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Hybrid quantum-classical algorithms and applications in scheduling problems

Kalamarakis Theodoros

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Summary

This thesis explores hybrid quantum-classical algorithms, focusing on their applications in scheduling problems. It begins by outlining the foundational principles of quantum mechanics, including the role of qubits, quantum gates, and entanglement. The study then examines Quadratic Unconstrained Binary Optimization (QUBO) and its significance in combinatorial optimization, highlighting the use of classical and quantum methods such as Grover’s algorithm and quantum annealing. Next, the thesis introduces qubit-efficient encoding schemes for quantum optimization, designed to enhance the representation and processing of binary optimization problems in near-term quantum computers. These schemes are analysed through theoretical exploration and practical testing on quantum simulators and cloud-based quantum hardware, focusing on the Max-Cut and Subset Sum problems. A significant portion is dedicated to the smart scheduling of EV charging, demonstrating how qubit-efficient quantum optimization can efficiently manage large-scale EV charging schedules. The study compares the performance of quantum algorithms against classical approaches, presenting detailed results and insights from noisy simulations and real-world executions on cloud quantum processing units (QPUs). The findings suggest that hybrid quantum-classical algorithms hold substantial promise in solving complex scheduling problems, offering more efficient and scalable solutions. This work contributes to the growing body of knowledge in quantum computing applications, providing practical frameworks and methodologies for future research and industry applications.

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