Complexity analysis of Quantum reinforcement learning

Quantum reinforcement learning has been systematically presented in a recent paper [Dong et al, Quantum reinforcement learning, IEEE Transactions on Systems, Man and Cybernetics, Part B: Cybernetics, Vol. 38, No. 5, pp.1207-1220, 2008], and such results have shown that quantum reinforcement learning is an effective approach for the solutions to some complex problems. The purpose of this paper is to analyze the complexity of quantum reinforcement learning. In particular, storage complexity and exploration complexity are defined and a collection of results are presented to demonstrate such complexities by several simple examples.