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Hybrid Quantum - Classical machine learning and applications

Michalopoulos Christos

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Summary

In this thesis, we study the interface between quantum computing and machine learning, and more specifically quantum machine learning (QML) algorithms and certain applications in financial problems. We start by defining the building blocks of quantum computers, such as quantum states and quantum gates, along with the analytic presentation of three key quantum algorithms for our work: the quantum Fourier transform, the quantum phase estimation and the quantum amplitude estimation algorithm. We continue with summarizing the basics of classical machine learning and analyze in detail the inner workings of neural networks and specifically, of the generative adversarial. networks (GANs). Next, we discuss how quantum algorithms can be incorporated in classical machine learning approaches. We analyze the two leading areas of QML, the fault-tolerant QML and the Noisy-Intermediate Scale Quantum (NISQ) friendly QML algorithms; in the former case, QML algorithms are shown to have proven quantum speedups against its classical counterparts but require fault-tolerant quantum hardware that are yet-to-be setup, while the latter can be realized on the current available devices but quantum speedups, or provable quantum advantages is yet-to-be demonstrated. In the next and main part of the work, we analyze and build on some of the NISQ friendly QML algorithms, i.e: hybrid classical-quantum variational models that consist of quantum and classical processing. Within this approach, we study in details the quantum version of GANs, QGANs, and show how they can be trained to produce quantum states that efficiently encode and learn target probability distributions. We compare the training performance of the QGANs using different initial input probability distributions in various settings, e.g: 3 and 4 qubits systems, and models with different numbers of quantum circuit repetitions. These trained quantum states are then used along with quantum amplitude estimation algorithms, to compute important quantities in the financial world, such as the European call option problem found in real world markets. We implement our quantum algorithms in classical simulators and benchmark the performance for different numbers of qubits and configurations and discuss possible follow up works and applications.

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