  In the task of quantum state learning, one receives some data about
measurements performed on a state, and using that, must make predictions on the
outcomes of unseen measurements. Computing a prediction is generally hard but
it has been shown that learning can be performed efficiently for states that
are generated by Clifford circuits, which are known to be efficiently
classically simulable. This naturally leads to the question, how does efficient
state learnability compare with efficient classical simulation? In this work we
introduce an extra condition on top of classical simulablity that guarantees
efficiently learnability. To illustrate this we prove two new examples of
efficient learnability: states with low (Schmidt rank) entanglement and states
described by an 'efficient' ontological model.
