By exploiting the properties of superposition and entanglement found in quantum systems Quantum Computation has been applied to the design of algorithms considerably more efficient than the known classical ones. Known examples are the Shor's factoring algorithm and the Grover's search algorithm. This paper investigates the possibility of employing Quantum Computing techniques to the design of learning algorithms for neural networks tasks such as pattern recognition. We propose a quantum learning algorithm for neural networks where all patterns of the training set are presented concurrently in superposition. In the process we propose a novel model of a quantum weightless neural node. The algorithm is a combination of a quantum search algorithm, a probabilistic quantum memory and a quantum neural network.