摘要：传统的Hopfield网络的存储容量是神经元个数的014倍（P=014N）。由于它在识别大量的图像或模式时遇到了巨大的困难，所以研究人员一直在寻找新的方法。由量子计算和神经网络结合而产生的量子神经网络是新兴和前沿的学科之一。为了提高图像识别的速度和增加图像识别量，在分析了量子线性叠加特性的基础上，提出了一种用于存储矩阵元素的基于概率分布的量子Hopfield神经网络，它在存储容量或记忆容量上提高到了神经元个数的2N倍，比传统的Hopfield神经网络有了指数级的提高。通过图像识别的实例分析和仿真试验的结果表明，该量子Hopfield神经网络能有效地识别图像或模式，并且工作过程符合量子演化过程。

Abstract：The storage capacity of the conventional Hopfield network is the 014 times of the number of neurons(P=014N). Because of the huge difficulty in recognizing a large number of images or patterns, researchers are looking for new methods at all times. Quantum neural network (QNN) is a young and outlying science built upon the combination of classical neural network and quantum computing. A Quantum Hopfield neural network (QHNN) whose elements of the storage matrix are distributed in a probability way on the base of quantum linear superposition is presented for speeding up the images recognition and increasing the number of the images recognition. Contrasting to the conventional Hopfield neural network, the storage capacity of the QHNN is increased by a factor of 2N, where N is the number of neurons. Besides, the case analysis and simulation tests have been carried out for the recognition of images in this paper. The result indicates that QHNN can recognize the images or patterns effectively and its working process accords with quantum evolvement process.