This article is devoted to the vectorization of textual data, in which the quantum bag-of-words algorithm is proposed. The quantum bag-of-words vectorization algorithm allows to represent the quantum states of each word through vectors. For the experiments, a set of consumer complaints was taken and classified by service types. Recognition was performed using machine learning methods based on the features formed by the classical and quantum bag-of-words algorithm. The quantum method of the bag-of-words algorithm showed 24% higher accuracy than the classical method. This indicates that the quantum algorithm of the bag-of-words has high efficiency. In recognition, the Naive Bayes and Passive Aggressive methods provided the highest accuracy of 97%. The results obtained showed the effectiveness of the quantum bag-of-words algorithm in vectorizing text data and its potential as a promising solution compared to classical vectorizing algorithms in natural language processing.