  We discuss a quantum version of an artificial deep neural network where the
role of neurons is taken over by qubits and the role of weights is played by
unitaries. The role of the non-linear activation function is taken over by
subsequently tracing out layers (qubits) of the network. We study two examples
and discuss the learning from a quantum information theoretic point of view. In
detail, we show that the lower bound of the Heisenberg uncertainty relations is
defining the change of the gradient descent in the learning process. We raise
the question if the limit by Nature to two non-commuting observables,
quantified in the Heisenberg uncertainty relations, is ruling the optimization
of the quantum deep neural network. We find a negative answer.
