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Hybrid quantum classical algorithms for optimization and applications in finance

Stratakis Andreas

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Summary

This thesis delves into the prominent topic of applying quantum computing to solving optimization problems and recent applications in the financial sector. We set the stage 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. Next, we dive deep into quantum approaches for binary optimization and the most popular hybrid algorithms for such problems, namely the Quantum Approximate Optimization Algorithm (QAOA) and the Hardware Efficient Variational Quantum Algorithm (VQA), as well as Quantum Annealing. We implement these algorithms to solve fundamental problems in computer science, such as the “Subset Sum” and the “Travelling Salesman Problem”, as precursors to the intricate challenge of applying them next to the financial world for portfolio optimization. In addition to formulating and adapting these problems to be amenable to quantum approaches, we present comprehensive benchmarks in cloud quantum hardware. In the last part of the thesis, we present a novel approach for solving portfolio optimization tailored for near-term quantum computers based on quantum amplitude encoding. This method transcends mere theoretical or ‘toy’ models, offering potential for handling real-world scale challenges specific to this domain. Our evaluations encompass predefined test sets and real-world data from the S&P100 and S&P500 financial indices.

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