Optimal Policies for Quantum Markov Decision Processes

Markov decision process(MDP)offers a general framework for modelling sequential decision making where outcomes are random.In particular,it serves as a mathematical framework for reinforcement learning.This paper introduces an extension of MDP,namely quantum MDP(q MDP),that can serve as a mathematical model of decision making about quantum systems.We develop dynamic programming algorithms for policy evaluation and finding optimal policies for q MDPs in the case of finite-horizon.The results obtained in this paper provide some useful mathematical tools for reinforcement learning techniques applied to the quantum world.