An exemplary embodiment may provide an explainable reinforcement learning system. Explanations may be incorporated into an exemplary reinforcement learning agent/model or a corresponding environmental model. The explanations may be incorporated into an agent's state and/or action space. An explainable Bellman equation may implement an explainable state and explainable action as part of an explainable reward function. An explainable reinforcement learning induction method may implement a dataset to provide a white-box model which mimics a black-box reinforcement learning system. An explainable generative adversarial imitation learning model may implement an explainable generative adversarial network to train the occupancy measure of a policy and may generate multiple levels of explanations. Explainable reinforcement learning may be implemented on a quantum computing system using an embodiment of an explainable Bellman equation.