input nodes and the length of the sequence satisfy a certain relations,the proposed model is obviously superior to the common artificial neural networks.
To enhance the approximation and generalization ability of classical artificial neural network (ANN) by employing the principles of quantum computation, a quantum-inspired neuron based on controlled-rotation gate is proposed. In the proposed model, the discrete sequence input is represented by the qubits, which, as the control qubits of the controlled-rotation gate after being rotated by the quantum rotation gates, control the target qubit for rotation. The model output is described by the probability amplitude of state |1〉 in the target qubit. Then a quantum-inspired neural network with sequence input (QNNSI) is designed by employing the quantum-inspired neurons to the hidden layer and the classical neurons to the output layer. An algorithm of QNNSI is derived by employing the Levenberg–Marquardt algorithm. Experimental results of some benchmark problems show that, under a certain condition, the QNNSI is obviously superior to the ANN.
To enhance the approximation capability of neural networks, a quantum neural networks model is proposed whose input of each dimension is in discrete sequence. This model includes three layers, in which the hidden layer consists of quantum neurons, and the output layer consists of common neurons. The quantum neuron consists of the quantum rotation gates and the multi-qubits controlled-not gates. By using the information feedback of target qubit from output to input in multi-qubits controlled-not gate, the overall memory of input sequences is realized. The output of quantum neuron is obtained from the entanglements of multi-qubits in controlled-not gates. The learning algorithm is designed in detail according to the basis principles of quantum computation. The characteristics of input sequence can be effectively obtained from the width and the depth. The simulation results show that, when the input nodes and the length of the sequence satisfy a certain relations, the proposed model is superior to the common artificial neural networks.
To enhance the approximation and generalization ability of artificial neural network (ANN) by employing the principles of quantum rotation gate and controlled-not gate, a quantum-inspired neuron with sequence input is proposed. In the proposed model, the discrete sequence input is represented by the qubits, which, as the control qubits of the controlled-not gate after being rotated by the quantum rotation gates, control the target qubit for reverse. The model output is described by the probability amplitude of state in the target qubit. Then a quantum-inspired neural network with sequence input (QNNSI) is designed by employing the sequence input-based quantum-inspired neurons to the hidden layer and the classical neurons to the output layer, and a learning algorithm is derived by employing the Levenberg-Marquardt algorithm. Simulation results of benchmark problem show that, under a certain condition, the QNNSI is obviously superior to the ANN.
A quantum BP neural networks model with learning algorithm is proposed. First, based on the universality of single qubit rotation gate and two-qubit controlled-NOT gate, a quantum neuron model is constructed, which is composed of input, phase rotation, aggregation, reversal rotation and output. In this model, the input is described by qubits, and the output is given by the probability of the state in which |1〉 is observed. The phase rotation and the reversal rotation are performed by the universal quantum gates. Secondly, the quantum BP neural networks model is constructed, in which the output layer and the hide layer are quantum neurons. With the application of the gradient descent algorithm, a learning algorithm of the model is proposed, and the continuity of the model is proved. It is shown that this model and algorithm are superior to the conventional BP networks in three aspects: convergence speed, convergence rate and robustness, by two application examples of pattern recognition and function approximation.
Sunspot is one of the most basic and obvious activity occurred in the solar photosphere, the number of sunspot have great influence on the production and life as well as climate change. Therefore, studying and predicting of sunspots have important meaning. Aiming at the problem of highly nonlinear in sunspot number and the conventional methods are difficult to convergence, a new prediction method based on neural network with quantum gate is proposed to improve the accuracy of the forecast for Sunspot number time series. The input data is expressed by the qubit, which rotated by the rotation gate, as the control qubits control the hidden layer qubits reverse. In the same way, the hidden layer qubits control the output layer. At last, the probability amplitude of state |1> is regarded as the network output. This proposed method has such advantages as high precision and strong generalization ability, and it is a new promising approach for solving time series prediction problem of sunspot number.