In this thesis, we present a quantum policy iteration algorithm that uses quantum neural networks [SSM21] to estimate the state values of a given policy and optionally another quantum network that represents the policy itself. Our main contribution are the quantum circuits that manage to compute the loss, given different methods of encoding the values into a quantum register. These circuits can be enhanced via a method presented by Wiedemann et al. [WHUM23] and the Powering lemma [JVV86], to achieve a quadratic speed up in the error, when estimating the loss. Continuing, we deduce that there is no linear relation, linking the loss of quantum supervised learning [SCH+22] and the loss of our algorithm and that the risk defined in quantum supervised learning is not proportional to the quality of a policy. Finally, we conclude our work with experiments on the FrozenLake [Gyma].