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Analog and digital quantum neural networks: Basic concepts and applications

Kastellakis Antonios

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Summary

In the scope of this thesis, we investigate how the rise of quantum computers can offer a new, potentially more powerful, way of machine learning. The study begins by defining the framework of quantum computation. This includes the building blocks of a quantum computer, such as the quantum bits and gates, but also the postulates of quantum mechanics, that determine their behaviour. Then we move the discussion to the field of machine learning, where we do a gentle introduction to the basic machine learning methods with the focal point being neural networks as generative models. To this end, we introduce a special type of energy based neural network, the Restricted Boltzmann machine (RBM). We discuss not only the theoretical background of the RBM, but also present an example, by coding and training on the MNIST data set of handwritten digits. Next, we examine Quantum Machine Learning (QML), the union of quantum computation with machine learning. There are two approaches of QML, the quantum advantage QML algorithms that have proven speed-ups over their classical counterparts but require fault-tolerant quantum devices, and hybrid classical-quantum variational models that can be executed on the Noisy Intermediate Scale Quantum (NISQ) devices of today. The QNNs models we implement for this study belong tothe latter case. We present two QNN approaches, the digital approach that considers the Quantum Circuit Born Machines (QCBM) and an analog approach, which refers to quantum information processing with analog quantum systems. These models are quantum analogues of classical neural networks that can be trained, using both classical and quantum resources, to learn target probabilitydistributions. We demonstrate how they learn from classical data and at the end, we attempt to compare their capabilities their capabilities of learning the same dataset. Our novel algorithms have been implemented on classical simulators as well as real quantum hardware available in cloud from IBM.

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