Quantum generalisation of feedforward neural networks

We propose a quantum generalisation of a classical neural network. The classical neurons are firstly rendered reversible by adding ancillary bits. Then they are generalised to being quantum reversible, i.e., unitary (the classical networks we generalise are called feedforward, and have step-function activation functions). The quantum network can be trained efficiently using gradient descent on a cost function to perform quantum generalisations of classical tasks. We demonstrate numerically that it can: (i) compress quantum states onto a minimal number of qubits, creating a quantum autoencoder, and (ii) discover quantum communication protocols such as teleportation. Our general recipe is theoretical and implementation-independent. The quantum neuron module can naturally be implemented photonically. We often want computers to tell us something about the input data, e.g. if a given image corresponds to a cat or a dog. It seems the human brain learns this by looking at examples whilst getting feedback from a teacher, rather than being given an algorithm. Such an approach to programming is now revolutionising the ability of machines to learn. The approach uses simplified models of the brain: neural nets. Quantum information processing devices are now emerging as the next generation of information processors. One may hope that the neural net approach will be similarly powerful there. We therefore designed quantum neural nets, processing quantum superpositions. The nets work well in two example tasks: compressing data stored in superpositions, and rediscovering a protocol known as quantum teleportation.