Abstract <p>Mathematical representations for creating so-called ‘‘virtual’’ pilots are under consideration. The approach in use is based on sequential transitions from the business processes, which plainly formalize subject activities but lack the capacity to apply meaningful mathematical tools, to the Markovian processes, which plainly formalize crew activities and enable the use of convenient and efficient mathematical methods, yet require substantial volumes of empirical data for their identification, and, finally, to the quantum representations, which plainly formalize crew activities and, when employing the quantum likelihood method, need practically acceptable volume of empirical data for the model identification, while enabling the application of novel relevant mathematical tools. The approach in use makes it possible to solve three topical applied problems: to implement simulation basing on small sample of empirical data for predicting behavior, to solve the classification problem for diagnostic purposes, and to plan a certain activity for adaptive training to improve professional skills. The activity model in use combines two types of qubit systems, viz.: the cluster system representing steps of a subject activity and the branch systems representing mistakes arising during the implementation of the given activity steps. The quantum cluster system is connected to the branch systems with the aid of entangling by collapse, and vice versa.</p>