Efficient Learning for Deep Quantum Neural Networks

Neural networks enjoy widespread success in both research and industry and, with the imminent advent of quantum technology, it is now a crucial challenge to design quantum neural networks for fully quantum learning tasks. Here we propose the use of quantum neurons as a building block for quantum feed-forward neural networks capable of universal quantum computation. We describe the efficient training of these networks using the fidelity as a cost function and provide both classical and efficient quantum implementations. Our method allows for fast optimisation with reduced memory requirements: the number of qudits required scales with only the width, allowing the optimisation of deep networks. We benchmark our proposal for the quantum task of learning an unknown unitary and find remarkable generalisation behaviour and a striking robustness to noisy training data.