  Quantum computing has shown the potential to substantially speed up machine
learning applications, in particular for supervised and unsupervised learning.
Reinforcement learning, on the other hand, has become essential for solving
many decision making problems and policy iteration methods remain the
foundation of such approaches. In this paper, we provide a general framework
for performing quantum reinforcement learning via policy iteration. We validate
our framework by designing and analyzing: \emph{quantum policy evaluation}
methods for infinite horizon discounted problems by building quantum states
that approximately encode the value function of a policy $\pi$; and
\emph{quantum policy improvement} methods by post-processing measurement
outcomes on these quantum states. Last, we study the theoretical and
experimental performance of our quantum algorithms on two environments from
OpenAI's Gym.
