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Quantum Neural Network

Quantum neural networks  [100] are parameterised quantum circuits that can be trained as either generative or discriminative machine learning models in direct analogy with their classical counterparts. In this chapter, we will consider parameterised quantum circuits trained as classifiers. In the most general case, a classifier is a function that takes an N-dimensional input and returns one of M possible class values. The classifier can be trained on a dataset of samples with known class labels by adjusting the configurable model parameters in such a way as to minimise the classification error. Once the classifier is fully trained, it can be exposed to new unseen samples for which correct class labels are unknown. Therefore, it is critically important to avoid overfitting to the training dataset and ensure that the classifier generalises well to the new data.

There are many similarities between quantum and classical neural networks. In both cases, the...