Research On Model Of Quantum Neural Network

Quantum neural network (QNN) is one of the young and outlying science built upon the combination of classical neural network and quantum computing. Its development just starts all over the world, which is in the state that the researcher explores it individually. The work of the scientists devoting to the QNN includes not only developing working algorithm and application of some models but also designing novel QNN models.On the base of the analysis of some principles and concepts of the quantum mechanics and quantum computation theory, this dissertation designs topology structure or learning algorithm of neural network and then forms the new QNN models. The main contributions of this dissertation are summerized as follows:(1)The quantum M-P and perceptron network models are proposed.Making use of quantum linear superposition, a quantum M-P neural network is presented. Moreover, the working principle of this proposed network and its corresponding weight updating algorithm are expatiated in the two cases of input state being in the orthogonal and non-orthogonal basic set, respectively. At the same time, a monolayer quantum perceptron network is presented using some merits of quantum computation, especially quantum parallelism. The case,performance analysis and simulation on the monolayer quantum perceptron show that the proposed network with only one neuron can realize XOR function unrealizable with a classical perceptron having a neuron.(2) A model of QNN with weight is presented.Upon the analysis of the Grover's quantum algorithm, a model of QNN with weight vector and its corresponding training method are proposed. It also can be shown that this model's training method works in quantum mechanism. Results on the data set show that this network model can deal with some classical problem and the proposed weight updating algorithm based on the Grover always can learn training examples with a certain percentage.(3) A quantum hopfield neural network (QHNN) model is proposed.This dissertation presents a quantum Hopfield neural network (QHNN) whose elements of the storage matrix are performed in a probabilitic way. Contrasting to the conventional Hopfield neural network, the storage capacity of the QHNN is increased by a factor of 2^N, and its working process accords with quantum evolvement process.(4) The models of QNN without weight are presented.Two kinds of the model of QNN without weight are proposed: one is the quantum competitive neural network (QCNN) that can recognize patterns and class patterns via quantum competition. Contrasting to the conventional competitive neural network, the storage capacity or memory capacity of the QCNN is exponentially increased by a factor of 2n. Another is the time-dependent quantum gate network, which has the initial quantum state that is the eigenstate of time-dependent Hamiltonian operator. Then Hamiltonian evolve in time and the eigenstate corresponding to the final Hamiltonian is the target state of the network after the time T. Seeing from the macroscopy, this quantum target state can be considered to evolve from the initial state.(5)A model of quantum multi-pattern recognition network is proposed.Three kinds of quantum multi-pattern recognition algorithms are designed for the quantum multi-pattern recognition network: The first one is the multi-pattern highprobable quantum search algorithm that can search targets highprobably in the pattern sets through a series of unitary transformation. This algorithm can find goals by only one searching of the pattern. The second one is the algorithm of multi-pattern recognition with spurious items, which introduces a new design scheme of initializing quantum state and quantum encoding on the pattern set. Owing to the power of quantum parallel speciality, this method can recognize simultaneously with a certain probability multi-pattern of the pattern set. The final one is the multi-pattern partial quantum search algorithm. It separates the database of N items into K blocks and this algorithm can search concurrently multi-pattern in the database. Besides, it takes about (3b/4p)^1/2-Ï€/6(b/p)^1/2 fewer iterations than the global multi-pattern search algorithm.