  Projective Simulation was introduced as a novel approach to Artificial
Intelligence. It involves a deliberation procedure that consists of a random
walk on a graph of clips and allows for the learning agent to project itself
into the future before committing to an action. Here we study and analyze a
quantum mechanical version in which the random walk is performed by two kinds
of Hamiltonians. The first kind is implemented by naively embedding the
classical model in a quantum model by turning the clips into qubits. The other
allows for storing clips in superpositions of qubits allowing for a potentially
purely quantum mechanical learning procedure in which the perception of the
environment is purely quantum mechanical but the action is classical. We lastly
introduce the concept of interacting projective agents for both the classical
and quantum mechanical case.
