  In this paper we propose a new approach to quantum neural networks. Our
multi-layer architecture avoids the use of measurements that usually emulate
the non-linear activation functions which are characteristic of the classical
neural networks. Despite this, our proposed architecture is still able to learn
any Boolean function. This ability arises from the correspondence that exists
between a Boolean function and a particular quantum circuit made out of
multi-controlled NOT gates. This correspondence is built via a polynomial
representation of the function called the algebraic normal form. We use this
construction to introduce the idea of a generic quantum circuit whose gates can
be tuned to learn any Boolean functions. In order to perform the learning task,
we have devised an algorithm that leverages the absence of measurements. When
presented with a superposition of all the binary inputs of length $n$, the
network can learn the target function in at most $n+1$ updates.
