  We consider quantum learning machines -- quantum computers that modify
themselves in order to improve their performance in some way -- that are
trained to perform certain classical task, i.e. to execute a function which
takes classical bits as input and returns classical bits as output. This allows
a fair comparison between learning efficiency of quantum and classical learning
machine in terms of the number of iterations required for completion of
learning. We find an explicit example of the task for which numerical
simulations show that quantum learning is faster than its classical
counterpart. The task is extraction of the k-th root of NOT (NOT = logical
negation), with k=2^m and m \in N. The reason for this speed-up is that
classical machine requires memory of size log k=m to accomplish the learning,
while the memory of a single qubit is sufficient for the quantum machine for
any k.
