量子计算在动态递归与自组织神经网络中的机理及应用研究
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摘要
量子计算研究的重要意义已经为许多科学家所共识，特别是将量子计算与神经计算相结合而得到的量子神经网络，已成为人工智能计算发展的一个主流方向。经历十多年的迅速发展，量子神经网络中知识表示的独特结构与信息处理的高效性能，使其在许多理论领域中取得了显著效果，成为信息处理的一个有力工具，为解决一些传统神经网络极难求解的问题提供了全新的思路。
为使量子神经网络的理论更加完善，并从理论走向实践，国内外许多专家学者，尤其是一大批年轻有为的国内外博士参与到这项研究中，为量子神经网络的发展作出了杰出贡献。本文在研究量子力学中一些原理和概念的基础上，将量子技术引入到神经网络中，通过对量子神经网络拓扑结构及其学习算法的设计，提出了几种量子神经网络模型。具体来讲，本文的工作可总结如下：
①提出量子门Elman神经网络模型。新模型由量子比特神经元和经典神经元构成。量子物理规律被应用于量子比特神经元与经典神经元之间的相互作用之中。增加的量子映射层，用于解决由于信息量子化所带来的上下文单元输出与隐藏层输入之间模式不一致的问题。新提出的标准量子学习算法，包含相关量子门参数的更新。新提出的梯度扩展量子学习算法，采用时间调度策略调整学习率参数，利用梯度扩展使得上下文单元的权值与隐藏层的权值同步更新。新提出的带自适应死区向量估计的量子学习算法，采用自适应死区向量控制学习参数，并证明该算法在李亚普诺夫意义下的收敛性。
②提出带时间延迟的量子Hopfield神经网络模型。从量子态演化规律出发，结合量子叠加原理和测量原理，提出带时间延迟的量子Hopfield神经网络模型，对Hopfield神经网络中的联想记忆机制，从概率角度给出新的诠释。新模型中，神经元状态及连接权值矩阵均采用量子态表示。当前时刻的量子态由前面若干个时刻的量子态叠加得到。在不同时刻的，与神经元相连接的量测矩阵，包含量子态在相应时刻被观测到的概率信息。在定义量子联想记忆中的量子记忆原型之后，通过计算量测矩阵中相关权值元素出现的概率值，得到量子关键输入模式在特定时刻，以特定量子记忆原型出现的概率。
③提出具有弹性邻域半径的量子SOM神经网络模型。新模型将实数对象量子化为量子初始态，在量子门的作用下，初始态历经量子中间态被激化为激发态。与量子化权值相连接的量子激发态在量子学习规则的驱动下，被竞争层神经元感知，实现有序的拓扑映射。新提出的量子学习规则采用量子化权值与量子激发态之间的距离，以及量子化权值与量子激发态之间的相似度共同定义邻域核函数中的弹性半径，从而避免某些竞争层神经元因采用固定半径缩放而形成死区。
④实现上述三种量子神经网络在特定背景下的具体应用。针对特定工程对象，分析相关工程现状及需求，实现工程对象与三种量子神经网络的有机结合。在短时载荷预测中，针对众多预测方法采用前馈类网络实现预测的现状，采用量子门Elman神经网进行载荷预测。在验证量子门Elman神经网络性能的同时，也提高电力载荷预测的准确性。在模拟电路故障诊断中，针对采小波分析和主元分析进行故障特征提取的前馈神经网络方法，通过小波包分析和新定义的能量函数提取故障特征，在检验新提出的基于Hopfield编码的故障诊断方法后，针对多故障耦合问题，采用量子Hopfield神经网络从概率角度对故障发生的机制进行新的诠释。在污水处理的出水水质预报中，针对处理过程的超强非线性和超大滞后性，采用量子SOM神经网络进行长时预报。在验证量子SOM神经网络性能的同时，提高预报的准确性。
The significance of quantum computing research has been recognized by manyscientists. In particular, the quantum neural network (QNN), being generated by thecombination of quantum computing and neural computing, has become a mainstreamdirection in the artificial intelligence area. After10-years rapid development, the QNNis considered as a powerful tool for information processing in many theoretical fields,because of its unique structure of knowledge representation and efficient performanceof information processing. It provides a new idea that some problems, being extremelydifficult to solve by the traditional neural network, can be addressed using the QNN.
To improve the theory of the QNN and practice it, considerable effort has beenmade by many researchers, especially, by a large number of young doctors whoparticipate in this study. This paper provides some novel QNN models by introducingthe quantum principles and concepts into the ANN. Specifically, the work of this papercan be summarized as follows:
①A quantum gates Elman neural network model is proposed. The new model iscomposed of qubit neurons and classic neurons. The law of quantum physics is appliedto the interaction between the qubit neurons and the classic neurons. For the newstructure, the quantum mapping layer is used to solve the mode inconsistent between thecontext-lyaer-output and hidden-layer-input. In the standard algorithm, it contains theupdating law of the parameters in the quantum gates. In the the gradient expansionalgorithm, the learning rate is adjusted by the time scheduling strategy. The context-layer-weights and the hidden-layer-weights are synchronized updated by gradientexpansion. In the adaptive dead vector algorithm, the learning parameters arecontrollable. The convergence of the algorithm in the sense of Lyapunov function isproved.
②A quantum Hopfield neural network model with time delay is proposed. It is anew idea that this quantum Hopfield neural network can be explained in term ofprobability. The states of neurons and connection weights are described as quantumstates. The evolution of quantum states, described by the quantum superpositionprinciple and the measurement principle, is introduced into this model. Themeasurement matrix connected with the neurons includes the probability information ofthe quantum states. Through the calculation of the measurement matrix elements appearing at different times, we can obtain the probability of the quantum key inputwhich is evolved into the quantum memory prototype.
③A quantum SOM neural network model with elastic radius is proposed. Thenew model objects the real data into the quantum initial states, then into the quantumexcited states. The weights connected with the quantum excited states are also quantized.The proposed quantum learning law make quantum excited states have an orderedtopology mapping. In addition, the elastic radius of neighborhood kernel function isdefined by the similarity degree and the distance between quantum excited states andquantized weights. It avoids dead zone to be formed so that neurons in competitive layercan not be trained.
④The application of the proposed QNN models is described here. The quantumgate Elman neural network (QEN) is used in the short-term load forecasting. Theaccuracy of forecasting results clearly shows that the QEN has a rapid convergencespeed and a good generalization performance. The Hopfield neural network (HP) andthe quantum Hopfield neural network (QHP) are employed in the analog fault diagnosis.The fault features are extracted by the wavelet packet analysis. The energy of the faultresponses are calculated by a new energy function. The multiple fault diagnostic resultsimply that the fault diagnosis method based on QHP is much more useful than themethod based on HP. To verify the performance of the quantum SOM neural network(QSOM), the experiments about the sewage treatment effluent quality prediction arecarried out. The corresponding results offer a high forecasting accuracy and verifyeffectiveness of of the theory.
为使量子神经网络的理论更加完善，并从理论走向实践，国内外许多专家学者，尤其是一大批年轻有为的国内外博士参与到这项研究中，为量子神经网络的发展作出了杰出贡献。本文在研究量子力学中一些原理和概念的基础上，将量子技术引入到神经网络中，通过对量子神经网络拓扑结构及其学习算法的设计，提出了几种量子神经网络模型。具体来讲，本文的工作可总结如下：
①提出量子门Elman神经网络模型。新模型由量子比特神经元和经典神经元构成。量子物理规律被应用于量子比特神经元与经典神经元之间的相互作用之中。增加的量子映射层，用于解决由于信息量子化所带来的上下文单元输出与隐藏层输入之间模式不一致的问题。新提出的标准量子学习算法，包含相关量子门参数的更新。新提出的梯度扩展量子学习算法，采用时间调度策略调整学习率参数，利用梯度扩展使得上下文单元的权值与隐藏层的权值同步更新。新提出的带自适应死区向量估计的量子学习算法，采用自适应死区向量控制学习参数，并证明该算法在李亚普诺夫意义下的收敛性。
②提出带时间延迟的量子Hopfield神经网络模型。从量子态演化规律出发，结合量子叠加原理和测量原理，提出带时间延迟的量子Hopfield神经网络模型，对Hopfield神经网络中的联想记忆机制，从概率角度给出新的诠释。新模型中，神经元状态及连接权值矩阵均采用量子态表示。当前时刻的量子态由前面若干个时刻的量子态叠加得到。在不同时刻的，与神经元相连接的量测矩阵，包含量子态在相应时刻被观测到的概率信息。在定义量子联想记忆中的量子记忆原型之后，通过计算量测矩阵中相关权值元素出现的概率值，得到量子关键输入模式在特定时刻，以特定量子记忆原型出现的概率。
③提出具有弹性邻域半径的量子SOM神经网络模型。新模型将实数对象量子化为量子初始态，在量子门的作用下，初始态历经量子中间态被激化为激发态。与量子化权值相连接的量子激发态在量子学习规则的驱动下，被竞争层神经元感知，实现有序的拓扑映射。新提出的量子学习规则采用量子化权值与量子激发态之间的距离，以及量子化权值与量子激发态之间的相似度共同定义邻域核函数中的弹性半径，从而避免某些竞争层神经元因采用固定半径缩放而形成死区。
④实现上述三种量子神经网络在特定背景下的具体应用。针对特定工程对象，分析相关工程现状及需求，实现工程对象与三种量子神经网络的有机结合。在短时载荷预测中，针对众多预测方法采用前馈类网络实现预测的现状，采用量子门Elman神经网进行载荷预测。在验证量子门Elman神经网络性能的同时，也提高电力载荷预测的准确性。在模拟电路故障诊断中，针对采小波分析和主元分析进行故障特征提取的前馈神经网络方法，通过小波包分析和新定义的能量函数提取故障特征，在检验新提出的基于Hopfield编码的故障诊断方法后，针对多故障耦合问题，采用量子Hopfield神经网络从概率角度对故障发生的机制进行新的诠释。在污水处理的出水水质预报中，针对处理过程的超强非线性和超大滞后性，采用量子SOM神经网络进行长时预报。在验证量子SOM神经网络性能的同时，提高预报的准确性。
The significance of quantum computing research has been recognized by manyscientists. In particular, the quantum neural network (QNN), being generated by thecombination of quantum computing and neural computing, has become a mainstreamdirection in the artificial intelligence area. After10-years rapid development, the QNNis considered as a powerful tool for information processing in many theoretical fields,because of its unique structure of knowledge representation and efficient performanceof information processing. It provides a new idea that some problems, being extremelydifficult to solve by the traditional neural network, can be addressed using the QNN.
To improve the theory of the QNN and practice it, considerable effort has beenmade by many researchers, especially, by a large number of young doctors whoparticipate in this study. This paper provides some novel QNN models by introducingthe quantum principles and concepts into the ANN. Specifically, the work of this papercan be summarized as follows:
①A quantum gates Elman neural network model is proposed. The new model iscomposed of qubit neurons and classic neurons. The law of quantum physics is appliedto the interaction between the qubit neurons and the classic neurons. For the newstructure, the quantum mapping layer is used to solve the mode inconsistent between thecontext-lyaer-output and hidden-layer-input. In the standard algorithm, it contains theupdating law of the parameters in the quantum gates. In the the gradient expansionalgorithm, the learning rate is adjusted by the time scheduling strategy. The context-layer-weights and the hidden-layer-weights are synchronized updated by gradientexpansion. In the adaptive dead vector algorithm, the learning parameters arecontrollable. The convergence of the algorithm in the sense of Lyapunov function isproved.
②A quantum Hopfield neural network model with time delay is proposed. It is anew idea that this quantum Hopfield neural network can be explained in term ofprobability. The states of neurons and connection weights are described as quantumstates. The evolution of quantum states, described by the quantum superpositionprinciple and the measurement principle, is introduced into this model. Themeasurement matrix connected with the neurons includes the probability information ofthe quantum states. Through the calculation of the measurement matrix elements appearing at different times, we can obtain the probability of the quantum key inputwhich is evolved into the quantum memory prototype.
③A quantum SOM neural network model with elastic radius is proposed. Thenew model objects the real data into the quantum initial states, then into the quantumexcited states. The weights connected with the quantum excited states are also quantized.The proposed quantum learning law make quantum excited states have an orderedtopology mapping. In addition, the elastic radius of neighborhood kernel function isdefined by the similarity degree and the distance between quantum excited states andquantized weights. It avoids dead zone to be formed so that neurons in competitive layercan not be trained.
④The application of the proposed QNN models is described here. The quantumgate Elman neural network (QEN) is used in the short-term load forecasting. Theaccuracy of forecasting results clearly shows that the QEN has a rapid convergencespeed and a good generalization performance. The Hopfield neural network (HP) andthe quantum Hopfield neural network (QHP) are employed in the analog fault diagnosis.The fault features are extracted by the wavelet packet analysis. The energy of the faultresponses are calculated by a new energy function. The multiple fault diagnostic resultsimply that the fault diagnosis method based on QHP is much more useful than themethod based on HP. To verify the performance of the quantum SOM neural network(QSOM), the experiments about the sewage treatment effluent quality prediction arecarried out. The corresponding results offer a high forecasting accuracy and verifyeffectiveness of of the theory.
引文
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