  We report a proof-of-principle experimental demonstration of the quantum
speed-up for learning agents utilizing a small-scale quantum information
processor based on radiofrequency-driven trapped ions. The decision-making
process of a quantum learning agent within the projective simulation paradigm
for machine learning is implemented in a system of two qubits. The latter are
realized using hyperfine states of two frequency-addressed atomic ions exposed
to a static magnetic field gradient. We show that the deliberation time of this
quantum learning agent is quadratically improved with respect to comparable
classical learning agents. The performance of this quantum-enhanced learning
agent highlights the potential of scalable quantum processors taking advantage
of machine learning.
