Quantum density matrix represents all the information of the entire quantum system, and novel models of meaning employing density matrices naturally model linguistic phenomena such as hyponymy and linguistic ambiguity, among others in quantum question answering tasks. Naturally, we argue that applying the quantum density matrix into classical Question Answering (QA) tasks can show more effective performance. Specifically, we (i) design a new mechanism based on Long Short-Term Memory (LSTM) to accommodate the case when the inputs are matrixes; (ii) apply the new mechanism to QA problems with Convolutional Neural Network (CNN) and gain the LSTM-based QA model with the quantum density matrix. Experiments of our new model on TREC-QA and WIKI-QA data sets show encouraging results. Similarly, we argue that the quantum density matrix can also enhance the image feature information and the relationship between the features for the classical image classification. Thus, we (i) combine density matrices and CNN to design a new mechanism; (ii) apply the new mechanism to some representative classical image classification tasks. A series of experiments show that the application of quantum density matrix in image classification has the generalization and high efficiency on different datasets. The application of quantum density matrix both in classical question answering tasks and classical image classification tasks show more effective performance.

翻译：量子密度矩阵表征了整个量子系统的全部信息，基于密度矩阵的新型意义模型能够自然建模语言现象，如下位关系与语言歧义等，在量子问答任务中已有所体现。我们自然认为，将量子密度矩阵应用于经典问答任务可展现出更优性能。具体而言，我们（i）设计了一种基于长短期记忆网络的新机制，以适应输入为矩阵的情况；（ii）将该新机制与卷积神经网络结合应用于问答问题，构建了基于LSTM与量子密度矩阵的问答模型。在TREC-QA与WIKI-QA数据集上的实验结果表明，该模型取得了令人鼓舞的效果。类似地，我们认为量子密度矩阵同样能增强经典图像分类中的图像特征信息及特征间关联。为此，我们（i）将密度矩阵与CNN结合设计新机制；（ii）将该新机制应用于若干代表性经典图像分类任务。一系列实验表明，量子密度矩阵在图像分类中的应用在不同数据集上具有泛化性与高效性。量子密度矩阵在经典问答任务与经典图像分类任务中的应用均展现出更优性能。