  We introduce a classical-quantum hybrid approach to computation, allowing for
a quadratic performance improvement in the decision process of a learning
agent. In particular, a quantum routine is described, which encodes on a
quantum register the probability distributions that drive action choices in a
reinforcement learning set-up. This routine can be employed by itself in
several other contexts where decisions are driven by probabilities. After
introducing the algorithm and formally evaluating its performance, in terms of
computational complexity and maximum approximation error, we discuss in detail
how to exploit it in the Q-learning context.
