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Hybrid quantum optimization algorithms and applications

Iliopoulou Artemis

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Summary

This thesis explores the application of quantum computing in solving optimization and, more specifically, scheduling problems. The first chapter provides an introduction to quantum computing. It covers introductory definitions, including single and multiple qubit states, quantum gates, and entanglement. It also analyzes the construction and importance of one of the fundamental quantum algorithms, the Deutsch-Josza algorithm. The second chapter focuses on the basic approaches to quantum optimization, such as Quadratic Unconstrained Binary Optimization (QUBO), the Ising model, and the notions of quantum annealing and adiabatic quantum computing. It also analyzes the Quantum Approximate Optimization Algorithm (QAOA) and demonstrates the MaxCut problem and how it can be solved using the QAOA. The third chapter delves into scheduling problems, precisely the Nurse Scheduling Problem (NSP). It explores two different QUBO models for JSSP in the Appendix and presents the results of the simulations conducted on various instances of NSP problems. The quantum algorithm ran on the quantum cloud service in D-Wave to obtain the results. Then, the performance for different problem sizes and topologies of the hardware is analyzed. Overall, this thesis presents a comprehensive overview of the fundamental concepts and techniques used in hybrid quantum-classical optimization and demonstrates its potential for solving optimization and scheduling problems.

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