  Artificial neural networks are becoming an integral part of digital solutions
to complex problems. However, employing neural networks on quantum processors
faces challenges related to the implementation of non-linear functions using
quantum circuits. In this paper, we use repeat-until-success circuits enabled
by real-time control-flow feedback to realize quantum neurons with non-linear
activation functions. These neurons constitute elementary building blocks that
can be arranged in a variety of layouts to carry out deep learning tasks
quantum coherently. As an example, we construct a minimal feedforward quantum
neural network capable of learning all 2-to-1-bit Boolean functions by
optimization of network activation parameters within the supervised-learning
paradigm. This model is shown to perform non-linear classification and
effectively learns from multiple copies of a single training state consisting
of the maximal superposition of all inputs.
