Quantum Bayes classifiers and their application in image classification

Bayesian networks are powerful tools for probabilistic analysis and have been widely used in machine learning and data science. Unlike the time-consuming parameter training process of neural networks, Bayes classifiers constructed on Bayesian networks can make decisions based solely on statistical data from samples. In this paper we focus on constructing quantum Bayes classifiers (QBCs). We design both a na\"{\i}ve QBC and three semina\"{\i}ve QBCs (SN-QBCs). These QBCs are then applied to image classification tasks. To reduce computational complexity, we design a local feature sampling method to extract a limited number of feature attributes from an image. These attributes serve as nodes of the Bayesian networks to generate the QBCs. We simulate these QBCs on the MindQuantum platform and evaluate their performance on the MNIST and Fashion-MNIST data sets. Our results demonstrate that these QBCs achieve good classification accuracies even with a limited number of attributes. The classification accuracies of QBCs on the MNIST data set surpass those of classical Bayesian networks and quantum neural networks that utilize all available feature attributes. Additionally, we simulate these QBCs in a quantum noise environment.